SFOS oe IOs Sg “a 4S phe ray: it BY ae ie Vale TAI \ vl ha i ie ip i i i w 7 6° oy Py a Ue Th) if roa : bina rt ie. om Yi f awl \ , is oe Bt ashi: 387TH CONGRESS, \ SENATE. { Mis. Doc. 3d Session. ANNUAL REPORT OF THE BCARD OF REGENTS OF THE SMITHSONTAN INSTITUTION, SHOWING TILE OPERATIONS, EXPENDITURES, AND CONDITION OF THE INSTITUTION FOR THE YEAR 1862. WAS DING TON: GOVERNMENT PRINTING OFFICE. 1863. In Tue Senate or THE Unirep States, February 28, 1863. Resolved, That five thousand additional copies of the Report of the Smithsonian Institu- tion for 1862 be printed—two thousand for the use of the Smithsonian Institution, and three thousand for the use of the Senate; Provided, That the aggregate number of pages contained in said report shall not exceed four hundred and fifty, without wood-cuts or p'ates, except those furnished by the Institution; and that the Superintendent of the Public Printing be authorized, if consistent with the public service, to allow the Smithsonian Institution to stereotype the report at its own expense, or to otherwise print at its own expense such additional copies as may be desired from the type set in the Government Printing Establishment. LETTER OF THE SECRETARY OF THE SMITHSONIAN INSTITUTION, TRANSMITTING ANNUAL REPORT OF THE BOARD OF REGENTS. SMITHSONIAN INSTITUTION, Washington, February 19, 1863. Sir: In behalf of the Board of Regents, I have the honor to sub- mit to the House of Representatives of the United States the annual report of the operations, expenditures, and condition of the Smith- sonian Institution for the year 1862. I have the honor to be, very respectfully, your obedient servant, JOSEPH HENRY, Secretary Smithsonian Institution. Hon. HannipaL Hamuiin, Vice President of the United States and President of the Senate. ANNUAL REPORT OF THE BOARD OF REGENTS OF THE SMITHSONIAN INSTITUTION, SHOWING THE OPERATIONS, EXPENDITURES, AND CONDITION OF THE INSTI- TUTION UP TO JANUARY, 1863, AND THE PROCEEDINGS OF THE BOARD UP TO FEBRUARY, 1863. To the Senate and House of Representatives : In obedience to the act of Congress of August 10, 1846, establish- ing the Smithsonian Institution, the undersigned, in behalf of the Regents, submit to Congress, as a report of the operations, expendi- tures, and condition of the Institution, the following documents: 1. The Annual Report of the Secretary, giving an account of the operations of the Institution during the year 1862. 2. Report of the Executive Committee, giving a general statement of the proceeds and disposition of the Smithsonian fund, and also an account of the expenditures for the year 1862. 3. Proceedings of the Board of Regents up to February 4, 1863. 4, Appendix. Respectfully submitted. R. B. TANEY, Chancellor. JOSEPH HENRY, Secretary. OFFICERS OF THE SMITHSONIAN INSTITUTION. ABRAHAM LINCOLN, £x officio Presiding Officer of the Institution. ROGER B. TANEY, Chancellor of the Institution. JOSEPH HENRY, Secretary of the Institution. SPENCER F. BAIRD, Assistant Secretary. W. W. SEATON, Treasurer. WILLIAM J. RHEES, Chief Clerk. A. D. BACHE, 7} JOSEPH G. TOTTEN, \ Executive Committee. R. WALLACH. J REGENTS Of PRE INS LET ULILON:, H. HAMLIN, Vice-President of the United States. ROGER B. TANEY, Chief Justice of the United States. R. WALLACH, Mayor of the City of Washington. W. P. FESSENDEN, member of the Senate of the United States. L. TRUMBULL, member of the Senate of the United States. GARRETI DAVIS, member of the Senate of the United States. S. COLFAX, member of the House of Representatives. E. McPHERSON, member of the House of Representatives. S. 8S. COX, member of the House of Representatives. W. B. ASTOR, citizen of New York. W.L. DAYTON, citizen of New Jersey. T. D. WOOLSEY, citizen of Connecticut. ALEXANDER D. BACHE, citizen of Washington. JOSEPH G. TOTTEN, citizen of Washington. LOUIS AGASSIZ, citizen of Massachusetts. MEMBERS EX OFFICIO OF THE INSTITUTION. ABRAHAM LINCOLN, President of the United States. HANNIBAL HAMLIN, Vice-President of the United States, W. H. SEWARD, Secretary of State. S. P. CHASH, Secretary of the Treasury. E. M. STANTON, Secretary of War. G. WELLES, Secretary of the Navy. M. BLAIR, Postmaster General. EK. BATES, Attorney General. ROGER B. TANEY, Chief Justice of the United States. D. P. HOLLOWAY, Commissioner of Patents. RICHARD WALLACH, Mayor of the City of Washington. HONORARY MEMBERS. BENJAMIN SILLIMAN, of Connecticut. A. B. LONGSTREET, of Mississippi. CALEB B. SMITH, Secretary of the Interior, (¢x officio.) PROGRAMME OF ORGANIZATION OF TUE SMITHSONIAN INSTITUTION, [PRESENTED IN THE FIRST ANNUAL REPORT OF THE SECRETARY, AND ADOPTED BY THE BOARD OF REGENTS, DECEMBER 13, 1847.] 6 INTRODUCTION. General considerations which should serve as a guide in adopting a Plan of Organization. 1. Witt or Smituson. The property is bequeathed to the United States of America, “to found at Washington, under the name of the SMITHSONIAN INSTITUTION, an establishment for the increase and dif- fusion of knowledge among men.”’ 2. The bequest is for the benefit of mankind. The government of the United States is merely a trustee to carry out the design of the testator. 3. The Institution is not a national establishment, as is frequently supposed, but the establishment of an individual, and is to bear and erpetuate his name. 4, The objects of the Institution are, Ist, to increase, and 2d, to diffuse knowledge among men. 5. These two objects should not be confounded with one another. The first is to enlarge the existing stock of knowledge by the addition of new truths; and the second, to disseminate knowledge, thus in- creased, among men. 6. The will makes no restriction in favor of any particular kind of knowledge; hence all branches are entitled to a share of attention. T. Knowledge can be increased by different methods of facilitating and promoting the discovery of new truths; and can be most exten- sively diffused among men by means of the press. 8. To effect the greatest amount of good, the organization should be such as to enable the institution to produce results, in the way of increasing and diffusing knowledge, which cannot be produced either at all or so efficiently by the existing institutions in our country. 9. The organization should also be such as can be adopted provi- sionally; can be easily reduced to practice, receive modifications, or be abandoned, in whole or in part, without a sacrifice of the funds. 10. In order to compensate, in some measure, for the loss of time occasioned by the delay of eight years in establishing the Institution, a considerable portion of the interest which has acerued should be added to the principal. 8 PROGRAMME OF ORGANIZATION. 11. In proportion to the wide field of knowledge to be cultivated, the funds are small. Economy should therefore be consulted in the construction of the building; and not only the first cost of the edifice should be considered, but also the continual expense of keeping it in repair, and of the support of the establishment necessarily connected with it. There should also be but few individuals permanently sup- ported by the Institution. 12. The plan and dimensions of the building should be determined by the plan of organization, and not the converse. 13. It should be recollected that mankind in general are to be ben- efited by the bequest, and that, therefore, all unnecessary expendi- ture on local objects would be a perversion of the trust. 14. Besides the foregoing considerations deduced immediately from the will of Smithson, regard must be had to certain requirements of the act of Congress establishing the Institution. These are, a library, aimuseum, and a gallery of art, with a building on a liberal scale to contain them. SECTION I. Plan of Organization of the Institution in accordance with the foregoing deductions from the will of Smithson. To Increase Know ence. It is proposed— 1. To stimulate men of talent to make original researches, by offer- ing suitable rewards for memoirs containing new truths; and 2. To appropriate annually a portion of the income for particular researches, under the direction of suitable persons. To Dirruse KnowLepcGe. It is proposed— 1. To publish a series of periodical reports on the progress of the different branches of knowledge; and 2. To publish occasionally separate treatises on subjects of general interest. DETAILS OF THE PLAN TO INCREASE KNOWLEDGE. I.—By stimulating researches. 1. Facilities to be afforded for the production of original memoirs on all branches of knowledge. 2. The memoirs thus obtained to be published in a series of vol- umes, in a quarto form, and entitled Smithsonian Contributions to Knowledge. 3. No memoir on subjects of physical science to be accepted for publication which does not furnish a positive addition to human knowledge, resting on original research; and all unverified specula- tions to be rejected. 4. Each memoir presented to the Institution to be submitted for examination to a commission of persons of reputation for learning in PROGRAMME OF ORGANIZATION. 9 the branch to which the memcir pertains; and to be accepted for pub- lication only in case the report of this commission be favorable. 5. The commission to be chosen by the officers of the Institution, and the name of the author, as far as practicable, concealed, unless a favorable decision be made. 6. The volumes of the memoirs to be exchanged for the transac- tions of literary and scientific societies, and copies to be given to all the colleges and principal libraries in this country. One Pe of the remaining copies may be offered for sale; and the other carefully pre- served, to form complete sets of the work, to supply the demand from new institutions. . 7. An abstract, or popular account, of the contents of these me- moirs to be given to the public through the annual report of the Regents to Congress. IIl.— Ly appropriating a part of the income. annually, to special objects of research, under the direction of suitable persons. 1. The objects, and the amount appropriated, to be recommended by counsellors of the Institution. 2. Appropriations in different years to different obje ae so that, in course of time, each branch of knowledge may receive a share. 3. The results obtained from these appropriations to be Salen with the memoirs before mentioned, in the volumes of the Smithso- nian Contributions to Knowledge. 4. Examples of objects for which appropriations may be made. (1.) System of extended meteorological observations for solving the problem of American storms. (2.) Explorations in descriptive natural history, and geological, magnetical, and topographical surveys, to collect materials for the formation of a Physical Atlas of the United States. (3.) Solution of experimental problems, such as a new determina- tion of the weight of the earth, of the velocity of electricity, and of light; chemical analyses of soils and plants ; collection and publi- cation of scientific facts accumulated in the oflices of government. (4.) Institution of statistical inquiries with reference to physical, moral, and political subjects. (5.) Historical researches and accurate surveys of places celebrated in American history. (6.) Ethnological researches, particularly with reference to the dif- ferent races of men in North America ; also, explorations and accurate surveys of the mounds and other remains of the ancient people of our country. DETAILS OF THE PLAN FOR DIFFUSING KNOWLEDGE. I.— By the publication of a series of reports, giving an account of the new discoveries in science, and of the changes made from year to year in all branches of knowledge not strictly professional. 1. These reports will diffuse a kind of knowledge generally inter- esting, but which, at present, is inaccessible to the public. Some of 10 PROGRAMME OF ORGANIZATION. the reports may be published annually, others at longer intervals, as the income of the Institution or the changes in the branches of knowledge may indicate. 2. The reports are to be prepared by collaborators eminent in the different branches of knowledge. 3. Each collaborator to be furnished with the journals and publi- cations, domestic and foreign, necessary to the compilation of his report; to be paid a certain sum for his labors, and to be named on the title-page of the report. 4. The reports to be published in separate parts, so that persons interested in a particular branch can procure the parts relating to it without purchasing the whole. 5. These reports may be presented to Congress for partial distri- bution, the remaining copies to be given to literary and scientific in- stitutions, and sold to individuals for a moderate price. The following are some of the subjects which may be embraced in the reports: I, PHYSICAL CLASS. 1. Physics, including astronomy, natural philosophy, chemistry, and meteorology. 2. Natural history, including botany, zoology, geology, &c. 3. Agriculture. 4, Application of science to art. II. MORAL AND POLITICAL CLASS. 5. Ethnology, including particular history, comparative philology, antiquities, &c. 6. Statistics and political economy. 7. Mental and moral philosophy. 8. A survey of the political events of the world, penal reform, &c. III. LITERATURE AND THE FINE ARTS. 9. Modern literature. 10. The fine arts, and their application to the useful arts. 11. Bibliography. 12. Obituary notices of distinguished individuals. Il.—By the publication of separate treatises on subjects of general interest. 1. These treatises may occasionally consist of valuable memoirs translated from foreign languages, or of articles prepared under the direction of the Institution, or procured by offering premiums for the best exposition of a given subject. 9. The treatises should, in all cases, be submitted to a commission of competent judges previous to their publication. 3. As examples of these treatises, expositions may be obtained of PROGRAMME OF ORGANIZATION. 17 the present state of the several branches of knowledge mentioned in the table of reports. SECTION II. Plan of organization, in accordance with the terms of the resolutions of the Board of Regents providing for the two modes of increasing and diffusing knowledge. 1. The act of Congress establishing the Institution contemplated the formation of a librar ry and a museum; and the Board of Regents, including these objects in the plan of organization, resolved to divide the income* into two equal parts. 2. One part to be appropriated to increase and diffuse knowledge by means of publications and researches, agreeably to the scheme before given. The other part to be appropriated to the formation of a library and a collection of objects of nature and of art. These two plans are not incompatible one with another. 4. To carry out the plan before described, « library will be required, consisting, first, of a complete collection of the transactions and pro- ceedings of all the learned societies in the w: rld; second, of the more important current periodical publications, aid other works necessary in preparing the periodical reports. 5. The Institution should make special collections, particularly of objects to illustrate and verify its own publications. 6. Also, a collection of instruments of research in all branches of experimental science. 7. With reference to the collection of books, other than those men- tioned above, catalogues of all the different libraries in the United States should be procured, in order that the valuable books first pur- chased may be such as are not to be found in the United States. 8. Also, catalogues of memoirs, and of books and other materials, should be collected for roudering the Institution a centre of biblio- graphical knowledge, whence the student may be directed to any. work which he may require. 9. It is believed that the collections in natural history will increase by donation as rapidly as the income of the Institution can make pro- vision for their reception, and, therefore, it will seldom be necessary to purchase articles of this kind. 10. Attempts should be made to procure for the gallery of art casts of the most celebrated articles of ancient and modern sculpture. 11. The arts may be encouraged by providing a room, free of ex- pense, for the exhibition of the objects of the Art-Union and other similar societies. 12. A small appropriatiow should annually be made for models of antiquities, such as those of the remains of ancient temples, &c. * The amount of the Smithsonian bequest received into the Treasury of the Wimitedy States ss 2. oat a stews anaes 6 aoc onmceemmeoasiaem sate we sicuue $515,169 00 Interest on the same to July 1, 1846, (devoted to the erection of the build- ING) pee Cee eeerie ates SaSe ewe sea ebcsamae coeeoeciscaeeooeee see 242,129 00 Annual income from the bequest -.... accneee sadeendlesacccmenticececs 30,910 14 12 PROGRAMME OF ORGANIZATION. 13. For the present, or until the building is fully completed, be- sides the Secretary, no permanent assistant will be required, except one, to act as librarian. 14. The Secretary, by the law of Congress, is alone responsible to the Regents. He shall take charge of the building and property, keep a record of proceedings, discharge the duties of librarian and keeper of the museum, and may, with the consent of the Regents, employ assistants. 15. The Secretary and his assistants, during the session of Congress, will be required to illustrate new discoveries in science, and to exhibit new objects of art ; distinguished individuals should also be invited to give lectures on subjects of general interest. This programme, which was at first adopted provisionally, has become the settled policy of the Institution. The only material change is that expressed by the following resolutions, adopted Jan- uary 15, 1855, viz: Resolved, That the 7th resolution passed by the Board of Regents, on the 26th of January, 1847, requiring an equal division of the in- come between the active operations and the museum and library, when the buildings are completed, be, and it is hereby, repealed. ftesolved, That hereafter the annual appropriations shall be appor- tioned specifically among the different objects and operations of the Institution, in such manner as may, in the judgment of the Regents, be necessary and proper for each, according to its intrinsic import- ance, and a compliance in good faith with the law. REPORT OF THE SECRETARY. To the Board of Regents : GENTLEMEN : I have the honor again, at the commencement of your annual session, to present the report for another year of the opera- tions of the Institution intrusted by the General Government of the United States to your special care. So much public attention has been absorbed during the last year by the exciting events of the war that we might at first suppose that little or no thought could be bestowed upon purely scientific subjects, such as fall within the province of this Institution to culti- vate, or indeed upon any kind of knowledge which has not an im- mediate bearing on the special requirements of the times. But even in the most sanguinary and gigantic warfare the responsibility for the important plans which are to determine the result of the conflict devolves upon the few, and leaves the many to fall into a condition of comparative mental inactivity. As arelief from the tedium of this condition, or a prevention from falling into it, a large number of subordinate officers, and even pri- vates, of the army have devoted themselves to pursuits connected with natural history, or to the solution of problems of a theoretical or practical character. Although the immediate object of war is the destruction of life and property, yet astate of modern warfare is not a condition of evil unmingled with good. Independent of the political results which may flow from it, scientific truths are frequently developed during its existence of much theoretical as well as of practical im- portance. The art of destroying life, as well as that of preserving it, calls for the application of scientific principles, and the institution of scientific experiments on a scale of magnitude which would never be attempted in time of peace. New investigations as to the strength of materials, the laws of projectiles, the resistance of fluids, the ap- plications of electricity, light, heat, and chemical action, as well as of aerostation, are all required. The collection of immense armies of individuals of different ages 14 REPORT OF THE SECRETARY. and nations affords the means of obtaining data of much interest to the ethnologist, while the facts which are githered from the unusual experience of the battle-field and hospital afford materials for the advance of physiology, surgery, and medicine, which a century of ordinary observation would fail to furnish. In illustration of what has been done in the line we have mentioned, I would refer to the extended labors of the Sanitary Commission and of the department under the direction of the Surgeon General. The one, besides aiding in the improvement of the health and com- fort of the soldiers, has collected a large number of interesting facts relative to the moral and economical condition of the army; while the other, in addition to its immense labors in the care of the sick and the wounded, has recorded the statistics of every part of its varied operations, and formed a collection of illustrations of surgical anatomy which is perhaps unrivalled in any part of the world. In reference to all the inquiries to which I have alluded, the Smith- sonian Institution has been called upon for aid and counsel, and has continually rendered active co-operation and assistance. Its labors, however, in this line, as well as in several other branches of its ordi- nary operations, are not attended with results which can be given to the world through its publications. During the continuance of the war we must expect to find that more attention is given to the collection of facts than to the deduction from them of general principles ; the latter must be deferred to a period of more tranquillity, when the mind is in a better condition for continued application to the development of a single idea; con- sequently the number of papers which have been presented to the Institution since the date of the last report is less than that of any previous year. The meteorological system which had been established, and was in successful operation for several years before the commencement of the war, has been much deranged, few records of observations having been received from the middle States and none from the southern; still, as I have before intimated, the labors of the Institution have been industriously pursued in lines more in accordance with the peculiar condition of the country. 14 Die We werdgert Alte a eieta\e apa Sais ete INOTWELY)= a mnrnre~a _ Ea on = Bogota, New Granada. Sociedad de Naturalistas Neo Grena- Cinder a Cee cs coeatecta cancers ae Boston, Mass. American Acad'y of Arts and Sciences American Statistical Association .... . Boston Society of Natural History... sowditch Gibranyae «eaeieeleres stele « mata Historic Genealogical Society---.--- Massachusetts Historical Society. .... Prison Disc‘pline Society -...-...--. Public Library ..... pisteiateiet ie a's Seats State Library scemnslseiaom sls = alateers een Boston Journal of Natural History .. North American Review.........--- By; Alger. amc ame inaaeiee ead DrMIBIGwerlacreseebaan Motdisiela.® = staleietste AA Goulds oe cape came sin seme tan Drop. VatV AS eeteettaltee's ep isleiete aaleiots Dr. Wilsonicdalsientee salaeia cmleneene aa Brattleboro’, Vt. Vermont Asylum for Insane .......- Brunswick, Me. Bowdoin College ..... Mince cosises cate Historical Society of Maine. .-...... Mrs. Parker Cleaveland .......ccee. Burlington, Iowa. Historical and Genealogical Institute - packages. Number of _ — = 2 a for) me DO Oe OR Re ee ei REPORT OF THE ASSISTANT SECRETARY. 51 D.—Addressed packages received by the Smithsonian Institution, §c.—Continued. Burlington, Vt. University of Vermont...........6-. Cambridge, Mass. American Association for the Ad- vancement of Science...... acamines Cambridge Observatory ......-.----- HAT VAG COMET Ce alc dasiteracs soneme Editor of Astronomical Journal...... IPTOLESSOL Ws AP ARSIZ con ceclsonaltaance GRP BONG see coos bees Coca wceaincioe IPTOLESSOL Els J. Clarke cnsccces soucee rH DA GOUlda cco. sceche ccac vocecs Professor Asa Gray - 2.2. coos cose cee PMT ST Oletatet a aetale lel slaie) = ainlale|ainial o sie Professor Julegy Marcou.....-.. ee---s Crbp NOL -teceseceeces cotetesnee IPVOlesSOLID. LOlCE 4s cnawee)aassteccous I PCHUD ED eeicisccrwscticl sete oeeeies mans Dee WWORCOSLELE po n.ciSieisinin.c'e © niu afop seni TOR VITA mem icinieipis nisin sea nin'mlawid's Chicago, Ill. Academy of Sciences...e0+ 20. secee. Mechanics’ Institute...-..00. scene ColiJ#D:; Graham's. BeAsis.s ceocsss Chuquisaca, Bolivia. University of Chuquisaca............ Cincinnati, Ohio. Astronomical Observatory.......-.--. Historical and Philosophical Society Of OM sect tamate) ow elel teelele'i gael costs Mercantile: Librarycociseiecss secclees- Obsenvatoryetaesocssonswsee ns cm Western Academy of Science......... Editor of the Dental Register of the ES eee ote aisteie elaine ea oie teeta mor mle Protessor Mitchell ccmepete-icesca. Clinton, Ne Xe Drs CO! EBS Letters ceenepeeah ons aaa Columbia, Mo. Geological Survey of Missouri........ Columbia, Pa. Professor §. S. Haldeman...... Weieiebis Dri MIGISBEID CIs an nals ania tw ain’ halen ea Number of whe Ort TO bo ~ _ roe eS ee er packages, Cilumbus, Ohio. Ohio State Board of Agriculture..... Stateslibraryiices csinjcocice coemesicon TCOMDCEQUICTECAU Rp este ao oo slubulcle nein '= WVepSUivalibere merets aletemetam sale antes Concord, N. H. New Hampshire Asylum for Insane-. New Hampshire Historical Society... State Library ....0+ eevee ate eeiate me ete Davenport, Lowa. Right Rev. Henry W. Lee.......... Des Moines, Lowa. State Library scence sess prema eteiaia Detroit, Mich. Michigan State Agricultural Society Dorchester, Mass. Dri Wo Tarvisensts eae soaeceee eee Easton, Pa. Dr. B. Clemens..... caaniaee aa marraee Professors). Ele Comin es smeciecemaane Erie, Pa. 17s OMMEGC ees sapdiena ce eieeeeee Fall River, Mass. NielsvATh Zen eee steacatteen Swais/es cletais Farmington, Conn. Hidw. NOrtonbcssteeemeacetenae conce- Frankfort, Ky. | Geological Survey of Kentucky..... State Tabrary, \ a 23s scbiorswebasack Mr: Shotinetens nesses oneness cae ees Gambier, Ohio. Menyon Collece wcesevasasuns. cdueys Number of packages. Rm boo oo Ore ee me or 0O 52 REPORT OF THE ASSISTANT SECRETARY. D.— Addressed packages recewed by the Smithsonian Institution, §c.—Continued. Georgetown, D. C. Georgetown College Dr. A. Schott Hanover, N. H. DartmouthyGollegesss#ssss2s2e2- 2 Harrisburg, Pa. Pennsylvania State Lunatic Hospital -- Huvtombibraryssesoescsecs ac ceene se Hartford, Cann. Hartford Society of Sciences_-....---- Historical Society of Connecticut-.--. Stateplitbrany sees eee eases Young Men’s Institute Havana, Cuba. Observatoire Physique et Météorolo- DIQUE ae sane tee eee eee Real Sociedad Economica -......---- Hudson, Ohio. Western Reserve College......... os Indianapolis, Ind. Indiana Historical Society_-.......--- Stateshibrangeesacsseeccsesssecee ss Lowa City, Towa. Plate OL Lowa ease eee sees s eee State University of Iowa:...-..--... Janesville, Wis. State Institution for the Blind-....-. Jefferson City, Mo. Historical Society of Missouri_...---- Statemnbranyesteeess S22 oo Sse seen Kalamazoo, Mich. Asylum for Insane-...... eee eee Lancaster, Pa. Thomas C. Porteresssesei 202022 ae 1 i Co OU oe co | IT. Apoleon Cheney Lansing, Mich. Agricultural’College=aeesese os. sees Statednbrary asso lsecccase ete See Lecompton, Kansas. | Statewhibrary Sess ccs ose coe cee Loon, N. Y. Louisville, Ky. Colonel hong. oso5--- eee ae Professor J. Lawrence Smith meee ee Madison, Wis. Historical Society of Wisconsin Skandinaviske Presse-Forening -.... State library: <2 225. oo COLORADO. — cea 3 = 4 | 3 ae z Ep Bg. 183 Name of observer. Station. County. 5 5 3 g & 2 s Ss = 2 Ss o = gS = 3 3 2 v Z is 3 5 Z Sid ea Feet. Ellis, Dr. Wm. T.... ......| Mountain City.| Arapahoe.....} 39 35 105 40 | 8,000 | T. we... 1 Stanton, Frederick J ......| Denver City, ..| Arapahoe.... «ve Sen: « wees 4 DISTRICT OF COLUMBIA. Mackee, Rev. C. B.... fi) Georgetown ...| Washington. .. 38 54 GROIN piarelater ote) (ir Lye) Ler ex cia) fades Smithsonian Institution,...| Washington Washington... 38 53 77 Ol GOP AN e(rersieint ole CONNECTICUT. Case, Jarvis..... + steer [MC ANILON | wicks oie iets Hartford....... 42 00 73 00 OOM |ipdee Rs veteratet| end Harrison, Benjamin ) eee Wallingford. ..| New Haven. . 41 27 72.50 Taio |eAeueeterarere| tueene Hunt, Rev. Danpelerece tac POmMErets tears ais) Windham. ... 4l 52 72 23 DO Meu teAciere ater (meee Johnston, Prof. Jobn.......| Middletown. ..| Middlesex... 41 32 72 39 UFSPEIMAT Satreers 12 Learned, Dwight W .... Plymouth. ... | Litehfield .... 41 40 MSeOBEe||loeamaiet Ely eieteralete a Leavenworth, D. C........| New Haven. ..| New Haven...| 41 18 72 56 AQW | (Bewlstisnet 3 kockwell, Charlotte. ......| Colebrook.. ..] Litchfield. ....| 42 C0 73N06)" lteiee,ceahi| CDs weenee | 12 Yeomans, William H......| Columbia. ....} Tolland. ...... 41 40 72 42 ws iDawareraternte je DAKOTA. Hill,G@ D.. Siai(siejels Lawson, George W- siersietele Yankton covoe jecccccsscccceees| 42 51 STI | ierereieisiarss)| sieleielesioveie 4 Williams, Herbert a... FLORIDA. | Dennis, William C.........]| Key West. ...| Monroe, ...... 24 33 81 28 16 | BaToR.s/. 12 Magnetic Ob- | Monroe. ...... 24 53 81 438 6 Balab se 5 Ferguson, G. F. .ceoe. + Been tGRVAICe Oltmanns, J.G..... eee Paey| ? West. | ILLINOIS. Fe VEO sae “2g Tiskilwa ......| Bureau........| 41 15 89 66 550 | N..seeee| 12 Babeock, E . Remeneleits Riley..... Seis oo PLIMECELONTYicctercte’e 42 3) &8 20 760! WPTOR Poe 12 Bacon, E. Bienes -»-.-..| Willow Creek.| Lee..... afeneiarars 4) 45 SS5008 |) 1,040) |) Nevis ole Ballou, N.E.M Dees .....| Sandwich .. DeKalb iecie cs 41 31 &8 30 Gye) | UUeliiaiag 12 Bandelier, Adolphus I°.,jr..| Highland ...... Madison, ..+... 38 45 &9 46 slcieie «l(a eulven bes lL Blanchard, Orestes A ..... Elinira ..0. 000.) Starks. cevee 41 12 90 15 yakeretets 5 Breeds Mi Als wias/e cies =- Peoria) ences Peoria ........| 40 38 89 46 TER setae 2 Brendel, Frederick, M. SD ..|Peoria’s;.. M.D...| Millersburg..,.| Bourbon ...... 38 40 84 27 804 | B.T.R.. 3 Swain, "Jobn, M. Dies ..».| Ballardsviile...] Oldham .... .. 33 36 85 30 461, WA aces 1 Voodrufi, EN Sccet acces MOUISVINIE: ice | Letersonune scene 38 22 B5TIB! | |]ia sie: = oip'e!| bp Aleverssle eis Young, Mrs. Lawrence....| Louisville.... | Jefferson......| 38 07 85 24 LOT WAT sietoietas i Pn MAINE. Brackett, George Emerson.| Belfast. ......-| Waldo. .sccveee 44 23 GONO8) iNieteetet oie! leek ste neal melon Dana, Wm. i),............| North Perry ...| Washington...| 45 00 67 05 a pats i ate ies ; Pembroke .....| Washington... 44 53 67 15 Bi aeles ON Elise. 4 Baldwinsville..| Worcester ....| 4237 | 7205 | 847 | BoT.....| 1 Gaines; Rev. As, Ga ces scree (Bethel eececcen| OxXtOrd ee. s oc, 44 20 70 52 CoO Ma ERA es. 2 Gardiner, R. H...... Gardiner ......| Kennebec .&.. 44 40 69 46 FOP Bry Ree Guptill, G@. W..eeeec0-e0e,| Cornishville ...] York ..... 2...) 43 40 70 44 SOON UR real le Moore, Asa P....c06 oovee-| Lisbon........| Androscoggin... 44 00 70 04 130) | MDCT A ys eee Bankers dln D tears ssisiate es «n|//SLOUVEN) a cic Washington...| 44 44 67 50 OOH Avreweese tte Pratt, J. Frank, M.D......; New Sharon...| Franklin ...... 44 37 FOROS Pl heteiietere e1| NT evetainerate 2 Reynolds, Henry ...eeeee... East Wilion....| Franklin ......| 44 44 TOL eit e'sist || Niesetegatetalsl melee Van Blarcom, James ......| Vassalboro’? ...} Kennebec.....| 44 28 GO ATi alosaise ws) Be Latent inate WVIES ty SUA ay=c.0/e(uisinre restate f CXOLDISIN wtelats'ate'el|/ MORI Geeluci ecciciary 43 40 70 44 WO4-- | N Re aria ates, * “Wilbur, Benj. F.....e.000>| Dexter... 0...| PenobsCot.....| 44 55 69 32 7100" >| TORRE eee nde METEOROLOGICAL OBSERVERS. MARYLAND. é g ie = = 3 rs S Ei 5 = 2 Name of observer. Station. County. 3 Ee fi S ES = = ‘Ss = & 5 = z = en ae 2 ° o ma ° Z E a 5 2 Sil oy gil Feet. Baer, Miss Harriott M......| Sykesville.....| Carroll .... 00. 39 23 76 57 (O00! WP Res!) ae Bell, Jacob E.........+.e..| Leitersburg....) Washington .. o9 35 MOO al iefein's: sveisies| edesibiciereie 6 Dutton, P:of. J. Russel.....| Chestertown,..| Kent ....- 89 12 EAD ail eae tate ayet | AS here tone 10 Goodman, Wm. K. ...... Annapolis. .... Aune Arundel . 33 59 76 29 20) | MAR si. 12 Hanshew, Henry E........ frederick . Frederick .... 39 24 Vile Oden I tsfalayey aceCeyn| lic A\chsteresie 12 Johns, Montgoniery, M. we Agric’l College. BrINGeG COTE ELS Piajeratarasielett |laretoseiiela(etetsl li fe(siaincevsiei||/ AN plelele islets 3 Lowndes, Ber jamin O ....| Bladensburg...| Prince George’s}| 38 57 76 58 WSL Le Sere 10 Stephenson, Rev. James...| St. [nigoes ....| St. Mary’s..... o8 16 76 41 Aa be Atersjeiecievel |r iilco MASSACHUSETTS. Astronomical Observatory.} Wil'iamstown..| Berkshire ..... 42 43 73 13 725 Beak. 1 Bacon, William .... ......| Richmond .. ..| Berkshire .... 42 23 320 F | PLST9O I Reese. 9 Brownsi Nathan Wiresscrsscc| “LOpSficld’. oic0.,|(MoSSCX 72.010. ~ cei] sine oe Mateiniecoreaaiel | eleleiensaieiel|eea eerste 6 Davis, Rev. Emerson .. ...| Wesifield..... Hampden ..... 42 06 72 48 LEO GAC recta sie 12 Falicn. ODM isis, cers Lawrence, ....| ESSeX ...00 ens: 42 42 aL UL LSS iA eteretoae 9 Metealf, John Geo., M. D.. Mendon...... | Worcester, .... 42 (6 WOES | Salaosrtet ||| Lic Mtere e's 12 Prentiss, Henry C., "M.D ..| Worcester ....] Worcester.....| 42 16 71 48 S26 me eat enterere 12 Reynolds, Orrin A.........| Randalph......| Norfolk ...... 42 10 71 C0 SUL | Nisicctarete ] Rodman, Samuel........-- New Bedford ..| Bristol .....0.: 41 39 70 53 £0 A eisisis 12 Snell, Prot. E.S..... eeees.| Amberst ......]| [fampshire .... 42 22 72 34 0 ian ea ctarerereta 12 MICHIGAN. Beene AR Ma 222 t] Marquette.....| Marquette.....] 4632 | 8741 | 630 | A.ses..] 12 Coffin, Matthew......3....| Otsego........| Allegan ...... 42 28 €5 42 662. | N.wve-s- 6 Crosby. J B...-....se.eee.| New Buffalo...} Berrien. ..... 41 45 &5 46 61 Beeler ro Pitcher, Zena, M.D. 22.0. Detroit ...-..| Waynes... 42 24 82 58 OTe le Aisiecteralote 4 Schetterly, Henry R.......| Northport .....| Leclenaw ..... 45 3 5 DAES Ileravereistavara| eNistatsieiere 7 Smith, Rev. L. M.S.-...-| Mill Point.....) Ottawa........ 43 06 SOM | | tereiststetere i beacon) jo Sireng ila Meee celaseittee ciel MOUANG) jecwes, | OCLAWASS~ «sve 42 00 85 00 GSO | Dei sre< 1 Van Orden, Wm., jr.......| Clifton. ......| Kcweenaw.... 47 U0 &8 00 800)» eee li Walter, Mrs. Octavia C. Cooper........| Kaiamazoo... 42 40 5 20 COD ARS sere |e UL Whelpley, Miss Florence E.| Morroe .......| Monroe........ 41 55 €3 23 DOO) fF Re reterers in Woodard, C. S...........| Ypsilanti. ....| Washtenaw.... 42 15 §3 47 Aes | ANsieretetere 12 MINNESOTA. a Garrisons|Os Pcijascciececis Paterson, Rev. A. Bell, D. D. Rigas. Reva Se Rie: seea ave SiN TENT YA Ln csiscc. Yeleters «i Thiekstun, T. Foo... .sc0ce Wieland, Gsiee wa a z E = ea ehuale Sa Feet. Welshfield ....| Geauga........| 41 23 SUF OS Lele ciel mele Adams, DP ye. st Marietia.......| Washington... 39 25 81 31 GOs ee uticie. 7 Atkins, Rev. L. 8S. .| Saybrook......| Ashtabula..... 41 52 81 Ol GSO dy scatsree 8 Benner, Josiah F..........}| New Lisbon ...}] Columbiana...} 40 45 80 45 961 | B.T.R 12 Clark, Wm. P.....00 eeee0-| Medina........| Medina........ 41 07 8147 | 1,255 | A. ... 12 Colbrunn, Edward... .....| Cleveland . Cuyahoga.....| 41 30 81 40 665. | Discone.| 12 Cotton, D. B., M.D... ~ .| Portsmouth....| Scioto .........| 38 45 82 50 523) 1 Be DeaR. | -'3 Crane, George W .ccvecvene| Bethel....0000./°Clermonts.cece 39 00 84 00 Ooo) ED sku. 1 Davidson, Wilson .........| Freedom ......| Portage........} 41 13 8108 | 1,100 | B.T.R..| 5 Dille, Israel.....ses0ce0...| Newark .......| Licking ....... 40 07 82 21 825) i Divseeens 10 Shin Case “++ 2) Austinburg....| Ashtabula.....] 4154 | 052 | 816 |T.R.....] 2 Fraser, James...,.0...2s..| Little Hocking.| Washington.... 39 25 81 00 welotoniat) Ni stseistalefsl acl: Hammitt, John W.........| College Hill...) Hamilton......] 39 19 84 96 SCOR IRIN GE serate 12 Harper; George W........ | Cincinnati.....| Hamilton......| 39 0 84 27 *500 | As. cccesc]’ 12 Haywood, Prof. John......| Westerville....| Franklin......- 40 04 83 WO |... eses| Accvevee 12 Aull, F. Circe ath caved Dallasburg..... Walren .aseces 39 30 84 31 S00) Tt Nicceicae «s 11 Huntington, George C .....| Kelley’sIsland.| Erie.... ....+- 41 36 82 42 Hoe NB DR] 2 eae sua MSM sine ' Cleveland.....| Cuyahoga......] 41 30 81 40 643 | B.T.R 12 Ingram, John, M.D...... | Savannah......| Ashland. o... 41 12 SATS | TO9E WP Asserasjere i) 12 Jerome, A. B...... suesseee| New Westheld:| Hood’. : sss. 41 13 83 49 602 | mw. Resse 9 Johnson, Thos. H.........}| Coshocton.....| Coshocton..... 40 18 81 53 OD) TWA siisiere.« 2 King, Mrs. Ardelia C ......| Madison.......] Lake.......-..| 41 50 &1 00 G20NT Ranker 12 McClung, Charles L.......) Troy...+..seee./ Miami... .-| 40 03 84 06 | 1,103 | B.T.R. 12 MeMillan, Smith B....... | East Pairfield.. Columbiana . baal oe eve B0K4S) S152) As arco 12 Newton, Rev. Alfred.......| Norwalk......-| Huren..ees cece 41 15 82 30 miatelcisieo le etelseciacih ke Peck, Wm. R.,M.D......| Bowling Green.| Wood .eseseeee 41 15 83 40 LOOM Bo Deakeec| 12 Peirce, Warren ...........| Garrettsville... Portage........| 41 15 81 10 SOON I ecereteiereis 8 Phillips, R C. and J. Ii....| Cincinnati..... Hamilton....., 39 06 84 27 0410 | B.T.R 12 Pillsbury, Mrs. M. A........| East Cleveland.| Cuyahoga...... 41 31 81] 38 659 BAT. 10 Smith, C. H., M. D........| Kenton......../ Hardin ....0.0. 41 30 84 41 Sisie}sisje 5) hey Liste 4 Thompson, Rev. David....| Milnersville ...| Guernsey..... 40 10 81 45 9 Thompson, Rev. Elias.....| Croton.........| Licking........| 40 13 82 38 12 Tappan, BliT ............| Cincinnati...,.) Hamilton......| 39 07 84 27 12 Trembley, J. B., M. D.....| Toledo... ....| Lucas..... © METEOROLOGICAL OBSERVERS. MEXICO. a » a =. 3 E es Name of observer, Station, = 5 : Ee = 2 5 rm = 5 -o 5 ee ‘E0 5 .2 3 3 3 = ore | A = = Zz rae ne Feet laszlo, Charles.... ......| San Juan Bautista, Tabasco .... 17 47 $2 36 AQT EAs crarelerets g INIETOS SVAN 7 VE OFF ULE ail 6a GENERAL APPENDIX TO THE REPORT FOR 1862. The object of this appendix is to illustrate the operations of the Institution by the reports of lectures and extracts from correspondence, as well as to furnish information of a character suited especially to the meteorological observers and other persons interested in the promotion of knowledge. LECTURES ON THE UNDULATORY THEORY O02 LIGHT, Bey eH Ae BAUR IN AS RD esa Die tly, LATE CHANCELLOR OF THE UNIVERSITY OF MISSISSIPPI. [In preparing the material of these lectures for publication, some transpositions have been made in the original order of topics, and the lecture form has been generally aban- doned. “Mathematical illustrations have also been occasionally introduced, which would not have been quite in place before a popular audience. | PART I. INTE OD UCT OR XN: OUTLINE OF OPTICAL DISCOVERY. The knowledge which we possess of the material objects surrounding us in the universe is principally received through the sense of vision. Irom the other senses we derive a much more limited range of impressions. 'The touch furnishes us with a valuable means of confirming or correcting the information we receive from sight; but its usefulness extends only to objects in our own immediate vicinity. The hearing, though t hrough it, by the aid of spoken lan- guage, we are supplied with a vast muiiarde of ideas which have had their origin in impressions previously made upon other senses, contributes of itself, in any other form, but very slightly to the great stock of our knowledge. Such therefore being the pre-eminence of vision among the senses, light, which is its medium, is, and has ever been, the most important of phy sical instrumentalities in promoting the intellectual development of the human race, and making progress a possibility. But, while occupying this peculiar relation to the history of our advancement in the knowledge of nature, while so fertile in the revelations it has unfolded to us of the properties and qualities of other things, it is remarkable that light has itself furnished, in its own nature, one of the most difficult and perplexing of all the subjects of physical inquiry; so that, even down to an advanced period of the present century, the world of science may be said to have been upon no other subject more widely at vari- ance than upon the elementary and fundamental question, What is light? Nor is it possible to explain this want of harmony by supposing the inquiry to have but recently originated. Since, in the physical world, light has been the ever present and ever most efficient handmaid of the human un- derstanding, its phenomena must, to some extent at least, have attracted the attention of the first intelligent inhabitants of our planet. The first man who breathed could not have failed to notice the images of visible objects, formed by reflection in the bosom of every quiet pool; and the first rude navigator 108 EARLY WRITERS ON OPTICS. who endeavored to float himself from shore to shore, across waters too deep to be traversed by ordinary and simpler expedients, must have been struck by the singular distortion of his paddle at the line where it entered the water. The natural alternations of light and darkness, their coincidence with the rising and setting of the sun, the appearance and disappearance of the stars, the changes of the moon, the rainbow in the clouds, the differences between different bodies as luminous and non-luminous, transparent and opaque, and finally the very fact of vision itself—all these phenomena constantly, from the earliest times, presenting themselves without being sought, must have excited the curiosity of men and invited investigation, centuries before the systematic study of nature, in any of her varied departments, had had a beginning. But the difficulties which perplex the inquiry m: uifest themselves in the im- perfection of the speculations which have come down to us from the earliest philosophers regarding the subject, and in the extremely slow progress of dis- covery which marks much of the later history of this interesting branch of science. A notion was for a very long time prevalent among the ancients that vision is effected by means of rays procee ding from the eye to the object. This idea is not found in Aristotle; but it was introduced into the schoo: of Plato, and continued to be received for many centuries. The persistency of the doc- trine is remarkable, inasmuch as the light which is self-evidently indispensable to vision, proceeds from sources foreign to the observer. The elementary phenomena of reflection and refraction suggest a natural division of the science of optics into two branches; and this distinction is made by the earliest systematic writer on the subject whose works have descended to us. This was Euclid—supposed to have been the geometrician of that name—who lived about 300 years before our era. The general laws which govern the reflection of light, being comparatively easy of detection, were stated by him with tolerable correctness; but what he has written on refraction is of little value. Ptolemy, the astronomer of Alexandria, who was born about the year 70 of our era, attempted to discover the law of refraction by experiment. “His appa- ratus was ingenious, and was not different in principle from that which has been employed by Silbermann, Soleil, and others, in our own time, for the same pur- pose. He measured the angles of refraction corresponding to various angles of incidence, between 0° and 90°, for both water and glass, and left his measure- ments recorded in his System of Optics. In order that we may judge of the degree of accuracy attained by him it is necessary to anticipate what is to follow, so far as to define, in this place, a few technical expressions. By the angle of incidence made by light falling upon a reflecting or refracting para is meant the angle between the ray and the perpendicular to the surface. By the angle of refraction is meant the angle between the ray which has passed through the surface and the same perpendicular on the other side. By the angle of reflection is meant, in like manner, the angle between the reflected ray and the perpendicular. By the plane of incidence, the plane of refraction, or the plane of reflection is meant the plane which contains the incident ray and the perpendicular, the refracted ray and the perpendicular, or the reflected ray and the perpendicular. All these planes are coincident, except in cases where double refraction takes place, when one of the planes of refraction is not usually coincident with the corresponding plane of incidence. As a measure of the amount of deviation or change of direction produced in a ray by refraction, the sine of any given angle of incidence is divided by the sine of the corres sponding angle of refraction, which latter is determined by ob- servation. The quotient is constant for the same substance, no matter what be the angle of incidence taken. It is called the cxdex of refraction. The con- stancy ‘of this quotient was not known to Ptolemy. The discovery of its con- SNELLIUS —LAW OF REFRACTION. 109 stancy, at a comparatively recent period, marks an era in the history of the science ; and it was, as we shall see, the discovery of the /aw of refraction. The ascertained index of refraction for water is 1.33582. If we make a com- putation of its value from the measured angles of Ptolemy, we find a mean of 1.30147. Butif we take his measurements at the incidence of 50°, where the relative variations of the angles of incidence and refraction are most marked and most easily measured, we obtain 1.33555, which is exccedingly near the truth. The true index of refraction for glass is between 1.48 and 1.60, according to the materials and density. Crown glass varies from below 1.50 to about 1.525. Ptolemy’s mean determination would be 1.484. But at 50° he approaches nearer the truth, his angles giving 1.5321. For rays passing from water to glass, the relative index computed from his measurements would be 1.1390, the true being 1.14145. ‘The near agreement of these numbers with modern determinations is remarkable, especially consid- ering that Ptolemy’s measures are given only to the nearest half degree. Ptolemy was unable, however, to derive any practical advantage from these results, since the magnitudes of the angles seemed to be governed by no law which he could detect. And in this unsatisfactory condition the whole subject of refraction remained for the fifteen succeeding centuries. As an astronomer, Ptolemy could hardly fail to notice the effect of atmos- pheric refraction upon the apparent positions of the heavenly bodies; and he has the merit of having recognized the fact, which others after him disputed, that the displacement is always in a vertical plane, and also that it attains its maximum in the horizon and is zero in the zenith. About half a century later than Ptolemy flourished Claudius Galen, the cele- brated Greek physician. Ina treatise on the uses of the members of the human body he speaks at some length of the phenomena of vision, and lays down the fundamental law on which the stereoscope has been very recently constructed, that the picture which we sce of a solid body is made up of two pictures dis- similar to each other, one seen by each eye separately. But it was impossible that optical science should make any important pro- gress so long as the law which determines the path of a ray in passing from one medium to another remained unknown. We are compelled, therefore, to descend to the earlier portion of the 17th century before we find a practicable ground on which to build a systematic science, or lay even a foundation for the splendid superstructure which the future had in reserve in this department of physical inquiry. In the year 1626 Willebrord Snellius, professor of mathematics at Leyden, died at an carly age, leaving behind him manuscripts, among which was contained a statement of the important law in question under the following form: If MN be a plane horizontal surface, dividing a denser medium below it from a rarer one above, and if a point at D be observed by the eye at A, the apparent place of D will be at B, vertically above D, in the line AC produced ; and what- ever be the inclination of the ray to the surface, the line CD Fig. 1. will be to the line CB in a constant ratio. Or, if CD be made the radius of the circular are FDQ, and DE be drawn perpendicular ‘to the surface, the radius CI, being the visual ray AC produced, will be divided at B in a constant ratio. If, at ', we draw to the circle the tangent FH, producing CD and CB to mect it at H and G, then CH and CG, which have the same ratio to each other as CD and CB, will be the secants of the angles HCI and GCF, or the co-secants of the angles HCQ and GCQ, (—ACP,) formed by the refracted and incident rays with the perpendicular, PQ, to the refract- ing surface MN, technically called the angles of refraction and of incidence. The geometrical law of Snellius, therefore, translated into the language of trigonometry, is this: That when a ray, passing from one medium to another, undergoes refraction at the common surface, the ratio of the co-secant of the 110 EFFECTS OF REFRACTION. angle of incidence to the co-secant of the angle of refraction is constant. As the co-secants of angles are inversely as the sines of the same angles, the law may be more conveniently expressed by saying that, in the circumstances sup- posed, the s¢mes of the angles mentioned are in a constant ratio. It was in this form that the law was first published by Descartes, eleven years after the death of Snellius. It is, therefore, frequently referred to as the law of Descartes. It may be proper to mention that, previously to the discovery of this impor- tant law by Snellius, it had been remarked by the illustrious Kepler that for incidences below thirty degrees a ratio almost constant exists between the angles of incidence and of refraction themselves. _ This is true because for small angles the increments of the are and of the sine are nearly proportional. But when the incidence is moderately large, the divergency of the two ratios becomes very wide, An examination of the figure given above will show that the refraction of a plane surface produces no distortion in lines which are at right angles to the surface, but only diminishes or increases their apparent length according as the medium in which the object is situated is denser or rarer than that on the side of the observer. Thus the line ED is reduced to the apparent length EB. The amount of this reduction increases with the obliquity of the visual ray, for the ratio of CD to CB, which is constant, is always less (except when the incidence is perpendicular) than the ratio of ED to EB, and the divergency of these ratios is always increasing. It follows that the apparent depth of a fluid is always less than the real depth, and that the illusion.is more striking in proportion as the point observed is more remote from that immediately beneath the eye. Thus the horizontal bottom of a cistern or pool of uniform depth presents a curved appearance like that here represented. If MN be N the surface and ICL the horizontal Ww plane at the bottom of a sheet of L water, the eye being placed at the point P above it, this plane will present a conchoidal appearance like that of the curve D’E’’A”, The position of the points of the bottom which, to an eye situated at P, appear in the directions PD, PE, &c, may be found by asimple geometrical construction. Drawing the perpendicular PAA’, divide the depth AA’ at the point A’, so that AA’ shall be to AA” in the ratio of 2 to 1:—mn being the index of refraction. Through A’ draw VW parallel to the surface. Produce PD, PE, &c., until they intersect the bottom at G and H, and with the radii DE and EH describe the circular ares GG’ and HH’. Through G” and H” where DG, EH, intersect VW, draw per- pendiculars to the bottom, intersecting the ares in G’ and H’, Join DG’ and EH’. The points D’ and E’, where the joining lines intersect the bottom, are the points which will be seen from P in the directions PD, PE, and the ap- yarent positions of those points will be at D” and E”, where the visual rays PD and PE produced meet perpendiculars drawn from D’, EY’, to the surface. Any number of points being thus found, the curve drawn through them all will show the appearance of the level bottom M/N‘ as it is seen from a point above the surface as P. This curve is a conchoid, whose polar equation is —psecy + # seeg’ ; HE Pe ee Cpt Ein G1 Rt ieee aap ae nee eI in which pis put for PA, qg for AA’, » for the index of refraction, g for the angle EPA, and ¢' for EE’E”. .It is apparent from the foregoing that all lines seen through a single plane refracting surface, unless they are perpendicular to the surface itself, are more UNEQUAL REFRANGIBILITY OF DIFFERENT COLORS sie la or less distorted. A straight rod partly immersed in water, as FD‘, appears sharply bent at the surface, and slightly curved beneath, assuming the apparent direction OD”. Moreover, though, as in this case, the real direction should pass through the eye, so that in a uniform medium, only the extremity could be visible, the effect of refraction gives a lateral view of all the part immersed. The next important step in the progress of optical discovery, after the detec- tion of the general law of refraction, was made by the illustrious Newton, who, in the year 1672, communicated to the Royal Society the experimental researches by which he established the compound nature of light, and the unequal refran- gibility of its component rays. He held that the common white light of the sun is made up of elementary rays differing at the same time in color and in refrangibility. The number of tints which he considered sufficiently distinct to be regarded as independent components is seven. It seems unnecessary, however, to suppose the existence of: more than three elementary colors, it being possible, by mingling these in various proportions, to produce all the rest, while the degrees of refrangibility between the extreme limits vary through an infi- nite number of infinitely small differences. Newton’s method of demonstrating the truth of his doctrine was as simple as it is ingenious. The colors which border the images of objects observed through prisms of glass or other transparent substances, or through cylindrical or globular vessels filled with water, had long been familiar. Newton placed such a prism in the path of a ray of the sun’s light, introduced through a small aperture into a dark room, and received the refracted image or spectrum upon a white screen placed at some distance. Before the interposition of the prism the beam produced upon the screen a white and circular image of the sun itself. But after the rays had been bent by refraction the image appeared very much elongated in the direction of the refraction, and brilliantly colored in a series of tints, passing by insensible gradations from red, through orange, yellow, green, blue, and indigo to violet. 'This last color was at the end most refracted. In turning the prism around an axis parallel to its edges, Newton observed that the deviation of the spectrum from the original direction of the sun’s rays was variable, increasing from a certain minimum (experimentally found) by turning the prism either to the right or to the left. This minimum corresponds to that particular position of the prism at which the angles of incidence and emergence are equal. Upon this observation he founded a test experiment in regard to the refrangibility of the rays of different colors. Making a small circular aperture in the screen upon which the spectrum was formed, at a point where, by turn- ing the prism, he could pass the entire spectrum over it, he placed behind the aperture a second prism, which thus reccived, successively, rays of a single color only. At a distance behind the second prism a second screen intercepted the light which passed through it, when it was observed that this second image, instead of being elongated like the first, remained sensibly circular, while the positions of the circles of different colors upon the screen were further and further removed from the original direction of the unrefracted rays as the tints ascended from red to violet. ‘This phenomenon of the separation of the compo- nent- colors of light by refraction has been called dispersion. Newton was of opinion that the dispersive powers of all bodies are equal; or, in other words, proportional to their refractive powers; and that, the mean refractive powers of two bodies being equal, their refractive powers for each particular color must be equal also. Both these suppositions, as we shall see, are unfounded. The discovery of Newton furnished an easy explanation of the interesting natural phenomenon of the rainbow. ‘This beautiful meteor had been the sub- ject of many unsatisfactory speculations; and though de Dominis, as early as 1611, had furnished a true theory of the manner of formation of the inner bow, he had not been able to account for its colors. He showed that there is a certain incidence at which, if the parallel rays of the sun fall upon the anterior surface ‘ 112 THE RAINBOW. of a transparent globe, they will be reflected from within so as to emerge, still parallel to each other, at a point on the other side of the centre. The emergent rays will form a constant angle with the incident rays, and, entering the « eye of the observer standing with his back to the sun, will form the same angle with a line supposed to be drawn from the sun through the eye. This line from the sun through the eye being made an axis, and the above supposed reflected ray being revolved around it, there will be traced out in the heavens a circle, from every part of which, if rain-drops are present, there will come an amount of light above that which is reflected from the surrounding cloud. This explanation satisfactorily determines the locus of the bow; but it fails to account for its tints, or the extent of surface over which they are spread. It would require that the are should be white, and that it should be no broader than the sun; that is to say, that its breadth should be only about half a degree. The actual breadth of the inner bow is, however, two degrees and a quarter; and that of the outer three degrees and three quarters. Newton’s discovery furnished the necessary supplement to the theory. In fact, if the circumference PP’/P” be a section through the centre of a transparent globe, and IP a ray of the sun falling on it in this plane, it is easy to see that this ray, or portions of it; will undergo many reflections within the globe, while portions will succes- sively emerge at the points in which reflection takes place. “E here will first be some loss by external reflec- tion in the direction PR. The portion which enters the globe will be bent, by refraction, from the original direction PIs to the direction PP’. At P’ a portion will emerge in the direction Pt, being bent from the direction PQ as much as PP’ was bent from PK. The same thing occurs at P’, P’’, and so on. Put ¢ = the angle of incidence (the angle made by the incident ray with the radius)—the angles of emer- gence are all of this same value. Put p for the angle of refraction. The figure shows that add the angles of internal reflection have this value. Let 6 represent the bending or deviation of the ray by refraction at each incidence or emer- eence., hen d—=:—p. And the amount of deflection of the successive re- flected rays from the original direction being sige by D Die), aud that of the successiv ely emergent rays s by A, 4’....D(™), we shall have (an entire circumference being denoted by 27) Deflection of PP’—d; deflection of PE—d—20. Deflection of P’P"—D—d+7—2p; deflection of P’E’—=4’—20-+7—2p. Deflection of P’ P’“—D/—0-+ 2z—4p; deflection of P’’E=4"—=20 + 22—4p. Deflection preceding mth emergence—D(™)—0+m(z—2p); deflection mth emergence— A(™)—20+ m(z—2p). If, for 0, we put its value — :—p, we shall have—~ A'—=2:-+n7—4p. = A" = 20+ 27—6op. A(™)==2¢-+mz—2(m-+1)p. The law of the formation of these eTon essions is obvious. The deflection of each of the successively emergent rays is increased at each reflection within the globe by the angular amount z—2p. Now, as all these values contain the angle ¢, it is obvious that the deflections cannot be equal when the incidences are uncqual; or, in other words, that the emergent rays will usually diverge from each other. Moreover, the deflections do not regularly increase and diminish with the incidence. Putting the Dna A'—180°2, and 4/’—=360°. Putting —662uand) ZM——24'S Putting the een 70°, Al == 390 and A200 °° nearly, for water. ' ’ THE RAINBOW. 113 Neither of the last values is intermediate between the two preceding in the same column. In both cases, therefore, there appears to be some point between the extreme incidences, where the deflection is a minimum; and it being the law of maxima and minima that variations in their vicinity are insensible, it follows that near the incidences corresponding to those values the emergent rays will be sensibly parallel. But when the general expression— A(™ )==2'-+- mnz—2'm-+-1)e becomes a minimum*, the cosine of the incidence must have the value— cos ex + / fee is V (m+1)?—1, in which » denotes the index of refraction. This determines, therefore, the incidences at which the deflections are minima; and hence, those at which the emergent rays are (to use the term employed by Newton) efficacious. It will be seen that, when the index of refraction is given, the value of cos: will be affected only by the variable m, which is the number of internal reflections. If this be made zero, cos: will be infinite; in other words, when the rays are not reflected at all, they do not emerge efficacious. By putting m—1 and m—2 we shall obtain values corresponding to the de- flections which produce what are ealled the inner and outer bows. J'rom these values we may deduce the apparent diameters of the ares; and the theoretic results thus obtained are found to accord with actual measurements. By putting m=3, 4,5, &e., successively, we may obtain the /oct of an infinite number of additional bows; but after the second reflection, the light ceases to be intense enough to produce an impression on the eye. Since, with a very slight alteration of ¢ the rays cease to be efficacious, it is evident that, if the sun were but a point, and the index x invariable, the bow would be reduced to a simple line of light. But as every point of the sun will produce its separate bow, the visible breadth, with » constant, would be that of the sun itself—that is, about half a degree. Newton’s experiments on dis- persion, however, showed that the value of the index » sufficiently varies, in passing from the red to the violet, to alter sensibly the angle of incidence cor- responding to the efficacious rays of the several colors, and sufficient, accord- ingly, to alter the amount of deflection which those several rays undergo before reaching the eye. As the bows appear in the direction of these deflected rays, it follows that the different colors will not be superposed, and that the breadth of the compound bow will be greater than the breadth of the sun by the total amount of their want of conformity. The index for the red may be taken at 1.346; that for the violet at 1.333. Employing these values, we have for the bow by one reflection: Violet rays. -t, == 58° 40’. 4’, == 139° 43’. Radius of bow —=.40° 17’. Red rays. - . -¢; = 59° 234’. 4', = 137° 584’. Radius of bow = 42° 12’. * The general expression for the deflection being— ol AV?) =21-++ma—(m-+1)p, its differential is dA(™)=2de—2(m-+1 dp; which, when A(™) is a minimum, is equal to zero. dé From this we obtain the ratio, inet. P From the Snellian law, sinv—=nsinp, » being the index of refraction. This furnishes an- another value of the same ratio, smce coscdi—=ncospdp. di ncosp oh Or, — = —=m-+-1; and (m+1)cost=ncosp. dp cose Squaring this, and adding to it 1—cos*:==n"sin’p, member for member, we obtain— [ (aw-+-1)?—1 ] cos*z-+-1—=n*\ cos*p--sin*p)—=n?, T'rom which we deduce the result in the text— 1?—-] a 8s coy pF 114 DIFFRACTION—-DOUBLE REFRACTION. And for the bow by two reflections: ‘ Violet rays.ty—= 71° 49/55". 4”, = 230° 58’ 50. Radius of bow 50° 58’ 50": Red rays. . -¢ == 71° 26/10". 4”; == 234° 9/20. Radius of bow 54° 9! 20" From the values of 4 it will be manifest that the rays which produce the bow by one reflection must enter the rain drops above the ray which passes through the centre; and that those which produce the bow by two reflections must enter below the same central ray. The differences between the values of 4, and 4, above, show the amount by which the breadths of the bows are increased in consequence of the variability of n. These amounts are, for the first bow, 1° 44’ 40’, and for the second, 3° 10 30’. The colors are produced by the want of conformity of the bows corresponding to the several elementary rays; and their feebleness is owing to the fact that, notwithstanding this want of conformity, they do, on account of the considerable diameter of the sun, very sensibly overlap, while they are also diluted by the white light reflected from the anterior surface of the drops. Were they entirely superposed upon each other the bow would be white. While the discoveries of Newton and Snellius, just mentioned, were: removing old impediments to progress in optical science, observation continued to add new ones more perplexing than those which had disappeared. In the year 1665 there was published, at Bologna, a posthumous work by Francis Maria Grimaldi, an Italian Jesuit, in which were, for the first time, described certain phenomena now very familiar under the name of diffraction. He stated that if any very small object be placed in a pencil of divergent light,admitted through a minute aperture into a dark room, its shadow will appear materially larger than it ought if light passes its edges in straight lines; and, moreover, that any opaque object, large or small, exhibits along the edges of its shadow a border of at least three distinctly tinted fringes, the brightest and broadest of which is next the shadow. He also observed that when two minute pencils of light are admitted through apertures very near to each other, the sereen on which the blended pencils fall, and which, as he supposed, ought to be uniformly illu- minated with a light equal to the sum of the two intensities, is streaked with lines absolutely dark. He was led by this observation to announce the paradoxicat proposition that there are circumstances in which the union of two rays of light produces darkness. Bold as this announcement must have originally appeared, the progress of scientific discovery has fully confirmed its truth. ‘This phenom- enon, being attributed to the bending of the rays of light in the immediate vicinity of the opaque body, was distinguished by the name inflection or diffrac- tion. It was carefully studied by Newton and others, and has occupied a prom- inent place in ali the discussions which have since arisen in regard to the nature of light. Not far from the time of the discovery of Grimaldi, just mentioned, the atten- tion of the scientific world was calied to a case of new and extraordinary refrae- tion observed to take place in crystals of carbonate of lime—a species of retrac- tion, which, from the circumstance of its dividmg an imcident beam into two beams entirely distinct, or of presenting two images of any object seen through the erystal, has been called double refraction. ‘The first publication on this subject was made by Erasmus Bartholinus, a physician of Copenhagea, who gave to the mineral the name of Iceland spar, from the circumstance that his specimens had been obtained from that island. Jt is now known that this property of double refraction is exceedingly common, being possessed by most crystallized bodies, and capabie of beg produced, transiently or permanently, in any trans- parent solid whatever, whether organic or mineral, in which it does not naturally exist. It is only in Iceland spar, however, that it manifests itself in a degree remarkable enough to attract the attention of a casual observer, and in most cases li can only be detected by special arrangements. DOUBLE REFRACTION. HED Iceland spar is favorable to observations upon double refraction, not only on account of its wide separation of the refracted rays, but also because of the size of the crystals which can be obtained of this mineral, and of their beautiful transparency. Its primitive crystalline form is the rhombohedron. Whatever may be the configuration of the mass as obtained from its native bed, it will be found to cleave with great facility in directions parallel to the faces of the original rhombohedron, and it is thus easily reduced to a form favorable for ex- periment. The angles of the rhomboidal faces are 101° 55’ and 78° 5’. The z inclinations of the faces upon each other are 105° 5! and. 74° 55’. Two of the solid angles are contained by-three of the obtuse angles of the rhomboids, and the other six by two acute and one obtuse each. “The diagonal con- necting the two exceptional solid angles is the shortest Fig. 4. of the diagonals of the rhombohedron, and is called the crystallographic axis. ‘These angles themselves are called the vertical, and the other six the lateral, angles of the crystal. If a mark be made with ink upon a sheet of white paper—a small cross for example—and a rhomboid of Iceland spar, two or three inches in thickness, be laid over it, then in whatever position the eye may be placed above the upper surface of the crystal, two crosses will be seen. If the erystal be turned about upon its horizontal face, one of these images will remain motionless, and the other will describe a circle around it. The motionless image will, moreover, appear sensibly nearer to the eye than the other. If, instead of a small mark, we take a straight line ruled entirely across the paper as an object, then, if the eye be placed vertically over the line, and the erystal interposed, it will be seen that the nearer image is always a continuation of the part of whe line seen beyond the erystal on each side, while the more distant one is more or less dis- placed laterally. In revolving the crystal, moreover, this second image will pass from one side to the other of the first, and.a position will be found (or rather two positions, differing from each other by 180°) ia which the two images apparently coincide, though, as they are differently distant, they are merely superposed. Until the discovery of this remarkable property in Iceland spar, refraction was supposed to be governed in all cases by the law of Snellius. But it is im- possible that this should be true of both the rays in the present case. It is, in fact, true only of that one which produces the nearer and fixed image. This is, for distinction, called the ordinary ray ; the other, the extraordinary. If the vertical angles of the rhombohedron he truncated perpendicularly to the crystallographic axis, and the artificial faces thus formed polished, it will be found that when the crystal is laid over a small object upon one of’ these faces, and the eye placed immediately over it, only one image will be visible. This is not an illusion occasioned by the superposition of images differentiy distant ; there is actually but oneimage. But if the emergeut ray coming tv the eye, by which the object is seen, be at all inclined to the surface, the image will be duplicated, and the degree of separation of the two images will increase with the inclination. If the lateral edges of the crystal are cui away, so as to form a parallelopipedon, whose faces are parailel to the erystaliographic axis, and the crystal be laid on its side, the separation of the images will be at its maximum. In this case, if the emergent visual ray be perpendicular to the surface, the tw images will be superposed, but the duplicity will be very perceptible. It appears, then, that there is one directiou in the erystal, in which light may pass without double refraction, and tha. this direction corresponds with that of the erystallographic axis. This direction is also called the eptic axis; but the term optic axis, it must be observed, is not intended to denote a particular Line, but only a particular direction, and in the present case it is a line anywhere in the crystal parallel to the axis of symmetry. 116 DOUBLE REFRACTION. Any plane parallel to the axis of ‘the crystal necessarily coincides with the optic axis, and every such plane is called a principal plane or principal section. This term is one of very convenient use. Any plane at right angles to the optic axis (and therefore to allthe principal planes) may be called a conjugate plane or section, which term will be also found to have its convenience. In every such conjugate plane the separation of the two rays by double refraction is at its maximum; and, what is also important, the extraordinary ray, as well as the ordinary, obeys in this plane the law of Snellius. ‘The indexes of refraction for the two are, however, necessarily different; that of the ordinary ray being 1.6543, and that of the extraordinary, 1.4833. In directions which do not correspond with either a principal or a conjugate plane, the index of refrac- tion of the ordinary ray will be found to be invariably the same, but that of the extraordinary ray will gradually increase from the direction perpendicular to the axis to that which coincides with the axis. In this last case the two in- dexes become equal, and double refraction disappears. The index of the ex- traordinary ray at any inclination (denoted by @) with the optic axis, may be found from the following formula, in which x= 1.6543, n’—1.4833, and N is the index sought: N=V 22 —(n?—n?) sin2a= V 2.7367 — 0.5365 sina. We see now why it is that one of the images seen through the crystal is apparently nearer than the other. ‘The general effect of refraction by a single plane surtace of a body denser than air, is, as has been already illustrated, to bring the object apparently nearer to the surface. This effect must depend for its degree upon the refracting power, and this power is a direct function of the index of refraction. ‘The indexes of the two rays are different, and therefore the apparent distances of their images are different likewise. One of the most remarkable facts connected with the refraction of the ex- traordinary ray is that, unless the incidence is in the plane of a principal section, or of a conjugate section, the refracted ray is not in the plane of incidence. And if the refracting surface, whether the natural surface of the erystal or one artifi- cially prepared, be not coincident with a principal or a conjugate plane, the extraordinary ray is bent at the surface, even when the incidence is perpendicular. In observing through the crystal prepared by truncating its vertices by conjugate planes. in which case we have the advantage of having both refracted rays in all positions in the plane of incidence, we shall see that the extraordinary ray is always the most distant from the normal to the surface. But this normal represents the direction of the optic axis. ‘The extraordinary ray, therefore, has the semblance of being repelled from this axis. As there are crystals in which the’ apparent effects are reversed, that is, in which the extraordinary ray is nearer to the optic axis than the ordinary. as if it were attracted, these two classes have been distinguished by the terms negative and positive. In the negative the extraordinary index is less than the ordinary; in the positive. greater. A curious observation in regard to the paths of the two rays through a erystal of Iceland spar, by which an object at a litle distance beyond it is scen, origi- nally made by Monge, may be mentioned here. The object being at O, and the eye being at E, the ordinary image will appear above the extraordinary and nearer, as at O’, O” being the extraordinary image. The emergent rays are therefore P/E and Q'E. But the rays incident on the under side of the crystal from the object must be resp-c- tively parallel to these. Draw then OP parallel to P’E, Fig. 5. and OQ parallel to Q’E, and join PP’, QQ’. The en- ' tire path of the ordinary ray is then OPP'E, and that of the extraordinary is OQQ’E, which lines, when the plane of incidence is a principal plane, necessarily cross each other in the crystal. DOUBLE REFRACTION. eT If a card be passed along the under surface of the crystal, in the direction RR, it will cut off the ray OP before interfering with OQ. The image 0’, which is most distant from the card, is therefore first to disappear—a phenome- non very striking when seen for the first time. The card employed in this experiment should be dull black in order to produce the best etiect, otherwise it is too conspicuous itself. When a ray of light, after having passed through one crystal and having been divided into two distinct emergent rays, is allowed to fall upon another similar and equal crystal similarly situated, the effect, as might naturally be expected, will be to increase the separation of the rays to the same extent as would have occurred had both the crystals been united in one. But if the second erystal be turned around the direction of the ray as an axis, other phenomena make their appearance, the character of which depends on the amount of turning. In speaking of this kind of revolution it will be convenient to employ the term azimuth. By this word is meant direction in space in a plane at right angles to any axial line. ‘Che term is adopted from astronomy and geodesy, in which sciences the assumed axial line is the vertical, and the azimuthal plane the horizon. In the case in hand, if we completely reverse the position of the second crystal in azimuth, that is to say, turn it round 180°, it will reverse the refract- ing effect of the first crystal and reunite the two rays, which will emerge as one. If we turn it only 90° in azimuth the separation of the rays will con- tinue, but that which was the extraordinary ray in the first crystal will become the ordinary in the second, and vice versa. Accordingly, if the original inci- dence is perpendicular, the ray which follows the normal in the first erystal will be bent at the surface of the second, and that which is bent at the surface of the first will follow the normal on entering the second. At any azimuth differing from the original position more or less than 90° or 180° there will be seen four emergent rays, of which two will usually possess a greater intensity than the other two. When the change of position of the second crystal is but slight, the two original rays will be vivid; but, in a linea right angles to that which connects them, two very faint ones will appear, nearer together than the original two. As the rotation advances these new rays will gain in strength, while the other two grow less intense. At the azimuth of 45° the four will be equal and equidistant. Beyond 45° the original rays go on fading and the new ones increasing in brightness, until, at 90°, the former become entirely extinct and the new ones remain alone. Beyond 90° again another faint pair appear, which go on, as before, increasing in brightness, at the expense of the companion pair, up to the azimuth 135°, when the four are again equal. Beyond 135° this second new pair still continue to gain strength and to approach each other, till, at the azimuth 1809, they reunite into one, and the others in their turn vanish. In the figure following, these successive phases are shown as they appear upon a screen when the experiment is performed in a dark room. ‘They are circumscribed by the outlines of the two rhombs in their relative sue- cessive positions. a yA @ °@ The phenomena of double refraction were carefully studied by the celebrated Huyghens, who devised a physical theory for their explanation, which has been pronounced by Brewster to be one of the most splendid of the triumphs of genius which illustrate the history of science. His theory did not, however, extend ta the explanation of the remarkable appearances last described, which present 118 COLORS OF THIN PLATES. themselves when two doubly refracting rhombs are combined—appearances which were observed by him with surprise and perplexity. They are now known to be owing to a remarkable modification of light which always accom- panies double refraction, though it may be produced in other ways, and which is called polarization. 'This will oceupy much of our attention further on. Soon after his announcement of the compound nature of light, Sir Isaac Newton made public the results of his ingenious investigations in regard to the colors exhibited by then plates of transparent substances, such as soap-bubbles, films of moisture upon glass and upon polished opaque solids, laminz of air confined in fissures of transparent minerals, &c. He showed that the tints dis- played by such thin plates, when viewed in common light, depend upon three conditions, viz: the thickness of the plate, its refracting power, and the angle of obliquity under which it is viewed. 'The determination of the relation of the tint to the thickness, was made by means of a very simple contrivance. A double-convex lens, of very long focus, was placed in contact with the plane surface of a plano-convex lens, the two being pressed together by means of screws. In Newton’s experiments the double-convex lens was beneath and the plano-convex above. ‘The convexity of the upper surface of the upper lens is advantageous when oblique observations are desired, as tending to reduce the refraction of the incident and emergent rays at that surface. The two touching surfaces have, theoretically, but a single point of contact, and that point is the centre of a thin plate of included air, of which the thick- ness increases from zero equally in all directions. The law of this increase will be apparent from the figure annexed. MN represents the lower surface of the supe- rior glass, and QR the upper surface of the inferior. Let C be the centre of the sphere of which QR is a super- ficial section. Put 7 for the radius CP. Then, if the ares Pa, P), are small in proportion to the whole circum- ference, we shall have 2 7 “ / / os Piel Ag Sind PR pe 2r 2r Or, if 2 stand generally for the thickness Aad or Bé,and y for the corres- ponding distance from the point of contact, PA or PB, we shall have the vari- ation, recy”. This furnishes a law by which, when the thickness corresponding to a single assigned value of y is known, the thickness for all other values may be com- puted with great facility. The apparatus being arranged as above described, the colors which are seen by reflected light are arranged in regular rings around a black centre and in suc- cessive series, as follows: Black, blue, white, yellow, red. Violet, blue, green, yellow, red. Purple, blue, green, yellow, red. Green, red. Greenish blue, red. Greenish blue, pale red. . Greenish blue, reddish white. These are what Newton calls the successive orders of colors, and, in referring lo any particular tint, it is designated as the blue, red, green, &c., of the first, second, or third order, as the case may be. Beyond the fourth order the colors become feeble or begin to fade rapidly out into whiteness, and, beyond the seventh, color can scarcely be at all perceived. he cause of this fading may be made manifest by employing homogeneous or monochromatic light; that is to say, light of a single tint only, obtained by isolating a portion of the rays of ee COLORS OF THIN PLATES. 119 the prismatic spectrum whose refrangibility and color are sensibly the same. Then very many more bright rings will be observed, separated by intermediate rings entirely dark. But what is of most importance at present is that those which are formed by the least refrangible rays are larger than any others, and that the diameters of rings of the same order regularly diminish as the refran- gibility increases. ‘This difference of magnitude between the rings of different tints occasions the overlapping of one color upon another when white light is used, so that the colors observed are not simple but resultant colors, determined in their tints by the simple colors which happen to be predominant at any point. The other components serve, with some portion of the predominant tint, to pro- duce white light, by which the tint is diluted and rendered more feeble than it would otherwise be. The truth of this explanation will be made apparent by viewing the rings through a prism. The effect will be to make the overlap- ping on one side more complete than before, and, on the other side, less. The rings will be less highly colored but more numerous and better separated on the side of greatest refraction, and more confused on the other. From a careful measurement of the diameters of all the bright rings, Sir Isaac Newton ascertamed that the squares of these diameters form a regular arithmetical progression, corresponding to the natural series of odd numbers, 1, 3, 5, 7, &e. And the squares of the diameters of the intermediate dark rings were found to constitute another similar progression, corresponding to the series of even numbers, 2, 4, 6, &c. From the law aay’, it therefore follows that the bright rings appear where the thickness of the plate is once, thrice, five times, &c., some constant value, and that the dark rings appear where the thickness is twice, four times, siz times, &e., the same constant value. The next question to be determined is, therefore, what is that constant? In order to ascertain this, Sir Isaac Newton measured with great precision the absolute diameter of the fifth dark ring. This, with the known radius of the spherical surface of the lens, enabled him to compute the thickness of the plate at that ring, this thickness being the versed sine in a great circle of the sphere of an are of which the measured diameter is the chord. The result gave him e000 Of an inch, very nearly, for the thickuess of the plate at the fifth dark ring. But the fifth number in the series 2, 4, 6, &c., is 10. Hence, the con- stant sought for is one-tenth of s5255 of an inch, or ;7),5), and this is the thickness of the plate at the point where the greatest brightness of the first bright ring is seen. Reduced to a decimal, it gives a little more than fifty-six ten-millionths of an inch. If the value of this constant be sought for the several homogencous rays, it will be found to be, for the violet, a little more than thirty- nine ten-millionths, and, for the red, not quite sixty-nine ten-millionths. As, in the space occupied by the colors of the first order, the thicknesses vary slowly, and as there is a certain range of variation in thickness within which each color may appear, though its greatest intensity is in the middle of this range, it happens that the colors of the first order are dilute, especially toward the centre of the system, and that the middle of the series is white. In the succeeding orders, the differences tell in such a manner that the bright rings of some colors fall more or less exactly upon the dark rings of others, and the tints become stronger. But, as the thicknesses soon begin to vary rapidly, every system of rings becomes crowded, and the separating dark intervals grow narrower and narrower, until there is a complete blending of tints at every point and the resultant is sensibly white. When water is introduced between the glasses, the rings become immediately smaller. If the thickness at which a given tint now appears is compared with that at which the same tint appeared in air, it is found to be reduced in the ratio of ” to 1, 2 being the index of refraction between air and water. This law admits of being generalized. In fact, whatever be the substance of the thin plates in which these tints appear, the thicknesses which produce them are inversely proportional to their indexes of refraction. 120 COLORS OF THICK PLATES. When the system of lenses described above is held between the eye and the light, another system of rings makes its appearance, which is formed by the transmitted light. In this case the tints are much feebler, being diluted by the intermixture of a great deal of white light, which, as we shall see hereafter, has nothing to do with their formation. Of these it is remarkable that the diame- ters of the bright rings correspond with those of the dark rings seen by reflec- tion. Thus the thicknesses at which the bright rings by transmitted light appear form a series corresponding with the progression of even numbers, 0, 2, 4, 6, &c.; and the thicknesses at which the intervening dark rings are scen cor- - respond to the progression 1, 3, 5,7, &c. Also the tints reflected and trans- mitted at any given point are complementary to each other, or are such as, united, produce white. The measurements above given are those which correspond to rings formed by light perpendicularly incident upon the thin lamina. But when the rings are observed obliquely, their diameters are rapidly enlarged with increase of obliquity. Sir Isaac Newton ascertained the law of this increase to be this: that the squares of the diameters are inversely as the cosines of incidence. When the incidence exceeded 602, it appeared to him that this law no longer held good; and this conclusion, which, up to a recent period, had not been invalidated, has formed a serious difliculty in the way of any theory of light. Recent experiments, however, made by Messrs. Provostaye and Desains, with monochromatic light, and with special arrangements to eliminate the sources of error in measurement which must have vitiated Newton’s results at high inci- dences, have fully established the universality of the law. ‘Their measurements extended to the forty-third ring, and to the great incidence of 86° 14’, beyond which the rings were no longer discernible. Colors resembling those of thin plates may be produced also, in various modes, by means of thick plates. Sir Isaac Newton employed, in an interesting experi- ment of this kind, a spherical glass mirror, with truly concentric surfaces, silvered on the back. A very small beam of light (about one twenty-fifth of an inch in diameter) having been intro- duced inté a dark room, he received it on this mirror in such a manner as to reflect it back toward the aperture. ili) At the centre of curvature of the mirror he placed a white ! card pierced, in order to allow the light to pass, with a very small orifice. Around this orifice he saw a series of rings resembling those of thin plates. When the light was homogeneous, the rings were alternately bright and dark as in the other case. The diameters were also observed to follow similar laws. As both surfaces of the mirror are concerned in producing these rings, and as, at the first surface, it is the irregular or seattered reflection only which is necessary to the effect, the experiment succeeds best with a mirror in which this surface is not highly polished. Instead of the perforated card, a lamina of mica, or of slightly tar- nished glass, may be employed to receive the rings. When light is transmitted through or reflected by a pair of thick plates of homogeneous glass, with parallel plane surfaces, and placed parallel to each other. colors may ap- pear, if the difference of thickness of the two plates is comparable to the absolute thickness at which such colors are produced by thin plates. ‘The figure shows the arrangement. Dr. Brewster pro- duced the same effects with a pair of plates of equal thickness, by inclining one of them so that the path of the rays within it should be slightly longer than within the other. ‘There is some sim ilarity between the first of these classes of phenomena and those of diffraction. The second have a nearer analogy to the eolors of Newton’s rings. Fig. 8. PROGRESSIVE MOTION OF LIGHT. 1Oq The next important step in the progress of optical science was the discovery of the progressive motion of light, and the determination of its velocity. 'Uhough every theory which had ever ~ been suggested to account for the phenomena ‘of light presumed that there must be a progress from the luminous origin, and feos that time must be an element in the solution of every optical proble m, still so nearly instantaneous are all the effects produced at the distances to which our ordinary observation extends, as apparently to render hopeless any plan for experimentally determining the velocity. This circumstance rendered the efforts made by the celebrated Galileo, and by the academicians of Florence, to settle the question, completely nugatory. ‘The method of proceeding adopted by Galileo was to place himself upon an eminence opposite to an assistant observer something more than a mile distant ; both being provided with lanterns which could be darkened by a slide. The lights being arranged, Galileo dark- ened his lantern; and the assistant, immediately on noticing its disappearance, darkened his also. Apparently both were extinguished at the same instant. The Florentine academicians repeated the experiment, increasing the distance between the stations, but the result was the same. The problem remained unsolved ; but its solution came at last, when demanded by the exigencies of a higher | branch of science. In 1675 Reemer, an astronomer of Copenhagen, in his observations upon the eclipses of the first satellite of Jupiter, became perplexed by irregularities for which he could conceive no means of accounting. It was suggested by Dominic Cassini that these difficulties might perhaps be re emoved by supposing that the time occupied by light in passing through the vast distance between Jupiter and our planet may be | arge enough to be. appreciable; and therefore that, as our dis- tance varies, this time must vary also. Assuming this hypothesis to be true, and that the epoch on which our computations of future eclipses are founded is the date of some eclipse actually observed when the two bodies were occupying their points of nearest approach, it will follow that if the accuracy of the deter- minations is affected only by the motion of light, all subsequent eclipses, observed when the distance is the same as at the epoch, will agree with the prediction, and all others will be in retardation by an amount of time equal to that which light requires to pass over she space by which the distance has been increased. In like manner, if the epoch had been an eclipse observed in the position of greatest distance between the bodies, subsequent eclipses would be in advance of the prediction; and if the epoch had been an observation made from some position intermediate between the points of greatest and least distance, the eclipses afterwards occurring would be sometimes in advance and some- times in retardation. The test of the correctness of the hypothesis would be a careful comparison of the observed irregularities of time with the variations of distance—a comparison involving no slight labor. Cassini, with whom the idea originated, seems to have abandoned it; but Roemer followed it up with such perseverance as at length conclusively to establish its truth. He demonstrated that the time occupied by light in passing over the entire diameter of the earth’s orbit is 16 minutes and 26 seconds. But at that period the dimensions of the earth’s orbit were not accurately known, and this determination was insuflicient to fix the absolute value of the velocity of light. Assuming the sun’s mean parallax to be 8.6, the mean diameter of the orbit must be about 190,000,000 of miles, and this number divided by 986, the number of seconds in 16 minutes and 26 seconds, gives for the velocity in miles 192,700. The velocity of light has, since the time of Roemer, been ascertained, with a probably near approximation to the truth, by ether independent methods, and the results tend to confirm the substantial correctness of his original determina- tion., The first of these methods is that which rests upon the measurement of the aberration of the stars, a phenomenon discovered by Bradley, afterwards 122 VELOCITY OF LIGHT. astronomer royal of England, in 1728. This aberration consists m an apparent displacement of the star from its true position by the com- 2 eg bined influence of the motion of the earth and the progressive , Bx f, motion of light. If, for instance, the line MN be taken to / B represent a small portion of the earth’s path, and 8 be a fixed PY AE 1] star, then while the earth advances in the direction of the Wf} arrow from O to O', O””, &c., if the propagation of light were Af fi) instantaneous through all distances, the star would be seen __ ool old ar in the true direction, OS, O's, O"s', &c., the telescope OP oie remaining parallel to itself as the earth moves, in conse- quence of the immense distance of the star. Also, allowing progressive propagation of light, if the earth were without motion, the star would still appear in its true direction. OS, the telescope OP remaining stationary ; but if we suppose both the earth and light to move, then a ray entering the centre of the tube OP, at the summit, would not be in the centre of the tube when it reached the lower end, but would be displaced toward the rear by a small space equal to the earth’s own motion while the ray is descending the tube. T'o the observer at O, therefore, the telescope would not appear to be truly pointed at the star, but would require to to be leaned forward in the direction OP, until the luminous elements which compose the ray (whatever they may be, should follow accurately the axis of the telescope from top to bottom. The star will accordingly seem to be at S’, in advance of its.true position, in the direction of the earth’s motion. The amount of this apparent displacement will vary with the angle made by the direction of the earth’s movement with the direction of the star. When this angle is zero, that is to say when the earth is moving di.ectly toward or from the star, the displacement is zero; when the angle is 90°, or when the earth’s motion is directly across the line drawn to the star, it is maximum. For a star in the plane of the earth’s orbit, the aberration is apparently an oscillation in a straight line, the duration of the movement in the aliernately opposite directions being six months ; for a star in the pole of the ecliptic, or in a direction at right angles to its plane, the apparent path would be a very small ellipse similar to the earth’s orbit. The major axis of this ellipse would measure the maximum amount of aberration on both sides of the true place, and this is found to be equal to 40.88; half of this, or 20”.44, is the maximum absolute amount of displacement. ‘The direction of a star, therefore, when its aberration is maximum, deviates from its true direction as the diagonal of a rectangle deviates from the side. If, in such a rectangle, the smaller side be made equal to the velocity of the earth, the larger will be the velocity of light, and the angle between the larger side and the diagonal will be 20'.44. But the earth’s velocity per second is known, and is about 18.9 miles; hence the velocity of light is 18.9 x cot20’’.44—=190,730 miles, a number less than that before obtained by about one one-hundredth part. This coincidence of results is sufficiently remarkable, when we consider the extreme delicacy of such measurements as those by which aberration is de- termined, and also the difficulty of fixing, by observation, the exact instant of the immersion or emersion of one of Jupiter’s satellites; but, these difficulties apart, there is nothing surprising in the agreement, since both depend at last for their absolute values upon our received horizontal parallax of the sun. Results very nearly similar, however, have been recently obtained by experi- mental methods founded upon principles entirely different from the foregoing. The first of these methods was devised by Mr. Fizeau, of Paris, and executed by him in the vicinity of that city. Having selected two stations, visible from VELOCITY OF LIGHT. 123 ‘ each other, and about 54 miles apart, he placed fwo tubes, something like tubes of telescopes, one at each station, looking towards each other, with their axes in the same straight line. One of these tubes, represented at AB, has a branch tube E furnished with lenses, through which is received the light from a radiant point S. This light is reflected by an inclined trans- parent plane mirror m, forming a bright image of the luminous point at s, which is in the principal focus of the large lens B. The rays being made parallel by this lens, are received at the other station upon the lens C, by which they are brought to a focus upon the surface of a plane mirror D. Being reflected back by this mirror, they return to the lens B, and once more form a bright image at s, which image may he observed through the trans- parent mirror m, by an eye placed at A. The upper side of the tube at F, just in front of the plane mirror, is cut through in order to admit the limb of a wheel, furnished with teeth, to descend so far into it that the i image s may be seen be- tween the teeth or cut off by them, according to the position of the whecl. The teeth amd the intervening spaces are of exactly equal breadth. By means of connected gear-work a ‘high velocity of rotation may be given to the wheel, while the number of turns per second admits of being ascertained. The velocity may also be retarded by a brake. When the wheel turns slowly the light is intermittent, and the passage of the teeth is perceptible, But when as many as ten tecth pass per second, the light is constant, owing to the dura- tion of the successive impressions upon the eye. By accelerating the movement the brightness of the image may presently be made to fade, in consequence of the interference of the successive teeth with the rays returning from the distant station, after having passed through the last preceding interval between the teeth. As the velocity increases this fading will become an absolute extinction, each tooth in its progress cutting off all the light which passed through the in- terval before it. When this state of things is reached, it is evident that the time occupied in the passage of light to the distant station and back—that is to say, 102 miles—is equal to the time which it takes for a tooth to advance a dis- tance equal to its own breadth. If there are five hundred teeth and five hun- dred intervening spaces, this time will be one one-thousandth part of that of a revolution; and if there are eighteen revolutions in a second, the absolute time will be one eighteen-thousandth of a second. By still further accelerating the velocity of rotation, the light may presently be made to reappear; the rays which pass through one opening to the distant station, returning through the next following opening to the eye. When the full brightness is thus restored, the velocity will be found to have been doubled. By carrying the acceleration still further, the light may be a second time eclipsed and a second time restored; and, in like manner, alternately extinguished and revived, as long as the driving power will allow: the velocities at which the several successive extinctions and revivals occur, constituting a regularly increas- ing arithmetical series. We thus are enabled to measure the small fraction of a second required for light to pass over twice the distance between the two stations; and dividing this double distance by this fraction we obtain the velocity of light per second. The result at first obtained by Mr. Fizeau, by means of this apparatus, was about 196,000 miles, being in excess of the results by the astronomical methods by one-sixtieth part nearly. It is manifest that « any mode by which very minute intervals of time can be accurately measured, is capable of being employed as a means of dete rmining the velocity of light. Mr. Wihtentapene. i in his researches upon the velocity of electricity, employed for this purpose a revolving mirror; and in 1839, Mr. LOA VELOCITY OF LIGHT. Arago made an effort, by the use of a similar mirror, to institute a comparison between the velocities of light in passing through water and through air. This was suggested by him as an experimentum crucis between the opposing theo- ries current in regard to the nature of light; in one of which light was sup- posed to consist of material particles actually thrown off by luminous bodies, while in the other it was assumed to be an effect of undulations propagated through an exceedingly subtle elastic medium pervading all space. If the first were ahie true theory, the velocity of light in a more powerfully refracting medium should be greater than in a less; and the reverse, if the second were true. Mr. Arago ava not carry out his design to its completion, but it has since been successfully executed by both Mr. Fizeau, whose original method has just been given, and by Mr. Foucault, well known for his pendulum demonstration of the earth’s rotation. The experiment served at once to compare the veloci- ties of light in air and water, and to determine the absolute velocity. The an- nexed figure may render the method intelligible. Suppose a small beam of Fig. 12. parallel rays to be admitted into a room otherwise dark, through an aperture R, and to fall wpon an achromatic lens, fixed at C, in the direction of its axis. Let CD be the focal distance of this lens; and at M let the beam be intercepted by a mirror capable of turning around a vertical axis coincident with its plane. At a distance, ME==MD, in any convenient position not very remote from R, let there be placed aspherical mirror having its centre of curvature in the axis of M. Let there be, further, across the aperture R a fine wire exactly vertical ; and in front of the aperture R a transparent plane mirror AB, inclined to the beam at an angle of 45°. The mirror M may obviously be turned on its pivot, so that the ray RCM falling upon it may be refle cted to E. If it remain stationary in this position, the light incident on E will be returned to M, and so again to the aperture R. But a portion of this returning light, being reflected by “AB towards O, will enable an observer at that point to see the im- age of the vertical wire. To assist the eye, a magnifying eye-piece may be em- ploy ed, and this may be provided with a spider-line micrometer at its focus. If the mirror be new put very slowly into revolution, the image of the wire will be seen intermittently and momentarily, once in every revolution. ‘The spider-line of the eye-picce is now to be brought to exact coincidence with this image. Accelerating the revolution, when the number of turns per second becomes as great as ten, the image will be permanent. If, now, a very high velocity be given to the mirror, the image seen by the observer at O will no longer coincide with the spider-line of the micrometer, but will be seen at a sensible distance from it in the direction of rotation. Thus, if the arrow represent the direction of rotation, the returning ray which originally met the mirror A B at 7, will meet it at 7’ or 7’, and the image which originally appeared at S will be seen at S’ or 8S”. This is evidently owing to the change in the position of the mirror M, while VELOCITY OF LIGHT IN WATER AND AIR. 125 the light is moving from it to the spherical mirror E and back again; and the angular displacement of the returning ray around the centre M will, ‘according to the well-known law of reflection, ie double the angular change of position oF the mirror. If the mirror makes 2 turns in a second, the time of one turn will be the zth part of a second, and the time of making the change of position of which the observation gives us the evidence, will be the same fraction of the nth part of a second that Hi alf the angle subtended by RR‘ or RR", as the case may be, at the centre M, is of 360°; or as 4RR’ is of a whole circumference. This distance RR’ or RR", being equal to ‘SSI or SS”, is directly measured by the micrometer. Let it be put — —0. The circumference of the circle whose radius is RM, (which put —~7,) is 2zxr. Put the space ME=s, or 2ME= 2s, and the time of passng 2ME=¢. Also let v represent the velocity of light. 'Then— O 2s 8zxrns 1 9 ; ana v—— — a ; t 6 her i This expression is, however, true only on the assumption that the returning ray suffers no deviation in passing the lens ©. But since, if its original path was, as we have assumed, the axis of the lens, it cannot, if sensibly deviated, return through the axis, it will be bent at C, and the displacement RM’ will be less than we have assumed it to be. If D be the actually observed eee and if RO be represented by 7’ and MC by s’, then the value of our assumed displacement in the above formula will become, as may easily be shown— Dr(s +s’) sr! — Substituting this value, we shall have for the velocity of light— Sxnr's? ~~ D(s+s/) With a distance s = 4 metres, and 800 turns of the mirror per second, Mr. Foucault found a value of D— 6”, whence the value of v is found to be, in English miles, 192,950.* By placing a second fixed mirror, I’, in any other convenient position, and interposing a tube, as GH, filled with water or any other transparent medium, the ends of the tube being closed with plate glass having parallel surfaces, the velocities of light in air and such a medium may be compared, The mirrors E and F will both give images of the wire at R; and if the value of v is the same for both, the two images will be coincident, and appear as one; but if v have dif- ferent values for the different media, one of the images will be more displaced than the other. Mr. Foucault performed this experiment; and, in order to identify the images, and to distinguish one from the other, he placed before the mirror E a sereen having a rectangular opening, such that one-third part of the image from that mirror should be cut off from the top, and another third from the bottom, the central third only being left unobstructed. In the image of the aperture at R, as seen at O, the middle third had, very sensibly, greater bright- ness than the top or the bottom, and the wire, as reflected from E, was appar- ently but one-third as long as it appeared reflected from F. The image from F was sensibly the most displaced, indicating lower velocity in water than in air; the displacement, D, in the formula above, being a factor of the denominator. The next discovery of importance in the progress of optical science was made near the close of the last century, by Dr. Wollaston, in his observations upon the prismatic spectrum. He discovered that, by employing a pencil of light * By Mr. Foucault's more recent experiments with this method, the velocity of light is reduced to 190,249.16 miles. 126 LINES IN THE SPECTRUM. very narrow in the direction of the plane of refraction, but broad parallel to the axis of the prism, five well-defined dark straight lines could be distinguished crossing the spectrum at right angles, and maintaining invariably the same posi- tions relatively to the colors. This number he afterwards increased to seven. These lines may very easily be distinguished by holding a prism near the eye, parallel to any small fissure through which light makes its way into a dark room. ‘The reason they escaped the notice of Newton and other earlier ob- servers is to be found in the fact that those observers employed a pencil so broad in the direction of refraction as to make the actually observed spectrum a compound of many superposed and unconformable spectra, thereby obliterating these very narrow markings. In fact, every point in an aperture of sensible magnitude, through which the light experimented on is introduced into the dark room, produces a spectrum of its own. Moreover, supposing that it is the sun- light which is introduced through the aperture; it may be said that every point of the aperture produces not only one spectrum, but as many spectra as there are points in the sun’s disk from which lines may be drawn to the assumed point in the aperture. As all these lines, so drawn, would, in the absence of the prism, produce a white circular image of the sun upon the screen in the dark room, having a diameter increasing with the distance of the sereen from the aperture, it follows that, when the prism is introduced, the spectrum produced by each point of the aperture will have a breadth equal to the diameter of this white image of the sun, and that its elongated form is due to the lateral unequal displacement of an indefinite number of circles, produced by the several elemen- tary rays of which white light is made up. ‘The interposition of a convex lens between the prism and the aperture may serve to reduce the breadth and sharpen the boundary of the image; but still it is manifest that with a circular aperture, there must, unless the diameter is made too small for convenient observation, be a considerable mixture of rays of different refrangibility in every part of the. length. It is therefore best, for the purpose of obtaining a spectrum at once broad and pure, to employ an aperture very narrow in the plane of rebraction, and broad in the direction of the axis of the prism. ‘This may be still further improved by the use of a convex lens of long focus, as above described ; or bet- ter, by the use of a cylindrical lens, with its cylindrical axis parallel to the length of the aperture. With an arrangement like this, the lines of Dr. Wollaston may be easily exhibited, and many more. By aiding the eye with a telescope, the number discovered becomes surprisingly great. Mr. Fraunhofer, of Munich, enumerated five hundred and ninety, and Sir David Brewster afterward in- creased this number to two thousand. Their general appearance under the tele- scope is shown in the figure annexed. Hie Tui — RANGE YELLOW RE! Hips, PS: The eight principal lines are distinguished by the letters A to H, of which the line A is at the beginning of the red, and the line H about the middle of the violet. ‘The line A does not appear in the figure. The positions of these lines being definitely fixed among the colors of the spectrum, they furnish valuable aid in comparing the refracting powers of different bodies, and have served to reveal the fact that bodies whose mean refractive powers are equal, do not always equally refract the several elementary rays. The line A is not among the most easily discernible, but Sir David Brewster has discovered others in the almost imperceptible light below A; and Sir John Herschel, and especially Professor POLARIZATION OF LIGHT. TAT Stokes, have discovered many others still beyond the violet. By his curious discovery of fluorescence, or the property possessed by some substances of ren- dering serisible to vision rays beyond the limit of the ordinary spectrum, Pro- fessor Stokes has in fact quadrupled its length.* In observing the spectra formed by light from other sources than the sun, as from the fixed stars, from incandescent solids, flames, &c., great differences are found to exist in regard to the lines observed. In the spectra of the fixed stars, dark lines are seen, which, like those of the solar spectrum, are unchangeable in position, but which do not occupy the same positions. In the spectra of flames, lines are observed which are not dark, but bright. Different salts added to the wick of an alcohol lamp produce different systems of lines, always bright. So, likewise, metals burned under the compound blow-pipe. The spectrum of the electrie spark exhibits bright lines also, the positions and numbers of which depend on the substances of which the electrodes are formed. A platinum wire made incandescent by an electric current, gives no lines at all; and none are seen in the spectrum formed from the light of the solid carbon electrodes which produce the galvanic arch. Experiments made by Sir David Brewster, by pass- ing solar or artificial light through different colored gases, led him to the con- clusion that the dark lines are caused by absorption—an absorption which he supposed to take place in the earth’s atmosphere.} In the year 1808 the French Academy of Sciences proposed the problem of the double refraction,of light as the subject of a prize to be awarded two years thereafter. The successful competitor for this prize was Malus. To him is due the discovery of the polarization of light by reflection. He was led to this re- markable discovery by an accident. In observing through a prism of Iceland spar the light reflected to his windows from those of the palace of the Luxem- bourg, he was surprised to see that, as he turned the prism around the ray, one of the two images vanished at every quarter revolution. By following up the indication thus given, he arrived at the important law that, when light is re- flected from glass at an angle of 54° 35’, or from water at an angle of 52° 45/, it possesses all the properties which belong to the pencils into which a ray of ordinary light is divided by a doubly refracting crystal. Accordingly, if such a crystal be placed in the path of such a reflected ray, with the principal plane of the crystal, or a conjugate plane, in the plane of reflection, the ray will not be doubly refracted. But if the crystal be turned in azimuth, two rays will make their appearance, unequal at first in intensity, but becoming equal at the azimuth of 45°. Beyond this azimuth the ray which was previously most in- tense fades gradually away, while the other gains in strength, until, at 90°, the former disappears entirely, and the latter remains alone. ‘Chese phenomenaare repeated in every quadrant. . If the ray which has been reflected as above described be incident upon a second surface of glass, at the same angle, (54° 39’,) as at firsi, the plane of second reflection corresponding with that of the first, it is in part reflected and in part transmitted, as is the case with common light; but if the second plane of reflection be at an azimuth of 90° with that of the first, no reflection at all will oceur, but the whole ray will be transmitted. A ray of light therefore, which has undergone the modification which is pro- duced by transmission through a doubly refracting crystal, or by reflection at an incidence of 54° 35! from glass, or at that of 52° 45’ from water, seems to pos- sess dissimilar physical properties on the sides which are at right angles to each other, and similar ones on the sides which are diametrically opposed. This “ The important researches of Kirchhoff and Bunsen on the chemical relations of the fixec lines of the spectrum have been published since the preparation of these lectures. 7 Karchhoff and Bunsen have demonstrated that this absorption takes place (at least in case ef many of the lines) in the atmosphere of the sun. 128 POLARIZATION OF LIGHT. circumstance, from a sort of fanciful analogy which it presents with the relations of the poles of the magnet, has suggested the name polarization, to distinguish this condition of light. An interesting experiment of Malus, illustrating the identity of the phenomena of polarization by reflection, and polarization by double refraction, is the follow- ing: Let a ray of light pass, at a perpendic ‘ular incidence, through a crystal of Iceland spar, undergoing division into two rays; and afterwards “let these rays fall at an incidence of 52° 45’ on water, or of 54° 35! on glass. Let then the crystal be turned in azimuth until the principal section coincides with the plane of reflection. The extraordinary ray will cease to be reflected altogether, though the ordinary ray undergoes reflection as usual. Turning the crys stal once more in azimuth, until the principal section is 90° from the plane of reflection, the ordinary ray will, in its turn, wholly cease to be reflected, and the extraordinary ray will revive. Another interesting and very curious exper iment by Brewster, analogous to the foregoing, may be performed thus: Let the light of a candle or other luminous object be polarized by reflection, and afterward received, at the polarizing angle. upon a plate of plane glass, which has its plane of reflection in azimuth 90° from the plane of polarization. It will, as we have just seen, be wholly trans- mitted, so that, to an eye placed anywhere in the direction in which reflection would ordinarily occur, the radiant will be invisible. The. eye remaining in thi- position, let now another person breathe upon the glass plate, and instantly the luminous object will appear, and will continue to be seen until the film cf moisture left by the breath has evaporated. This is because the polarizing ang! for water is not the same as that for glass. The ee may be varied and made still more striking by placing a second plate by the side of the first, and adjusting this one to Y the polarizing angl« for water. ‘The radiant wil) then be visible in the second plate, but not in the first. In this state of things, if both plates be breathed on simulta- neously, the light in the second plate will be extinguished and that in the first revived by the same breath It is only at che angles which have been mentioned that polarization by re- flection is complete. But partial polarization takes place in reflection at any angl-«; being zero at the incidences 0° and 90°, and. increasing from those inci- dences up to the polarizing angle. Light is polarized by reflection from all polished surfaces; but it is onl the case of bodies whose indexes of refraction are in the neighborhood of 1.4 that the modification which it undergoes has the simplicity which belongs to the examples we are considering. sue index of water is 1.336, and that of crown glass 1.48 to 1.53. It was the conclusion of Mules that the angle of polarization of a given body is independent both of its refractive and of its dispersive power. Dr. Brewster. however, demonstrated that this angle depends on the refractive power; and is connected with it by the law that ‘the index of refraction of any body is the tangent of the angle of polarization.” Irom this law we derive one or two interesting consequences; first, at the angle of polarization the reflected ray is perpendicular to the refracted ray, for, putting « for the angle of incidence, p for the angle of refraction, and » for the index, the law of Snellius gives us zsing—sin:; and the law of Brewster, just mentioned, gives n—tant. Hence— sine tan: sino = sinp—sint; or, sine—cos:, and ¢-+p==90°. cose Secondly, when light falls upon a transparent plate having parallel surfaces, if the angle of incidence at the first surface is the polarizing angle, the angle of incidence at the second surface will also be the polarizing angle for that surface LAW OF MALUS. 129 In this case p is the angle of incidence and: the angle of refraction for the : ; Shel second surface, the index of refraction being : And we have— BUN Ec lea Or ae uM ote d a Sint—=sinp ; or, Sint——cosp, and ¢-+p==90 tanp sine == cosp 4 We have seen that when the two polarized rays into which a single ray of common light is divided by double refraction in passing through a rhomb of Iceland spar fall upon a second similar rhomb, they are both of them subdi- vided in most of the positions of the second rhomb; but that the intensities of the rays of each pair are unequal, except when the principal planes of the rhombs differ in azimuth 45°, and that one member of each pair disappears en- tirely when the principal planes are coincident or normal to each other. The inequality of intensity is variable, and is dependent on the angle between the principal planes. If one ray of either pair be observed through all its varia- . tions, it will be found to begin from zero of intensity, to increase regularly in brightness for 90°, and then to diminish through the second 90°, to zero again. The other member of the same pair passes through a similar series of changes, but its maxima correspond in azimuth to the minima of the first, and its minima to the maxima of the first. A ray which has been polarized by reflection possesses the same character as those which have been produced by double refraction in Iceland spar; and accordingly, if such a ray be transmitted through a doubly refracting rhomb which is turned in azimuth in the manner just described, it will be divided into ‘two rays which will alternately increase and diminish in intensity; and of which one will become zero in the azimuth 0° or 90° between its plane of polarization and the principal section of the rhomb. Assuming the united intensities of the two rays into which a single one is thus divided by double retraction to be equal to the total intensity of the original ray, Malus inferred that their several inten~ sities should vary as the squares of the sines and the cosines of the azimuth. Thus, if J be put for the total original intensity and a for the azimuth, reckoned from the position of coincidence of the plane of polarization with the principal section of the rhomb, then the ordinary ray would have the intensity J cos’a; and the extraordinary, I'sin’a. These values fulfil the condition of constancy of sum; since— Icos’a + Isin?a = I. If a ray which has been polarized by reflection fall, at the polarizing angle, upon a second mirror of transparent glass with parallel faces, it will be divided into two rays; one of which will be reflected and the other transmitted. When the second mirror is turned in azimuth around the incident ray, these two de- rivative rays will undergo changes of intensity somewhat resembling those which have just been described as produced by double refraction. When the two planes of reflection are coincident, the intensity of the reflected ray will be maximum, and that of the transmitted ray, minimum. This minimum will not, however, be zero. When the two planes differ in azimuth 90°, the intensity of the transmitted ray will be maximum, and that of the reflected ray, minimum. This minimum wll be zero; and the simultaneous maximum of the transmitted ray will be equal to the total intensity of the incident light. The alternations in this case resemble, therefore, to a certain extent, those previously described as produced by double refraction; but they are not represented by the law of Malus. The plane of polarization—an expression which we have just used without defining it—is the plane in which a polarized ray is capable of being reflected at the polarizing angle.. Accordingly, when a ray of common light is polarized by reflection, the plane of incidence and reflection is itself the plane of polariza- tion. In the arrangement of two mirrors, as above described, when the second s ¥ 13¢ POLARIZATION BY REFRACTION. mirror is rotated in azimuth, its plane of incidence and reflection is constantly changing its inclination to the plane of polarization of the ray incident upon it. Suppose the incidence upon the second mirror zot to be at the polarizing angle. It is found that after reflection in an oblique azimuth, the plane of polarization is nearer to the plane of reflection than it was at incidence. If the azimuth at incidence be represented by a, and that after reflection by a’, there will be found to be a constant ratio between tana and tana’; tana’ being always less than tanz. By many reflections, with the same azimuth between the mirrors, the plane of polarization may be brought indefinitely near to the plane of re- flection; but it can never be made, in this way, absolutely coincident with it. When common light is reflected from any surface at an angle greater or less * . . * ° . . ° . . than the polarizing angle it is found to be partially polarized: that is to say, it is made up of a mixture of polarized light with common light. By repeated reflections at the same incidence the polarization may be made sensibly com- plete.- The number of reflections necessary for this purpose will be greater as the angle of incidence is further from the polarizing angle. Tt must not be overlooked that, though at the angle which we have called the polarizing angle, all the light that is reflected is polarized, yet that this is after all but a small portion of the incident light. From a single surface of glass it amounts to less than eight per cent. The manner of determining this ratio will be seen hereafter. When, for purposes of experiment, it is desired to obtain a large and intense beam of polarized light, it has accordingly been found useful to employ many reflecting plates placed one upon another, forming a bundle or pile. It is obvious that the thinner these plates are made, (so that they are not so thin as to produce color,) the more convenient they will be in use, and, from the diminution of absorption, the more economical of light. Not fewer than sixteen are usually employed. The amount of light reflected at different angles of incidence goes on increas- ing from 0° to 90°. The amount which is polar zed in the reflected beam also goes on increasing, but not throughout the quadrant. For glass having the index 1.5, the incidence of maximum polarization is 79°. At this incidence the total intensity of the reflected light is expressed by the decimal 0.355, the intensity of the incident light being 1. The amount which is polarized in the reflected beam is, however, only 0.1518, which is still about double of that which is reflected at the polarizing angle. But, comparing this value with the fore- going 0.355, we shall see that it is less*than half the total light reflected, (forty- four per cent.,) and accordingly it is not suited to exact experiments in polariza- tion. When a transparent reflector is employed as a polarizer the transmitted beam will be found to contain light which is polarized in a plane perpendicular to the plane of refraction. ‘The amount of light so polarized is exactly equal to the amount polarized at the same time by reflection, and in the plane of reflection. And as the maximum amount polarized by reflection from one surface of glass having the index 1.5, is 0.1518, this also is the maximum amount which can be polarized at one surface by refraction. But since, at this angle of maximum polarization, the total reflection is only 0.355, the total transmission will be 0.645, and of this amount the polarized portion will be but twenty-three and a half per cent. But if this light, already partially polarized, be transmitted through other refracting surfaces, though it will continually lose in total intensity by reflection, it will gain in the proportion of the polarized light which it contains ; and if the incidence is that of the polarizing angle for reflected light, the quan- tity transmitted which is polarized, will continue to increase im absolute amount, notwithstanding the decrease of total intensity, until polarized light only is trans- mitted. Moreover, if the number of refracting plates employed should happen to be greater than is necessary to produce complete polarization, the supernu- merary plates will not reduce the amount of polarized light transmitted ; since, at the incidence supposed, they are incapable of reflecting light polarized trans- versely to the plane of reflection. This statement presumes, of course, that NICOL’S PRISM. 1 = the refracting surfaces are perfect, and that no light is lost by absorption in the media. Tt isa curious fact, resulting from the polarizing power of a pile of glass plates, that the pile is more transparent when held at an obliquity greater than the angle of polarization than it is at that angle; and that the transparency in- creases with the obliquity. This is owing to the fact that the light which has been polarized by the first few laminze undergoes very little loss by reflection on increasing the obliquity; but the amount polarized in those first refractions increases as the obliquity increases, more rapidly than the loss by reflection of the natural light falling on the same surfaces is increased. The intensity of the transmitted beam, therefore, becomes actually greater as the obliquity is greater: a fact which is the reverse of what happens with a single plate. A remarkable fact in regard to the condition of light emitted at great obli- quities from luminous solids or liquids, was discovered by Mr. Arago. When- ever the light of an incandescent body of either of these classes is examined as it proceeds directly from the body and with no great inclination to the luminous surface, it is found to be unpolarized. But when the rays whose obliquity to the surface is very considerable are the subject of examination, they are found to be partially polarized. The inference is, that these rays have been polarized by refraction; and hence that they must have originated beneath the surface of the luminous body. From the law of equality between the quantities of light simultaneously polarized by refraction and by reflection, it follows that there is areflection toward the interior of such bodies, of some of the light which they generate. The light of flamés and incandescent gases exhibits no such polarization. The light of the sun is always unpolarized, whether it be examined at the limb or at the centre of the disk. From tls observation, Arago was led to consider the luminous envelope of the sun to be gaseous, and not liquid or solid. An incidental corroboration of the ingenious suggestion of the elder Herschel in regard to the constitution of the solar photosphere, is thus derived from opties; and although that hypothesis is by no means universally received, and though there seems recently to have been manifested an increasing disposition among men of science to call it into question, it will be found difficult to recon- cile the optical properties of the solar light with any supposition which implies that the luminous-surface which we see is either liquid or solid. In observations upon polarized light, there are some inconveniences attending the use of a mirror, which, when turned in azimuth, obliges the observer to - change his own position; or of a doubly refracting prism or erystal, which pre- sents two images often not sufliciently separated. Both these disadvantages are obviated by means of a prism invented by Mr. Nicol, which is now in almost universal use. This contrivance is represented in A _ FP the figure. It is an elongated rhomb, formed of Iceland i __ # spar, its length being about three times its breadth. d a Having been brought into this shape from the natural Fig. 14. crystal, it is carefully sawed asunder in the plane which divides it symmetrically through its shortest diagonal, AD, and then reunited by means of Canada balsam. This substance is per- fectly transparent, and has a refracting power whose index is 1.532, interme- diate between those of the ordinary and extraordinary rays, viz., 1.654 and 1.488. The relative index between the crystal and the balsam for the ordinary ray is 1.0796, and the limiting angle of emergence from the former to the latter is 68°. The ordinary ray from R meets the surface, AD, at a greater angle than this, and is totally reflected at O. The extraordinary ray passes through. The sides of the prism are blackened to prevent a second reflection. This ingenious contrivance is invaluable to the observer in this interesting branch of optical investigation. Its advantages are, however, in some respects limited. The necessary length of the prism, as compared with its lateral di- 132 POLARISCOPES. mensions, renders it difficult to employ light of any considerable convergency or divergency. The cost of the construction of such prisms increases also very rapidly with their magnitude; and few have been made at all which mea- sured more than an inch on the side. Those commonly found with opticians are much smaller than -this. The eye-piece of Mr. Delezenne is a very good substitute for Nicol’s prism; although it affords a less intensity of light. In this, the surface CD is a pol- ished mirror of black glass; ABD is a prism of trans- parent glass. Rv, Rr, rays of light falling at the pola- rizing incidence upon CD, are reflected at a perpen- dicular incidence upon the first surface of the glass prism; and after being totally reflected on AB, emerge at right angles to the surface AD, meeting the eye of the observer at O. Another convenient eye-piece, which may also serve, like Nicol’s prism, as a polarizer for small beams, is formed of a lamina of tourmaline cut parallel to the axis. This mineral possesses the very remarkable property, when not in exceedingly thin lamine, of suppressing one of the rays into which incident common light is divided by it, and transmitting the other. The ray transmitted, as in Nicol’s prison, is the extraordinary ray. Cut perpendicularly to the axis a plate of tourmaline is opaque. Two equal plates, cut parallel to the axis, are opaque when crossed upon each other. The disadvantages of the tourmaline eye-piece are, first, the color of the erystal, which mars the beauty of the tints exhibited by polarized light, and to some extent neutralizes them. It is rather unfortunate that the crystals which are least colored are usually bad polarizers. In this respect different crystals very much differ. Some, which are light green, transmit a notable amount of the ordinary ray even when quite thick. Those which polarize best are usually brown or yellowish brown. Occasionally one of this kind will be found which polarizes well without being very disagreeably dark. But an equal if not greater disadvantage of the tourmaline is the great brittleness of the crystal and the rarity of specimens in which fissures do not naturally exist. It is difficult, therefore, to obtain clear plates of any considerable size. Finally, the supply seems, of late years, not to have kept pace with the demand; and op- ticlans intimate that it is almost impossible to obtain specimens fit for optical purposes at all. A few years since Dr. Herapath, of London, announced the discovery of a property like that of the tourmaline, in artificially prepared crystals of the iodo- disulphate of quinine. These crystals are but slightly colored; and could they easily be prepared and made permanent would probably come into general use. Dr. Herapath succeeded in obtaining specimens half an inch across. The peculiar property of the tourmaline was also early observed by Sir David Brewster, in agate; but that substance is not sufficiently transparent for the purposes of optical experiment. When large polarizers are needed, resort must be had to reflection from mir- rors made of black glass, which reflect only from the first surface, or of trans- parent glass whose surfaces are truly parallel. If great purity in the polarized beam is not an object of importance, bundles of thin plates may be employed as heretofore described, to polarize either by reflection or by refraction. In the year 1811 Mr. Arago communicated to the Academy of Sciences of Paris, one of the most remarkable and beautiful discoveries which has ever been made in the history of optics. Upon examining thin plates of certain transparent crystals, such as mica, selenite, or quartz, by means of transmitted polarized light, he found that when the light was received upon the eye through a prism formed of Iceland spar, the richest, conceivable colors made their ap- pearance, which were complemertary to each other in the two images, and which varied in intensity with the azimuth of the lamin or of the prism. COLORS IN CRYSTALLINE PLATES. 133 When the principal plane of the prism coincides with the plane of polarization of the light, and the azimuth of the lamina is varied, the maximum brillianey of coloring is found in the azimuth of 45° between the principal section of the lamina and the plane of polarization. When the azimuth is 0° or 90°, the color entirely vanishes, and the light appears entirely unchanged. At inter- mediate azimuths the color has an intermediate intensity, regularly increasing and diminishing between the positions of minimum 2 ea maximum. ‘These variations, as well as the thickness of the lamine themselves in which the phe- nomena appeared, satisfied Mr. Arago that the colors could not be owing to the same causes which produce the colors of Newton’s rings. Still they had evi- dently some relation to the thickness; for it was not difficult to remove them entirely, either by considerably increasing the thickness or by excessively diminishing it. In the rotation of the lamina as just described, the colors which appeared between the successive positions of minimum were always the same in the same image. But when the lamina itself remained fixed, while the prism at the eye was rotated in azimuth, the two images interchanged their colors in passing each successive position of minimum. If, instead of a doubly refracting prism as an eye-picce, a mirror, presented to the ray at the polarizing angle, be employed, only one of the images is re- flected; but the other, if the mirror be transparent, will be seen in the light transmitted. In consequence of this separation of effects, Mr. ae was led to distinguish the mirror when used in this way as the analyzer. In observa- tions with the analyzer, then, it appears that when the lamina is snguatel in azi- muth, the same colors come and go in the successive quadrants; but when the analyzer itself is rotated, the colors in the alternate quadrants are comple- mentary to each other. The colors thus seen in crystalline laminz recur in several successive series, as the thickness of the laminz is increased. Accordingly, if in a plate of selo- nite we hollow out a spherical cavity of very large radius, we shall find it to exhibit several orders of rings resembling those of Newton, and following the same laws; though the thicknesses at which the colors of the same order oceur are very much ereater. According to the determinations of Biot, the compara- tive thicknesses at which the same colors app w in air, in Iceland spar, in quartz, in selenite, and in Siberian mica, are as the numbers 1, 13, 230, 230, and 440; the thickness for selenite and quartz being sensibly the same. The limits of absolute thickness below which pp ilas plates fail to give colors in polarized light, are, for selenite, 0.017 in.; for mica, 0.0323 in.; and for Iceland spar, 0.001 in. The maximum thickness for this last erystal is but six or seven one-thousandths of an inch. Mica and selenite are therefore prepared with facility for this class of chromatic experiments; but this is not equally true of Iceland spar. If a lamina of selenite—a mineral which is very easily wrought—be secured by transparent cement of any kind to a plate of glass, very fanciful effects may be produced by grinding it away unequally in different parts according to any definite pattern. Figures of various kinds, images of insects, flowers, gothic windows, &c., &c., may thus be prepared, which will come out in polarized light in very brilliant colors. When laminz are presented obliquely to the polarized ray and the inclina- tion varied, the colors change with the obliquity; sometimes ascending in order with an increase and sometimes with a decrease of obliquity, according to the character of the crystal and the direction in which the lamina has been taken from it. For these experiments it is best to cut the laminze parallel to the optic axes of the crystals. If two lamine, either or both of which execed the limits at which colors are seen, but whose d7fference of thickness is within those limits, be placed one upon the other with their principal sections crossed—that is to say, placed at right angles to each other—colors will be seen corresponding to those of single 134 CRYSTALS CUT ACROSS THE AXIS lamince whose thicknesses are the differences of those employed in the experi- ment. ‘This supposes that the lamine are of the same kind. If they are not, the actual thicknesses are not to be employed in the calculations, but what may be called the b:-refringent equivalents of thickness—that is to say, their measured thicknesses divided by the numbers expressing their chromatic relation to th plates of air which give Newton’s rings—which latter numbers may be called their chromatic equivalents. If, then, the difference of these quotients, multi- plied by the chromatic equivalent corresponding to the greater quotient, is within the limits at which the crystal to which the greater quotient belongs gives colors, the combination will give the color belonging to the value of that product. If the laminze belong to erystals of which one is positive and the other negative, they are not to be crossed in this experiment, but their principal see- tions must be parallel. This furnishes an easy test for determining whether a given crystal/is positive or negative. Having prepared a lamina of the crystal to be examined, (which may be of any convenient thickness,) apply it upon laminz of Tecland spar of different thicknesses, with the principal sections sue- cessively parallel and crossed. If the colors appear when the planes are parallel, the signs are opposite, since, either plate being too thick to produce color alone, the sum of their effects cannot, of course, do so. If the erystals are of similar sign, the colors will appear when the planes are crossed. Another class of chromatic effects produced by crystalline plates viewed in polarized light was first observed by Dr. Wollaston in Iceland spar, in which the display is, perhaps, the most brilliant. In these cases, the crystal is cut perpendicularly across the axis. The arrangements for observation are the same as in the experiments already described. If a mirror be employed as an analyzer, and be turned to azimuth 90° before the introduction of the erystalline plate, no light will, of course, be reflected to the eye. But the moment the crystal is introduced a system of concentric rings will make its appearance, colored with the richest conceivable tints, and marked by a black cross, whose arms are in the plane of reflection, and at right angles to it, passing through the centre. Fig. 16. HigselT: The ends of these arms are enlarged, and have the appearance of brushes. If the analyzer is transparent, another set of rings may be seen by the trans- mitted light, in which the colors will be complementary to the former, and the cross will be white. As the analyzing mirror is revolved in azimuth, the colors fade and a new set of rings gradually appears with colors complementary to the first, and distinguished by a white cross. In short, in this case, the colors before transmitted are reflected, and those before reflected are transmitted. ‘The annexed figures exhibit the two aspects of the rings which have been just described. CRYSTALS OF QUARTZ ACROSS THE AXIS. 135 These rings make their appearance at thicknesses much greater than those which produce color in laminz parallel to the axis. In examining plates of quartz cut across the axis as above described, Mr. Arago observed a peculiarity of a remarkable kind, which is seareely found in any other natural crystal. The centre of the field was not dark in any position of the analyzer, but was deeply and uniformly colored with a tint which varied as the analyzer was turned. When a bi-refringent prism was employed as an analyzer, the two images seen were constantly complementary in color, and as the analyzer was turned they ascended in tint, in the order of Newton’s seale, from red to violet. Mr. Biot, in subsequent experiments, discovered that in some crystals the ascent of the tints in the scale is produced by a right-hand rotation, (the ordinary direction of a screw,) and in others, by a left-hand rota- tion. These classes of crystals have been distinguished by the names right- handed and left-handed crystals, or dextrogyre and levogyre. Sir John Her- schel, at a later period, made the remarkable observation that these optical peculiarities of the crystals are associated with a geometrical or crystallographic peculiarity. The tetrahedral angles where the prism and terminal pyramid of the crystal meet, are sometimes replaced by planes which encroach more on the neighboring planes of one side than on those of the other. The same occasionally happens with the lateral edges of the crystal. These faces are called plagihedral. If, as the crystal is held in the hand horizontally, with the pyramidal vertex toward the observer, the plagihedral faces lean to the right— that is, if they encroach most upon the faces to the right of them—the crystal will be found to be optically dextrogyre, and the analyzer will have to be turned in the direction of the movements of the hands of a watch, in order that the tints may ascend. Sir David Brewster’s observations on these erystals led to the discovery that, when the crystal is not very thick the uniformly tinted field is confined to the centre, and is surrounded by a system of rings resembling those seen in Ice- land spar, but in which the cross is imperfect. The figure exhibits the appearance. He also found in that remarkable spccies of coloxcd quartz called amethyst, veins of right-handed and left-handed erystallization alternating with each other in many parallel layers, ana producing at their surfaces of contact lines of neutral character. In some specimens the layers were found to be Fig. 18. so extremely thin as to neutralize the rotatory power of the whole erystal, and in these instances the ordinary system of rings with a perfect cross makes its appearance. Tn all these observations upon crystals in the direction of their optic axes the number of rings is greatly increased by the use of monochromatic light. The intervals between the rings are also, in such light, intensely dark. In the case of quartz crystals, monochromatic light presents appearances in the centre very little different from those seen when the crystal is not present—that is to say, it exhibits, as the analyzer is turned, a succession of maxima and minima, separated from each other in azimuth 90°. But the absolute azimuths of these maxima and minima are no longer what they were before the introduction of the crystal: in other words, the plane of polarization has been turned to the right or to the left, according to the nature of the crystal, through an angular distance proportioned to the thickness of the crystal. The peculiar kind of polarization produced by quartz has, on this account, been called rotatory polarization. aS Kun F x 2 ; Sen 136 AIRYS SPIRALS—FRESNEL’S PRISM. It will be easily conceived that a right handed and a left-handed crystal of equal thickness, superposed upon each other, will produce a resultant rotation equal to zero. But two such plates so super- posed, examined in polarized light, ex- hibit a remarkable spiral cross, such as is seen in the figure annexed. ‘These spi- rals were first observed by Mr. Airy, and are commonly known as Airy’s spirals. Two contrary plates of wnequal thick- ness, superposed as above, produce an amount of rotation proportional to their difference of thickness. The power of rotation of the same Fig 19 crystal is different for the different colors, being, on the undulatory theory of light, an inverse function of the length of the undulations. By employi ing the successive colors of the spectrum | sepa- rately, Mr. Biot determined the absolute rotatory power of a crystalline plate of quartz one twenty-fifth of an inch in thickness, for each, as follows : Oo Oo extreme medina: Stow. ao 17.4964 Limit, green and blue ...... 30.0460 Limit, red and orange. ....-.-- 20.4798 Limit, blue and indigo .....- 34.5717 Limit, orange and yellow....22.3138 Limit, indigo and violet.-.... 37.6829 Limit, yellow and green... ..- 25.6752, Extreme violet 242425 .--ee 44.0827 This property of rotatory polarization does not exist in plates of quartz cut parallel to the axis. In such plates ordinary double refraction exists ; but it is the extraordinary instead of the ordinary ray whose velocity is least, or the crystal is a positive one. The physical cause of rotatory polarization is unknown. Mr. Biot supposed it to belong to the ultimate molecules of the substance; but this hypothesis Sir David Brewster believed to be disproved by the fact ‘that the property ceases to appear in quartz whose crystalline structure has been destroyed by fusion. This argument seems, nevertheless, not to be conclusive. If the BIOBCry. be- longs to the ultimate molecules, the fact that it does not appear when the crys- tals are examined across the axis, proves that a regular arrangement of them, presenting their similar sides in a common direction, 1 is necessary for its display. Fusion breaks up the regular arrangement, and thus destroys this essential condition. ‘he fact, however, that different crystals turn the ray in different directions, is apparently decisive against the hypothesis of Mr. Biot; and the connexion of this difference of property with difference of cry stallographic mc di- ficaiion,-seems to indicate that the phenomenon i is an effect of the structural arrangement of the molecules. Indeed, it is observed, in. the fracture of quartz crystals, that there is occasionally something actually resembling a spiral ar- rangement of parts. The double refraction,of quartz along its axis was experimentally analyzed by Fresnel by means of a very ingenious arrangement. The difference of velocity of the:two rays being so slight : as to render their separation by ordinary cexpedients difficuli, he devised and constructed a ceepeand prism by which to double their G@vergency. In the annexed figure, ABF and CDF represent similar triangular prisms of right-handed quartz, with the faces AB, CD, cut perpendicularly to the axis. The obtuse-angled prism BID, having the angle BED equal to the supplement of DAR B, has its base, BD, parallel to the axis of a crystal of left- handed quartz. The incident ray 1’ falling per- pendiculariy upon AB, is separated into two, whose A a CIRCULAR POLARIZATION—FRESNEL S RHOMB. 137 velocities differ, but which pursue the same path, which is the axis. At the surface BF their paths become different, the velocity of one of them passing from — to +, and that of the other from + to—. At the surface FD this divergency is increased, the velocities again interchanging their relations. At final emergence from the face CD, the diver gency ‘will be further slightly increased in consequence of the inclination of the emergent rays to the surface. By this arrangement a sufficient separation of the two rays is obtained to make it possible to examine them singly. And it is obvious that a duplication of the system of prisms here shown, ora still greater increase in the number of ele- ments employed, would, if necessary, make the separation still wider. If quartz were like other uniaxial crystals in the law governing refraction along its axis—that is, if the velocities of the two rays were in that direction equal in this crystal as they are in others—the system of prisms just described would produce no separation of the rays. 'The fact of the separation proves quartz to be in this respect an exceptional case. When the separated rays are examined, however, the extent to which quartz is exceptional is discovered to be much greater than is implied in the difference just indicated. The peculiari- ties are the following, and are true of either of the separated rays. Examined with a doubly refracting prism, two pertectly equal images appear in all azimuths of the prism. Received upon a mirror at the polarizing angle, equal reflection takes place in all azimuths of the mirror. In these respects the rays resemble ordinary unpolarized light. But in the following particulars they differ: Transmitted through thin erys- talline plates they display, on being analyzed, tints like those produced by polarized light, only they are such tints as ordinary polarized light produces in thicknesses of crystal greater or less, by a determinate amount, than those used in the experiment. Transmitted through a rhomb of glass, like that represented in the figure, of which the acute dihedral angles are 544°, they emerge, after two internal total reflections, at Q and P, polar- ized in planes, one in azimuth 45° on the right, and the other in azimuth 45° on the left, of the plane of reflection. If both are transmitted through the rhomb simultaneously, so as to emerge together, they will form a single ray polarized in the plans of reflection. Rays in this condition are said to be circularly polarized. Fig. 21. And as it appears that a circularly polarized ray becomes plane polarized by two internal reflections in glass, at an angle of incidence of 54° 307, the resultant plane of polarization being inazimuth 45° from the plane of reflee- tion, it follows that a plane polarized ray may be circularly polarized by caus- ing it to make two similar reflections, the plane of its original polarization being 45° in azimuth from that of the first reflection. This is effected by the use of arhomb such as has been just described, and which, from its originator, has been called Fresnel’s rhomb. It is obvious that, ifa plane polarized ray be thus passed through ¢wo of Fresnel’s rhombs successively, it will emerge plane polarized. Mr. Fresnel was led to the discovery of the remarkable property of the thomb which bears his name, by theoretic considerations. When light is pass- ing from a denser to a rarer medium, the angle of refraction is greater than the oO angle of incidence, and the law of Snellius, sins =A”, sing gives a value for m, the index of refraction, less than unity. Now as 1 is the greatest possible sine, if we put sino— 1, we shall have sinc—=z,; and there- fore ¢ itself less than 90°. For an incidence greater than this value of ¢ there 138 TOTAL REFLECTION—ELLIPTIC POLARIZATION. can be no emergent ray; and hence this is called the limiting angle. For all incidences from ¢ to 90° the whole of the light is reflected; and this is what is meant by total reflection at second surfaces. Mr. Fresne! found that the mathematical formule which he had deduced from his theory of light, to express the intensity of reflection at different incidences, . became ¢maginary in the case of total reflection; and in reasoning on the prob- able causes of their failure, he was led to predict that a rhomb of glass, having the angles above stated, would produce precisely the effect which has just been described. Experiment proved the truth of this anticipation. The nature of the modification which light undergoes in these circumstances will be more fully explained further on. Reflection from metals presents characters which resemble those of reflection from the second surface of transparent media. There is this difference: that common light ¢otal/y reflected exhibits no traces of polarization; but common light reflected from metallic surfaces 7s partially polarized. When the incident light at second surfaces is polarized in an azimuth between 0° and 90° the modi- fications which it undergoes 1esemble those produced by metals. ‘This subject was first systematically investigated by Sir David Brewster. He first discov- ered that polarized light, after having unde:gone one total reflection in an azi- muth between 0° and 90°, produced colors, when examined with an analyze., analogous to those produced by thin crystalline lamin. He afte: waids ascer- tained that a polarized ray which has undergone successive reflections from plane metallic mirrors placed parallel to each other, when the original azimuth of reflection is 45° from the plane of polarization, will exhibit similar tints. The angle of incidence at which the effect is best produced varies with different metals, but is in all, or nearly all cases, above 70° and below 80°. The bright- ness of the tints increases with the number of reflections. Sir David Brewster also found this analogy between the effects of such a pair of parallel metallic mirrors and a pair of Fiesnel’s rhombs: that at a ce: tain angle of incidence, different for different metals, the effect of the reflection on the first mirror would be exactly compensated by that on the second, and the ray would emerge plane polarized. But he found also this difference between the eases: that while (the azimuth of incidence being + 45°) the ultimate plane of polarization with the rhombs was — 45°, that with the metallic mirrors was always less than this, being for silver, in which it was greatest, — 39° 48’, and for galena, in which it was least, no more than — 2°. There is also this addi- tional and very remarkable difference: In the case of the rhombs, after the light has undergone reflection in the first, it will be restored to its original con- dition by the second, no matter what be the azimuth between the planes of reflection in the two rhombs. But in the case of the mirrors, if the second be turned in azimuth, it will no longer restore the ray, unless the angle of incidence be changed also. If it be turned quite round, the angle of incidence required to effect restoration will pass through a series of regular variations between determinate limits, which variations may be represented by the varying radii of an elfipse. It was on this account that the term e//iptical polarization was originally applied to light in this physical condition. We shall see, further on, that the propriety of the term may be established on other grounds. Common light reflected from metallic surfaces is more or less elliptically polarized. In fact, the recent investigations of Mr. Jamin and others have proved that there are very few substances which furnish by reflection from their surfaces absolutely pure plane polarized light. None are capable of doing so whose indexes ‘of refraction exceed or fall short of 1.414. Water and glass do so sensibly; but in this respect they are nearly exceptional. CRYSTALS OF TWO AXES. 139 The rings seen in, crystals cut across the axis, when examined in circularly polarized light, exhibit some singular peculiarities. They are divided into quadrants by a cross which is neither very dark nor very brig!tt, \ and which does not change in intensity with ' the revolution of the analyzer, but turns with lit.’ The rings in the alternate quadrants are unconformable, those in one opposite pair being nearer to the centre, and those in the other more distant from the centre, by a quarter of an interval, than the corresponding rings in plane polarized light. This singular arrangement is shown in Fig. 22. Mr. Airy found that light may be circu- larly polarized by refraction, in passing through laminz of erystals which doubly refract ; provided the thickness of the laminz used is such as, on the undulatory theory of light, is just sufficient to effect a.retardation of one of the rays produced by the double refraction, one- quarter of an undulation behind the other, or to advance it one-quarter of an undulation before the other. The mineral employed by him for this purpose, and which is more conveniently prepared of suitable thickness than most others, is mica; of which the lamine are easily separable, and cleave in large sheets without breaking. A lamina reduced to a thickness proper to produce circular polarization is commonly called a “ quarter-wave lamina.” For some time after the discoveries had been made of which a brief account has here been given, it was supposed that all doubly refracting crystals have but a single optic axis. In the year 1817, however, Sir David Brewster announced the remarkable fact that most crystals have two optic axes instead of one. The rings seen in crystals of two axes are elliptical, when the axes are so far apart that only one can be observed at a time; and thcy form lemniscate curves, or curves resembling the figure 8, when they are near together. In topaz Nh nT i att ta Ai aa Wy nn ya | na ‘I Ny Ni Ni i au Ki — NTN i wt Ay, r \ d 1 " INN Ni ' i ‘ ‘ sili tl Fig. 23. Fig. 24. the axes form an angle with each other of 65°, and the rings present the appear- ance shown in Fig. 23, when the analyzer is crossed upon the polarizer, the plane of the axes of the crystal being in azimuth 0° or 90°. This erystal pos- sesses the peculiarity of showing its own rings without the help of an analyzer when the plate subjected to experiment is cut across the line intermediate between the axes, the opposite surfaces being parallel. In such a plate, in order that the ray may follow the line of one of the axes within the crystal, its angle of incidence must be 624°. The angle of refraction will then be 32$°. The incident angle at either the first or the second surface will, therefore, be very nearly equal to the polarizing angle for the substance, since the reflected and refracted rays make an angle of 85° with each other; whereas, according to the law of Brewster, at the polarizing angle they should be at right angles. If, therefore, instead of observing the light transmitted through the plate, we 140 | POLARIZING STRUCTURE ARTIFICIALLY PRODUCED. veecive upon the eye the rays reflected from the second surface and emergent from the first, the reflecting surface itself forms an analyzer sufficiently perfect to exhibit the rings. But as the angle of reflection is not truly the polarizing angle, when the crystal is in azimuth 90° the dark band will not be as large as is the case in the rings seen with a better analyzer by transmitted light. Fig. 24 exhibits the appearance of these reflected rings. In Figs. 25 and 26, which follow, are seen the appearances presented when the subject of examination is saltpetre, (nitrate of potash,) in which the axes are inclined to each other 6°. The plane of the axes of the crystal being brought Hig. 26, into coincidence with the plane of polarization of the incident light, and the analyzer being crossed upon the polarizer, a system of lemniscate curves is seen, like that shown in Fig. 25, intersected by a dark cross, of which the bar coinciding in direction with the plane of the axes is longest. If the analyzer be turned 90°, the colors become complementary, and the cross becomes white; but if, the analyzer and polarizer remaining fixed, the crystal itself is turned in azimuth, the cross will break at the centre, forming two curves, which, when the rotation becomes forty-five degrees, assume the form of two opposite hyper- bolas. This appearance is exhibited in Fig. 26. In the prosecution of his investigations, Sir David Brewster arrived at the discovery that the polarizing structure could be artificially produced in glass by heat or by rapid cooling; that this effect is transient when the heat is below the point of softening or fusing the substance; but that when it is carried beyond that point, and cooling rapidly follows, as in glass which is not annealed, the structure is permanent. He found that the same structure could be produced by pressure, by torsion, by tension, or by flexure; and traced the transient con- dition of the same kind produced by heat to the mechanical effects of unequal expansion. Any solid transparent substance, organic or mineral, was found by him to be capable of receiving this structure transiently or permanently. Among these may be named horn, indurated jellies, tortoise shell, gums, resins, the crystalline lenses of fishes or animals, &c., &c. When cylinders, tubes, rhombs, or other geometrical forms of well-annealed glass are subjected to a sudden increase of temperature acting upon all their sur- face, as by immersing them in hot water or hot oil, there will be seen within them, by polarized light, systems of symmetrical figures, circular and concentric in cylinders, and dependent on the form of the solid for their shape in other cases, bearing a striking resemblance to the rings seen in crystals. Like those rings, 5 these figures are marked by a cross, which changes from black to white with -ROTATORY POLARIZATION OF LIQUIDS. 14] the rotation of the analyzer. But these figures will alter their forms if the glass be broken, which is not true of the rings formed in crystal. When the heat has fully penetrated the glass, and the interior temperature is uniform, the figures cease to be seen. At this time, if the heated glass be removed from the bath, and allowed to cool rapidly, a new system of figures will spring up within it. This is related to the former one, as the rings of a positive erystal are to those of a negative one; and, therefore, if two similar solids, in one of which the former set of figures is seen, and in the other the latter, be superposed when the intensities are equal, they will neutralize each other’s effects, and the rings will disappear. ‘This structure may be made permanent in the glass solids we have been considering by heating them nearly to the point of fusion and then suddenly cooling them. Many common articles of glass are so imperfectly an- nealed as to display the doubly refracting structure in a striking manner. The stoppers of bottles, if cut across the axis and polished, will invariably show it; so will the stems of wine glasses, the stirring-rods of the chemist’s laboratory, and many, if not all, glass tubes. The effects of heat are also remarkable in altering the doubly refracting character of crystals. Mr. Mitscherlich discovered that heat expands crystals unequally in different directions. Iceland spar is expanded in the direction of its axis, and slightly contracted at right angles to the axis. Its doubly re- fracting power is thus diminished. In sulphate of lime, which is a crystal of two axes inclined to each other 60°, he found that the inclination diminishes with elevation of temperature, until the two axes unite in one; after which, with further increase of heat, they open out ina plane at right angles to the first. Dr. Brewster discovered an example even more remarkable in glauberite. At the freezing point, this crystal has two optic axes for every color of the spectrum, the inclination of the axes of the red being greatest, and that of the violet being least. At ordinary temperatures it has two axes for red and one for violet. When heat is applied, the other axes approach, as in the case just described, and, after successively uniting, successively open out in the transverse plane. In comparing the erystals which possess the power of double refraction, (being by far the greater number of the whole,) there is found to be a certain relation between the optical character of the crystal and the erystallographic structure. All crystals whose primitive form is the cube, the regular octahedron, or the rhomboidal dodecahedron—figures whose geometrical axes are all equal—are des- titute of the property. All crystals which have one axis greater or less than the others are crystals of one optic axis. All crystals whose geometric axes are all three unequal have two axes of double refraction. In the year 1815, Mr. Biot made the remarkable discovery that many liquids possess the power of rotatory polarization—a discovery which was independently made by Mr. Seebeck ; the effect was first observed in oil of turpentine, but has since been found in most essential oils, in solutions of sugar, dextrine, the vege- table alkaloids, camphorie and tartaric acid, and the tartrates. In some of these substances the plane of polarization is turned to the right and in others to the left. Their relative rotatory forces are estimated by a comparison of the amount of angular change in azimuth produced upon a polarized ray in passing through a column of given length; but as yet there has been no universal agreement upon astandard length. ‘The statements of experimenters, therefore, usually-embrace both the angular rotation and the length of the column by which it has been produced, rendering a reduction to a common length necessary before a correct comparison can be instituted. It would perhaps be most convenient to adopt as a standard length, the length of the tube introduced by Mr. Soleil into his saccharimeter, or instrument for measuring the rotation in solutions of sugar, which is twenty centimetres. With this length the dextro-gyration of the oil of bitter oranges is, for red light, 157°.89, which is the maximum observed in 142 HEMIHEDRISM——-THE TARTRATES. this class of’ liquids. The laevo-gyration of narcotine, in alcohol and ether, is 151°.4; that of sulphate of quinine, in water acidtlated with sulphuric acid, is 192°.95 in the same direction. Solution of crystallizable cane sugar is dextrogyre ; that of uncrystallizable cane sugar, or molasses, is levogyre. Solution of sugar of grapes is also dextrogyre when prepared from the juice, and before solidifica- tion; but if evaporated to dryness and redissolved, it is levogyre. Crystallizable cane sugar is made uncrystallizable by heat, and its rotatory power is accordingly reversed by the same cause. In many solutions the introduction of an acid modifies the rotatory power. Narcotine, from being —151°.4, becomes, after the addition of hydrochloric acid, +83°. Cane sugar has its rotatory power inverted in the same way. Upon this principle is founded the construction of Soleil’s saccharimeter just mentioned. A solution of the sugar to be examined is made of a definite density, and its rotatory power observed in a tube twenty centimetres in length. There is then added to the solution a measured amount, one-tenth of its volume, of strong hydrochloric acid, and a heat of about 150° F., applied for ten minutes; after which it is cooled and observed again in a tube one-tenth longer than before. Its rotation will now be wholly negative. The original observation will give the difference between the rotatory effects of*the crystal- lizable and unerystallizable sugar present, and the second observation will give the sum of the same effects. From these data the relative quantities of the two kinds contained in the solution may be deduced. For convenience, tables to accompany the instrument are prepared in advance, from which the values sought may be found by inspection. A saccharimeter has also been contrived by Mr. Mitscherlich. Mr. Pasteur has made a very elaborate examination of the salts of tartaric and paratartaric acid in their relations to polarized light. All the tartrates are dextrogyre; the paratartrates have no rotatory power at all. Myr. Pasteur made the interesting discovery that paratartarie acid which is the same as racemic, and which differs from tartaric acid only in having an additional atom of water, is composed of two acids, one of which has a positive and the other a negative rota- tory power. The dextro-racemic acid is simply tartaric acid, and the dextro-race- mates are tartrates. Paratartaric acid and its salts owe their neutral character to the balance of opposite forces belonging to their components. In considering the crystalline forms of these different salts, Mr. Pasteur de- tected a relation between them and their polarizing properties, such as has already been described to exist in quartz; that is to say, the salts which possess rota- tory power have plagihedral faces leaning in the direction of rotation. The crystals are all of the kind called by Mr. Weiss hemzhedral ; that is to say, not in all respects symmetrical. Mr. Pasteur observed that there are two kinds of hemihedral crystals, which he has distinguished as the superposable and the non-superposable. When a crystal, or any solid, or surface is such that another may be conceived or constructed like it in every particular as to form and dimen- sions, yet incapable of being made to oceupy the same matrix or mould, such a crystal, or solid, or surface belongs to the class of the non-superposable. 'The image of the face in a mirror, as compared with the face itself; the left hand or the left foot, as compared with the right, and many analogous objects natural and artificial, may serve to illustrate this conception. Mr. Pasteur found that all the crystals whose salts possess the rotatory power are hemihedral and non-super- posable; and, conversely, that all salts whose erystals are non-superposably hemihedral have the power of circular polarization, with two exceptions only thus far known, which are formiate of strontian and sulphate of magnesia. In the latter case the crystal is so very nearly superposable, that it is hardly sur- prising that it should not sensibly conform to the law. In the instance of the formiate of strontian, Mr. Pasteur thinks that the hemihedrism does not depend on the arrangement of atoms in the chemical molecule but on that of the physi- cal molecules in the entire crystal; so that, on solution, the structure on which ATMOSPHERIC POLARIZATION. 143 the rotatory power depends, disappears in the same manner as it is known to do in quartz on fusion. It is impossible within the limits to which we are here confined to pursue this interesting subject further. Mr. Arago early made the discovery that the light which comes to us from the atmosphere is polarized. Observations made in the vertical plane passing through the sun show sensible polarization in that plane up to about 150° from the luminary—a point which can only be observed, therefore, when the sun is low. The polarization at this point becomes: zero, and it is hence known as Arago’s neutral point. Below this point down to the horizon, polarization is found in a horizontal plane. Mr. Babinet discovered a second neutral point 17° above the sun, and Dr. Brewster a third, 8° 30’ below. Neither of these is easy of observation. in consequence of the proximity of the sun himself and his ereat light. Between them the light is probably polarized horizontally; but the fact, for the reason just mentioned, has not been verified. The plane of polar- ization in the vertieal between the neutral points of Arago and Babinet is easily accounted for by ascribing the polarization itself to direct reflection of the sun’s rays from the molecules of. the atmosphere. The polarization in a horizontal plane below Arago’s point is a less simple phenomenon. It is believed, however, to be oceasioned by rays which have undergone two reflections from the atmos- pheric molecules. Of the rays of this class those which will come most effectively to the eye of the observer will be such as are reflected in the lower parts of the atmosphere in planes nearly parallel to the horizon. These will, of course, be polarized in planes nearly horizontal, and if in force sufficient to overcome the light polarized vertically, will produce a resultant in their own direction. At an altitude at which the two opposite polarizations balance each other, will be found a neutral point, and this is the point of Arago. Regarding atmospheric reflection of the sun’s rays as the cause of atmospheric polarization, it will follow that every plane passing through the sun (in the superior portions of the atmosphere at least) must be a plane of polarization. This will therefore be true of the howr-circle or meridian in which the sun happens at any time to be. And as all hour-cireles pass through the pole of the heavens, it results that a delicate polariscope, directed toward the pole, may follow the horary motion of this plane. Such a polariscope, furnished with a dial and index, becomes a chronometer. This is the principle of an elegant little instrument invented by Wheatstone, called the polar clock. When acecu- rately adjusted, it will indicate, in the hands of a practiced observer, the apparent solar time within a very few minutes. It will operate even when the sky is overeast with clouds, provided there be an unobscured spot at the pole, through which the blue sky may be seen. In the foregoing very suceinct outline of the history of optical discovery, the object kept in view has been to present simply facts, without entering into any discussion of the physical causes to which they are to be attributed. It is now proposed to consider in what manner these facts may be most satisfactorily explained. THEORIES OF] LIGHT. Two theories have been maintained in regard to the nature of light, either of which is supported by the authority of very illustrious names. According to the first of these, light is a material emanation thrown off by the luminous body, and its particles constantly traverse and fill the entire illuminated space, so long as the source continues unexhausted. According to the second, there is no transfer of matter from the source of light to the surrounding region, but there is a transfer of force through the medium of an elastic fluid which fills all space, and whose molecules in contact with the luminous body, being disturbed by that body, transmit the disturbance to those more remote, by means of undulations 144 MATERIAL THEORY OF LIGHT. which succeed each other uninterruptedly until the cause which produced them ceases to act. The first of these two hypotheses seems to have been of very early origin. It received the sanction of Newton, and was made by him the basis of his reasonings in regard to optical phenomena. It is hence commonly called the Newtonian theory. Until an advanced period in the present century it may be said to have been the generally accepted theory. Laplace, in his great work on celestial mechanics, has founded all his investigations in regard to aberration and astronomical refraction upon it. Yet it must be admitted by its advocates, if there remain any who adhere to it still, that it presents, even before we follow it into its applications to the ex- planation of the phenomena we have described, many serious difficulties. In the first place, if light consist of material particles, these particles must be of inconceivable minuteness, or their living force would be sufficient to destroy every structure, no matter how solid or how tenacious it might be, which they should encounter in their flight. A single grain of matter, moving with the velocity of light, would have a quantity of motion equal to that of a cannon ball of 100 pounds weight, moving with the velocity of 1,500 feet per second. But since destructive power is proportioned, not to the quantity of motion, but to the living force, which varies as the square of the velocity, a single grain of matter moving with the velocity of light would have a destructive power equal to that of a mass of 3,350 tons moving with the velocity of 1,500 feet. If light be material, therefore, its particles must be many millions of times less in weight than a single grain. We have no instruments sufficiently delicate to detect a weight so minute. Still it would be possible, by optical arrangements, to concentrate many millions of particles upon a single point. Attempts have been made to test the question by the use of such expedients. Dr. Priestley, in his History of Light and Colors, deseribes an experiment in which he directed the light of the sun, by means of a concave mirror having four square feet of surface, upon a balance of exceeding delicacy, without producing any sensible impression. The conclusion is expressed in his own words, as follows: “ Now the light in the above experiment was collected from a surface of four square feet, which, reflecting only about half what falls on it, the quantity of matter contained in the rays of the sun incident upon a square foot and a half of sur- face in one second of time, ought to be no more than the twelve hundred millionth part of a grain.” Dr. Priestley does not consider that, in such an experiment, it is the moment, and not the weight, of the particles of light that would be measured. The amount of inertia in any balance, however delicate, is sufficient to render it an instrument not very well adapted to the purpose in view. 'The presence of the air is also a disadvantage, both on account of its own resistance to motion and on account of the currents created by the heat which attends the direction of the solar focus upon any solid. The following experiment by Mr. Bennet avoids these objections. This brief account is taken from Professor Lloyd’s Essay on the Undulatory Theory, edition of 1857. ‘A slender straw was suspended horizontally by means of a single fibre of the spider’s thread. 'To one end of this delicately suspended lever was attached a small piece of white paper, and the whole was enclosed within a glass vessel from which the air was withdrawn by the air-pump. The sun’s rays were then concentrated by means of a large lens, and suffered to fall upon the paper, but without any perceptible effect.” These results are negative, it is true, but it must be admitted that they are such as to render the truth of the material theory of light in the highest degree improbable. Another difficulty in the way of this theory is found in the uniformity of velocity with which light reaches us from distances all but infinitely unequal, and from luminous bodies of every magnitude. This equality of velocity in the propagation of the light of the stars is evinced in the universality of the law of THEORY OF EMISSION—DIFFICULTIES. 145 aberration. But it might be inferred from the equality of the refraction which all light, whether natural or artificial, undergoes in passing from medium to ee dian Now, if light be material, it must ie regarded as subject, like all other projectiles, to retar dation by the gravitating power of the weds from which it is emitted. And, moreover, it is a phenomenon inconceivable that so perpetual a shower of projectiles, so infinite in number, should all be thrown with the same initial velocity, and that this initial velocity should be the same for every source. The only hypothesis upon which it is possible to mect this last objection is to assume, according to a suggestion of Mr. Arago, that the eye is insensible to luminous impressions, except for a certain definite velocity of the luminiferous particles, or for that narrow range of variation of velocity, within which are embraced the velocities which we attribute to the different colors in refracting media. In regard to the retardation of the particles by the attracting power of the luminous body itself, it may be observed that, with our present means of measurement, this would not be appreciable for distances so small as that which separates us from the sun, or even for distances no greater than the extreme dimensions of the solar system; at least without supposing an enormous increase in the mass of the luminous body beyend that of any aggregated form of matter known to us. An attracting body can destroy, in a projectile thrown from it, no greater an amount of velocity than it can impart to a material mass falling toward it. And this limit is reached if we suppose the falling body to commence its motion at an infinite distance. Now, the velocity acquired by a body falling from an infinite distance to the sun’s surface, under the influence of solar at- traction, would be less than four hundred miles (391 miles) per second; and of this velocity about fourteen-fifteenths (365.1 miles) would be acquired after passing the limit of the earth’s orbit. But the body would be twenty-seven and a half days in reaching the sun after passing this limit, while light is only eight minutes and thirteen seconds in traversing the same immense space. The effect of an accelerating or retarding force being as its time of action, and, in this case, the two times to be compared being in “the ratio of about one to four hundred and eighty, it may easily be shown that the retardation of light by solar attraction, during its transit from the sun to the earth, could not be so much as a mile per second in its velocity. But the light of stars coming from distances so vast as to require years, and many years, to reach us, must undergo such retardation as to render aberra- tion a phenomenon exceedingly variable, unless we admit Mr. Arago’s assump- tion just mentioned in regard to the sensibility of the retina. Moreover, in cases in which the rays, in their long travel, had becbme reduced to velocities paratively moderate, the gravitating power of heavy bodies near which they mit pass, ought to produce a acasible: deflection of their course, and. modify, in a remarkable manner, the phenomena of occultations. Nothing of this kind is observed. It is here assumed that there may be suns much more massive than ours. Laplace has examined the question, what ought to be the mass of a luminous body, in order that its gravitating power may be great enough to destr roy the velocity of the particles “of light entirely, at some distance less than infinite— the initial velocity being assumed to be that which observation has determined in the sunlight as it reaches us. ‘The expression for the velocity acquired in falling from an infinite distance to the sun’s surface—his mass being assumed to be unaltered, is— 2mgr om in which m is the sun’s mass, that of the earth being unity; g¢ is the measure of the foree of gravity at the earth’s surface, being the velocity it is capable of imparting in one second, or 321 feet; 7 is the earth’s radius, and R the radius 108 146 THEORY OF EMISSION—-DIFFICULTIES. of the sun, both expressed in feet. If we put v == 192,700 miles, (reduced to fect,) and make m indeterminate, we shall find that the mass must be increased 860,000,000,000 fold to be capable of creating, and therefore of destroying, a velocity equal to that of light. ‘This supposes the bulk of the sun to be un- altered. But if she mass is increased without altering the density we shall have— 2mgrax? ese in which z is the radius of the sun under its supposed enlargement ; whence— —_ oR® as rv 22mg Replacing the symbols by their values, we find that the sun must be enlarged to nearly five hundred times his present diameter in order to possess the power of entirely arresting the progress of light, considered as material, at any distance. The surface of such a sun would extend more than seventy millions of miles beyond the orbit of Mars. That there may be bodies in the universe so large as this is possible, but we may esteem it hardly probable. If there are, and if light is material, they may be invisible to us. A final objection to the material theory of light is found in the phenomena of refraction and reflection. This, though it seems to have been overlooked, is really the most serious of all. We have seen that the effect of the immense power of solar gravitation is insufficient to produce more than an inappreciable variation in the velocity of light, during the nearly eight minutes and a quarter which is occupied in its passage over the space between us and the sun; and yet, if the hypothesis we are considering be true, there is a force residing in the superficial stratum of transparent bodies—a stratum so thin that no attempt has ever been made, or can be made, to measure it—which is capable of instantane- ously doubling and, in some instances, almost tripling this velocity. Thus light which has passed the surface of glass of antimony or chromate of lead must, if this theory is true, have its velocity raised, in the instant of passing, from 192,700 miles to 574,000 miles per second. In common glass the velocity becomes 289,000 miles. In ordinary reflection, also, the reflecting force has first to destroy the original velocity, and then to impart an equal velocity in the opposite direction. This is more easily conceivable than the acceleration produced by refraction, as it corresponds with the ordinary phenomena of elas- ticity. But refraction, on the theory we are considering, is only explicable on the hypothesis of attraction; and the immensity of an attracting force which is capable of accomplishing in so short a time what gravity is totally unequg] to in a time greater beyond measure, is totally inconceivable. But, if objections of this weighty description to the material theory of light did not exist, the impossibility of finding in it any satisfactory explanation of the remarkable phenomena which have presented themselves in the later pro- gress of optical discovery, would be conclusive against it; while the opposing theory finds in these very phenomena its strongest recommendation to accept- ance. It is to that theory, therefore, that attention will be confined in the fol- lowing attempt to conncet the facts which have been detailed with their proba- ble causés. ‘To repeat the imperfect explanations which have been founded on a hypothesis which is now generally abandoned, would be an unprofitable waste of time and space. THEORY OF UNDULATION—VIBRATION. OG PART Hi. UNDULATOERY THE OR Y. § I. VIBRATION. In order to understand the mode in which undulations are propagated through an elastic medium, it is necessary to attend first to the subject of vibration. If a body be so held in equilibrium between opposing forces, as that, when dis- placed from its position of repose, it is urged to return by a force always pro- portional to its distance from that point, then the time occupied in returning, supposing it to be left at liberty to obey this impulse, will be the same, what- ever may be the magnitude of the displacement. Moreover, if the extent or amplitude of the displacement be taken as a radius, and a circle described about the point of repose as a centre, the velocity of the body in its returning move- ment will be proportional, at every point of its path, to the per- pendicular to the path drawn from that point and cut off by the circular are. Thus, if C be the point of repose, and CA the amplitude of displacement, the force urging the body to return being proportional to CA, CI’, CH, &c., when the body is at the : points A, I’, and H, then the velocities at these several points will Fig 27. be proportional to zero at A, to EF at F, and to GH at H. These elementary propositions in physics, which admit of easy demonstration,* *The demonstration referred to is the following: Put CA—a, CH=z. Put also ¢ for the time from the beginning of movement, v for the velocity, and p? for the force drawing the body toward C at the distance umty. Then if dx be the small space described in the small time dt, rdt—=—dz; dx being negative because, when v is increasing, it diminishes z. Also, if dv be the small increase of velocity in the time dt, we shall have the force, at the distance z, equal to p*z, and p*adt—=dv. Whence, vdv =— p*zdx; and v7? =— p?2? ++ C, But when v= 0, =a: consequently, v= p(a?—zx?); or, v= pV a?—x?=(in the figure) pV CR — CH? =p.GH. Therefore v is proportional to GH. Also, the time of vibration is constant, irrespective of the value of a. For, substituting in the first equation the value of » just found, — —dx pV @—a.dt=—dz ; or, ee pV a ae ye Tela This gives t=—~sin —-+C. Pp a lf et 1 ly When t=0, z=a: whence t=—=— | 90°—sin a) = 1COSieSs Pp a p a Now, taking ¢’ and ¢” for two particular values of t, one at the beginning and the other at the end of a complete double vibration, t’’ — t’ will be the duration of the vibration, and will i. p : —ly P ; . be measured by the increase which the are cos ~ undergoes during one complete series of a 5 vw. ee aie eke : ele hire : : all the possible values of ~ in diminishing and in increasing order—that is, from «=a to x a =-+qaagain. Hence, putting r=t//—t'= the duration of a vibration, we have, me (20 (m-++1)—27m) Bee which is constant. P P The symbol a disappears from this expression, showing that the duration of the vibration is independent of the amplitude. We have here also a proposition essentially the same as that demonstrated by a different 148 UNDULATORY THEORY OF LIGHT. may be assumed as established. When the body in its return arrives at C, it will accordingly be moving with the velocity represented by CD, the radius of the circle, and its inertia will carry it forward in the direction CB. It will now be resisted by forces similar in degree but contrary in direction to those which urged it from A to C, and its velocity will decrease as it before increased, until it is brought to rest again at B, when it will once more return. Supposing no forces or resistances to be called into action but those embraced in our hypothesis, there is no reason why this reciprocating motion should not continue indefinitely. We have an approximate illustration of the case under consideration in an ordinary pendulum. When the pendulum is drawn from the vertical position, the component of gravity which urges its return is a force very nearly propor- tional, at every instant, to its distance from the position of rest. Were its path a cycloidal instead of a circular are, this proportionality would be rigorously exact. Its beats are therefore sensibly equal in time, whether it swing through twenty degrees or through only one. If we suppose the pendulum to be so suspended that its vibrations are not of necessity restricted to a single plane, we shall be able to conceive, without much difficulty, what must happen in another case important to be considered, viz: that in which a body, already in a state of vibration, is acted upon by a second disturbing force, not directed in the same plane with the first. To simplify the ‘supposition as much as possible, let us imagine that, at the moment when the body, in its return from A, is passing the centre C, it receives an impulse in the direction D, at right angles to its actual movement, capable of giving it, in- stantaneously, the same velocity towards D, which it already has towards B. By the law of the composition of forces, it will take the direc- R_2— _™ tion CM, which is the diagonal of the rectangle formed upon CB, CD; and its subsequent vibrations will be represented in = RB extent and direction by the lime NM. It will be seen that the yo extent of its excursions in the direction AB remains unaltered, Pe since the lines MB and AN are parallel ; but it performs, at the same time, an equal vibration in the direction DP, since DM Ries and NP are also parallel. Let us suppose, however, that the second impulse takes effect on the body not at the point C, of its greatest velocity, but at A, where its motion is null, and at the instant when it is about setting out on its return to C. It will vibrate, as before, between the parallels NP and MDR;; ‘but it will reach the limits of its vibration in this direction when it is at the middle of the vibration in the other. At the end of half a vibration, therefore, it will be found at D instead of at C, as in the former case; at the end of the next half at B; at the end of the third half at P; and at the end of the fourth, or of a complete double vibration, at A, the point of starting. Apparently, therefore, under these cir- cumstances, the orbit of the body is a circle. We shall see that this is really so. In fact, if we represent by 7 the radius vector of the body, and by x and y its co-ordinates to the axes AB and DP, we shall have the equation 2?+7’==7*. Whence, taking the differential— A zdxz+ydy =rdr. (a) method, a little further on in the text, in regard to the measure of the time elapsed since the beginning of the vibration, at any given moment, and in any position of the vibrating body. Since t varies as cos it is obvious that, if a circle be described on the path of the vibra- a ting body as a diameter, and if an ordinate to the circumference be drawn from the position of the vibrating body at any moment, the are of the circle intercepted between the origin and this ordinate will be the measure of the time elapsed since the vibration began. The are must be taken always in the same constant direction around the circumference, and the ordinate must be positive for the advancing and negative for the returning movement. In like man- ner, the are intercepted between two such ordinates, will measure the time intervening between the moments when the vibrating body occupied the points from which the ordinates are drawn. VIBRATION. 149 Now, by the law of velocities above given, if @ be put for the maximum ve- locity, or that which the body has in passing ©, and if ¢ be put for the are of the circle on AB which is included between the origin, ae and y, the velocity in the direction AB, will be asing; and that in the direction CD, acose¢. Hence, for the differentials of the co-ordinates x and y, we have, putting ¢ for the time— dx—=— asingdt; and dy = acos¢dt. But by construction z—rcos¢g, and y=rsing. Substituting these values in equation (a) there results— — arsingcosgdt+ arsingcosgdt = rdr. dr Or, — = dt From which it appears that the radius vector is constant and the orbit a circle. Also the motion in the circle is uniform. For if dg be the increment of the arc, dg? = dx’? + dy’. i And substituting the values of dx and dy, given above, we have, de’? =a’ sin*¢dt? + a’cos*ed?’ =a'dt’. And Ue Sy es) dt That is to say, the velocity of the movement in the circle will be uniform, and will be equal to the maximum velocity of the plane vibration. Hence it follows that if, at the moment when a body, vibrating in a recti- linear path, is at the limit of its movement, a second body sets out from the same point, in a circle of which the path of the first is a diameter, with a uniform ve- locity equal to the maximum velocity of the first, the line which joins the two will move parallel to itself, and will always be perpendicular to the path of the plane vibration. We hence obtain a convenient measure of the time which has elapsed since the beginning of ieee Oy when the body is at any point, as H, Fig. 27, of its path. ” For, taking as the unit of time the duration of a complete double vibra- tion, and employing the ordinary symbol, 2z, to denote the circumference of a circle whose radius is 1, 27¢ may express the entire space passed over by a body making its revolutions in such a circle isochronously with the movements of the vibrating body, and ¢ (whether its value be integral or fractional) will then de- note at once the number of vibrations which have taken place and the number of units of time which have elapsed since the beginning. Assuming the starting point to be at the commencement of adouble v ibration, every integral value of Z will denote a return to the original position, and every fractional excess will de- note a corresponding progress in a new vibration. ‘Thus if the body be at H, the fractional part of 2<¢ will be the are AG, and this will have the same ratio to the entire circle which the time of describing the. portion of path, AH, has to the total time of double vibration. Let us now suppose that the second impulse (still normal to the first) is not equal to the first, but greater or smaller ; and that the vibration which it would independently produce has an amplitude (measured from the centre) represented by a’. The figure of the orbit will, in this case, be an ellipse, with the greater or lesser axis in the direction of the original vibration, according as.a is ereater or less than a’. The velocities in the direction of @ will still, as before, be represented by asin2zt, while those in the direction of a’ will be represented by a'cos2zt; and these expressions will also stand: for the ordinates of the orbit, y and x. 2z¢ here takes the place of the former symbol, ¢. 150 UNDULATORY THEORY OF LIGHT. Let us now suppose that the second impulse, though still normal to the first, is not imparted either at the limit or in the middle of its path, but at a point corresponding to 2z¢, where ¢ may have any value whatsoever. The velocity of the body at the time ¢ will be qsin2zt. The velocity produced by the second impulse necessarily commences with the maximum:—, that is, with the 5 : : 1 : au : velocity belonging to the time = and hence is a’.sing z, or a’.sin90°. Then the difference of the two, in respect to phase—that is, to the degree of their advancement in their respective vibrations—will be 2z¢—90°, or 90°—2z¢; which, for convenience, put equal to 0. After a further time ¢’, the two veloc- ities will be— 1. a. sin(27t-+2z7t')—=a. sin(90°L0+ 2zt')—=a. cos(2zt! 4 0)—=y. 2. a’. sin(90° 4+ 2z¢') =a’. cos2zt' =a. Expanding y, and eliminating 272’, there results the equation, ay + a&x?—2aa'xy.cosd =a?a' sind, [1.] This is the general equation of the ellipse referred to its centre. It follows, therefore, that any two impulses, applied in directions at right angles to each other to a body susceptible of vibration, will cause the body to describe an ellip- tical orbit, whatever be the interval between the impulses. If, however, we suppose the second impulse to be in the direction of the orig- — inal vibration, and not at right angles to it; and, as before, that there is a differ- ence of time corresponding to the are 0, then the body will be impelled by two conspiring or conflicting forces, capable of producing the simultancous velocities, a sing, and@ sin(g+0). Let us put (a+a’cos0)?+ (a’sind)?’= A’. (a+a'cosd)? (a’sin@)? Se oe the symbol w denoting a determinate angle. Then, Or, =1—cos*w+sin2w. a+a'cos0—=Acosw; and a! sin0d= Asinw, Let the first of these equations be multiplied by sing, and the second by cos¢: their sum, added member for member, will be— a sing-+a’ sing cos0-+a’ cosg sind=A sing cosw+A cos¢ sinw. Or, a sing+qa’ sin(g+0)=A sin(g+e). [2.] The first member of this equation is the expression for the velocity which the body will possess at any time answering to ¢, after the commencement of the vibration a, which is least advanced in phase, and the second member shows that this velocity is that which would exist in the body at the same time, had it been acted on by one impulse only, capable of imparting the velocity A, and applied at a moment earlier than @ by the time corresponding to o, and later than a’, by the time corresponding to 0—w. The value of the velocity A, in terms of the original velocities @ and a’, may be obtained by developing the assumed equation above, when it takes the form, A? =—a?+a?+2aa'cosd; or, A-L V @ +a? + 2aa'cosd. [3.[ This expression is remarkable, as being the value of the diagonal of a par- allelogram, of which the sides are @ and a’, and the A £B angle of their inclination 0. In the figure annexed, i\ let AB == DC— Bk ae : . : d==-,~ which is the equation of a straight line. [15.] Qe At any considerable distance from AQ, therefore, as compared with AC, the hyperbolic trajectory sensibly coincides with the asymptote to the curve. In fact, the equation of the asymptote being— A And Dina ——— ie 16. BY? V 21? Y [ ] by rejecting the minute term under the radical, we obtain— niy' sna hae ie / ; 5.5} which is identical with the former. aC aC ' << O By substituting different numerical values for x, this equation serves for all the fringes, light or dark. The even numbers give the loci of the bright stripes, and the odd those of the dark. The distance 0 is in all cases measured from the middle of the central bright stripe. The expression for the value of 6 indicates, at sight, that the fringes will increase in breadth, as the opaque intercepting object diminishes in diameter. In fact, 0 is inversely as c, and to double the breadth of the fringes, we have only to reduce the diameter of the object one-half. Accord- ingly, if a tapering object, as a sewing needle. be employed, the fringes will spread out toward the top with a beautiful plumose appearance. This becomes still more striking when the taper is is more rapid, as when we use an acute-angled Fig. 42. or even a right-angled plate of thin metal. ‘The fringes, which in this case are very remarkable, have been called Grimaldi’s crests. : DIFFRACTION BY MINUTE APERTURES. Ad, The next case which presents itself is that in which a small portion of the wave only is allowed to pass through a narrow opening in the obstructing screen, having straight and parallel sides. In this case a position may be found for the screen B, in which, if RAB (Fig. 43) be drawn from the radiant through the centre of the aperture, Ba and Ba’, drawn from B to the edges, may exceed BA by one-half an undulation. All lines drawn from B to points of the wave front nearer to A than aor @’, will differ from BA less than half an undulation, and the point B will be fully enlightened. If then the screen B be advanced toward A, there will be found somewhere another position in which Ba and Ba' will exceed BA Fig. 43. by an entire undulation. The spaces Aa, Aa’, may then be divided somewhere, so that lines drawn from the points of division to B shall once more differ from BA by half an undulation. All the molecular movements excited at B by the segments next to A will then be in conflict with those which are generated by the segments next to a and a’; and accord- ingly in this position of B the middle of the luminous image will be occupied by a dark stripe. By advancing B still nearer, another point may be found, where Ba and Ba’ will differ from BA by three halves of an undulation; and in this case the ares Aa and Aq’ may be divided each into three parts, such that the distances of the points of division from B may successively exceed each other by half an undulation. The pair next to @ and the pair next to a’ will then neutralize each other, while the central pair will be efficient, and the point B will be again illuminated. Thus, by varying the distance of B from a, the dark stripe in the centre of the luminous image will alternately appear and dis- appear. It is obvious, however, that when the distance is fcund at which Ba—BA is exactly one-half an undulation, the dark stripe will not return at any greater distance. As the screen B approaches A, on the other hand, the entire bright image becomes filled up with fringes, increasing in number, with the central one alternately dark and bright. It is also sufficiently remarkable and striking that if, when B is at the maximum distance producing a dark centre, a very narrow opaque object be placed over the aperture, parallel to its edges, so as to intercept exactly one-half the light, leaving equal portions on each side of it to pass, the brightness of the centre will instantly return. It will disappear again when the opaque object is removed. When B is at other positions nearer to A, producing the dark centre, the restoration of central brightness will not necessarily take place on cutting out the central half of the beam; but it may be effected by cutting out a portion which is somewhat more or less than half. In order to understand the conditions upon which this difference depends, we must consider that the dark stripe appears in the centre only when La—BA is equal to an even number of half undulations. But even numbers of two kinds, the even-even, and the odd-even.. The even-even are all of them multiples of 2 by the arithmetical series of even numbers 2, 4, 6, &e.; the odd-even are mul- tuples of 2 by the odd numbers 1.3.5, &e. If, then, Bea—BA—nx d/, the light will be restored to the central dark stripe by stopping out the middle half of the beam, whenever » is an odd-even number; and the interposed opaque body must exceed or fall short of half the breadth of the beam by the breadth of two, at least, of the divisions of the wave front, (2z in all,) into which the space aa! is Supposed, in the foregoing explanation, to be divided, in order to restore the brightness when x is an even-even number. We here assume the several divi- 1278 178 UNDULATORY THEORY OF LIGHT. sions of the wave front to be equal in extent, which is sufficiently exact for the purpose in view. The other dark stripes which form within the bright image of the opening aa’ are sub- ject to fluctuations of intensity similar to those of the central one. ‘lo understand this, let d be a point so 7\" taken, that da!/—ba—=2. Join bR, and let the line = A zie Np ba revolve round Ré to the position le. Then dc= SZ ae ba, and ba'’—be=2. Divide ca’ at d into parts, LY such that bda'—bd=4/, and bd—bc=3i. Then, so far as this portion of the wave is concerned, the point J will be obscure in every position of & which preserves this relation, whatever be the distance from A. Also, at any distance of & for which the divisions » Fig. 44. of the wave front ac, made as heretofore described, are an even number on each side of Rd, the whole effect of the wave at & will be null, and the point 4 will be obscure. But if the number of these divisions on each side of R& be an odd number, there will be a portion of the wave un- neutralized, and 4 will be illuminated. : The fringes exterior to the bright image of the opening are more beautiful than those interior to it, being, especially when the aperture is very narrow, richly colored. They are not subject to the fluctuations of brightness, as the distance of B from the aperture varies, which attend the interior fringes; since the lines da and da’, drawn to any point in any of those fringes from @ and a’, the limits of the aperture, will be both on the same side of Ré. The distances 0 from the central line B are all determined by the same equation which was found for the fringes formed by a narrow opaque object. Indeed, the geometrical conditions in the present case are identically the same as those in that. he optical difference is, that the even values of 2 give the loct of the dark stripes, and the odd those of the bright. The breadths vary, as before, inversely as c, which is the diameter or width of the aperture. With apparatus in which the opposed edges are movable, the expansion of the fringes, as these edges are made gradually to approach each other, is very striking. When the aperture is a very slender isosceles triangle, they spread out widely toward the vertex. The expression, pateh, 2c also shows that the breadth varies directly as the length of the undulation. © In homogeneous light, therefore, the broadest fringes are obtained with red, and the narrowest with violet. In such light, a dozen or twenty may easily be counted. When white light is employed, the overlapping of the colors, while it improves the beauty of the display, reduces very much the number that can be distinguished. When monochromatic light cannot conveniently be obtained, the same effects may be substantially produced by viewing the fringes made by white light through colored glasses. When, instead of a long and narrow aperture, a small circular opening in an opaque plate is used, the fringes are, of course, circular. In this case, the cen- tral dark stripe of the preceding experiment becomes a central dark round spot. This spot disappears and reappears as the screen is brought nearer the plate, at the same distances at which this effect was observed in the-central stripe in the image of the oblong aperture. Referring to the last figure, and regarding aa! as the diameter of the circular opening, when Ba—BA=2 x3), there will be some point between a and A (suppose a’) which, if joined to B, will give Ba’ —BA=32. Now, it has been shown that Ba—BA varies as y’; the radius of the aperture (or of the part of it considered) being represented by y. Hence, for the point supposed, a”, we have Aa@’?=A2a!”; or the circle of which Aa is DIFFRACTION OF OPAQUE DISK. 179 the radius, is double in area of the circle of which Aq” is the radius. But since Ba—Ba"'=3A, and Ba”—BA=d,, it is obvious that the resultant molecular movement produced at B by the circle of which Aa” is the radius, will be in total conflict with that produced at the same point by the portion of wave front which forms the ring between this circle and the circumference of the orifice. It is this conflict which produces the dark spot at B. If now a small opaque disk could be introduced into the middle of the orifice, exactly equal to the cirele Aa”, stopping out the central pencil of light, B would immediately become bright again. If Ba—BA=4~x #, the circular aperture will be made up of a central circle and ¢hrce concentric rings, of equal areas, producing movements at B alternately equal and opposite. B will accordingly be obscure. If we stop out now one-half the area in the middle—that is to say, the central circle and the first ring—B will still be obscure; but if we stop out the central circle and the two interior rings, the light at B will be restored. Or if we stop the central circle only, or, instead of that, the exterior ring, or (which is the same thing) apply over the aperture a smaller one, having only three-fourths the area of the first—in either case the light will be restored. But if we stop the central circle and the outer ring at the same time, B will remain ovscure. Generally, if Ba—BA=x x $A, » having any integral even value, the centre of the bright image of the aperture will be dark. If'z be odd-even, stopping out one-half the area from the middle of the aperture will restore the light. If n be even-even, stopping out one-half the area will produce no change ; but the light may be restored by stopping a portion of the area which is by a certain amount greater, or by the same amount less, than one-half. In all these cases the light at the centre, when restored, will be sensibly equal in intensity to that which would reach B through an orifice of the size which would give Ba'’—BA=3,. This incidentally leads us to the remarkable result that if, in this experiment, instead of a circular aperture in an opaque plate, we employ an opaque disk attached to a transparent plate, ‘the centre of the shadow will be as highly illuminated as it would be if the wave were not interrupted at all. For an open circle whose centre and circumference give the relation Ba'’—BA=#), and a ring whose exterior and interior circumferences give Ba—Bu''—$)/, pro- duce sensibly the same illumination at B. In either case all the remaining ob- structed portion of the wave exterior to them may be divided into rings, whose relation to the unobstructed part will be alternately negative and positive, and whose total resultant (which takes the sign of the first term) will be op- posed to that of the unobstructed portion. If then this exterior portion be allowed to pass, the etiect, in either case equally, will be somewhat to diminish the intensity of the brightness at B, which brightness therefore will still remain equal for the circle and for the ring. But in the first instance, this is to allow the entire wave to pass; while in the secoud it leaves the disk. The centre of the shadow of the disk, therefore, which is the point B, is as much illuminated as the same point is when the wave is wholly unobstructed. ‘This curious cir- curnstanee, wh'ch was first announced by Poisson from theoretic considerations, is easily verified by experiment. When it is said that an open cirele which gives at its centre and its circum- ference the relation Ba’—BA—x x $/, ora ring of which the outer and inner circumferences furnish a similar relation, will exhibit a dark spot at B whenever m is an integral even number, it must be remembered that this proposition is true only of the rays whose undulation lengthis 2. If 2 is the undulation length of the red rays, and 2! that of the blue or violet, then at the distance at which red disappears, the blue or violet will not be entirely suppressed. We have 180 UNDULATORY THEORY OF LIGHT. (7s) seen that Ba'—BA has a value expressed by the formula A= 3 rs y”, y being the radius of the circle. This may be resolved into the paris, ya Qr ° Qs’ of which the first is constant when y is constant, and the second varies inversely as s, which is the distance BA. ‘The less the value of 2 (=x 42), the greater will be the distance at which the color corresponding to 2 will be suppressed. And as the color which remains is the difference between the color suppressed and white, it follows that, as the eye approaches A, in the line BA, the ring or the aperture will assume successively all the tints of the spectrum from red up- ward, and that this series may be several times repeated. Moreover, putting A for the length of the red, and i’ for the mean length of undulation in the com- pound color complementary to red, which will correspond nearly to the wave length in the green, when Ba’—BA=(2n+1) X $4! <(2u+1) x $4, a point b may be found on any side of A, but very near it, at which 6a’—bA—(2n-+1)x 4A. A green circle will therefore appear surrounding A, while A itself, whether it be an aperture or a ring, will be red. Also, at other distances, greater or less, circles of other tints will appear; so that the ring or aperture will be encircled by a corona displaying all the prismatic colors, from red to violet, shading outward. As the eye approaches A, the equation da’—bA=(2n+1)xX4A will be true of points nearer and nearer to B, until 6 and B coincide. 'The rings will therefore appear to be successively absorbed into the aperture. In withdrawing the eye, they will seem to be, in like manner, evolved out of it. In this experiment the aperture should be very small or the ring very narrow, in order that the tints may be vivid. It will readily be understood that the obscurity and the sharp edges of shadows of bodies of considerable size are owing to the smallness of the values of 4 for all the rays of light. On this account, if any point be taken within the line of the geometrical shadow, and if the wave front, beginning at the edge of the opaque body, be divided into portions whose extremes are remote from that point by distances differing $2, these portions will neutralize each other’s effects, except for positions of the assumed point for which the divisions have (as they may near the shadowing body) some slight inequality, and no material obliquity. Such positions can only be found very near the line of the geometrical shadow. To the same cause it is owing that, in refraction and reflection, the beam re- fracted or reflected is as sharply defined as the incident beam. ‘The demonstration which we have given of these effects, from Huyghens, contains an imperfection on this point, which I*resnel has supplied. Referring to the figure, suppose that an undulation originating at b should take the direction BA, different from that of the main reflected wave, BQ’. ‘There Vig. 33. will always be found, to the left of B, a point, as 7, from which another undulation will follow in the parallel and nearly coincident line xh, differing from the first by half an undulation. Draw wo per- pendicular to BB’ and B¢ perpendicular to 2h; onB is the angle of incidence. Put p for xBé. Then Bo=Bn sin:, and xt—Bz.sinp. Now, when the wave whose front is Bé starts from 2, the movement which is to produce the wave from Bis ato. There will accordingly be interference, if nt—Bo—=}A; that is, if Bu.(sine—sin:)=$4. But since 4 is very small, if sinp sensibly exceed sint, Bn will be very small; showing that interference will take place from a point very near B. As sing approaches sins, the distance of the origin of the interfering wave will be greater; but there will de an interfering DIFFRACTION OF GRATINGS. 181 wave, (if the surface AB is unlimited,) in every case except that in which sinp—=sin ¢; that is, in which Bé coincides in direction with the regularly re- flected wave. ; In like manner, in the case of refraction, if we suppose a wave to diverge in the direction Br, draw ng parallel to Br and Bp perpendicular to it. Call the angle nBp, p, as before. ‘Then Bo==Bu.sin:, and xp—Ba.sinp. But np being the path of a wave in the denser medium, it must be multiplied by the index of refraction, in order to obtain the equivalent distance, or distance which the wave would have moved in the same time, in the rarer. Let x be the index of re- fraction, and we have, for the condition of interference, Bz.(msinp—sins)—=dA. If nsinp is sensibly greater than sins, Bx must be very small. And for any value of xsinp—sin:, there will be a distance Bx furnishing a wave of inter- ference, if the surface AB is unlimited; except only for the value xsinp—sin:-—0, when the ray Br ceases to diverge from the direction of the main refracted wave. These reasonings assume that the forces of the elementary derivative waves are the same in all directions. But it is probable that these forces are less in lines oblique to the direction of progress of the primitive wave than iz that di- rection. How far this is true could be casily investigated experimentally, by employing apertures less than the length of a haJf undulation in diameter, were it not that the extreme minuteness of such apertures (the mean length of a half undulation not exceeding one one-hundred-thousandth of an inch) would render the light too feeble for the purpose. Some material for the formation of an opinion on this subject may, however, be gathered from certain phenomena of diftraction first observed by Fraunhofer, more remarkable and more brilliant than any which have been thus far men- tioned. If a single very minute aperture will not furnish light enough for experiment, an assemblage of very many very minute apertures, closely grouped, may do so; and if these be so arranged that, for any determinate point in the shadow, they shall allow only such portions of the wave front to pass as conspire in their effects at that point, while the intervals between them obstruct those portions which conflict, we shall possibly find that the tendency of a wave originating in a single molecular impulse to expand equally in all directions, is much more decided than had been supposed. Fraunhofer’s original experiments were made with gratings formed by stretching an exceedingly fine wire across two parallel screws of a great number of threads to the inch—the threads serving to keep the wires equidistant. He subsequently employed gratings formed by cementing leaves of gold to glass and cutting them through in very fine parallel lines ruled with a sharp instrument. Instead of these, also, he employed similar lines ruled with a diamond on glass itself. The results of such an arrangement may easily be predicted. The image of an aperture closed by such a grating will appear bright, as though the obstruction were not interposed. But toward either side, in the direction perpendicular to the lines of the grating, will be found several points for which the part of the wave which the grating obstructs would if allowed to pass be more or less in conflict with those which it transmits; and which, therefore, are bright when the grating is pres- ent, and dark when it is absent. Suppose, for simplicity, that the open spaces and the opaque bars are equal in breadth. Let da, a, a, represent several of these open spaces, and 4, b, b, &c., the intermediate bars. A point, P, may be found from which lines being drawn as in the figure, and perpendiculars le: fall upon them from the edges of the aper- tures, as at c, c, d, d, will give cd = $A, db =$A, and therefore ch 2. The distances from P to the corresponding parts of the sev- Fig 45. eral openings will thus differ by an entire un- dulation, and besee the waves which reach P through them will be in harmony. 18 Lo UNDULATORY THEORY OF LIGHT. The distances from P to the corresponding parts of the obstructing bars will differ from the distances to the adjacent openings by half an undulation; and, accordingly, if the bars were removed, the wave which would proceed from those points would neutralize the effects of the former: but being obstructed, P remains illuminated by the resultant effect of all the first set of waves. Furthermore, since the position of P is determined by the condition that cd shall be the length of an undulation, it will be necessary to take P further from B for the longer undulations and nearer for the shorter. The different colors will thus be separated, and a perfect spectrum will be formed on the screen. Should the point P be taken so that cd is equal to two undulations, there will be no spectrum: for in this case ed will.be equal to one undulation, and as in the cases we have considered of a single aperture, one-half of each opening, a, will hold in check the other half. If we find still another point where dc is equal to three undulations, then ed will equal one undulation and a half; two- thirds of each opening will then be neutralized, but the remaining third will be effective; and there will be another spectrum, but less brilliant than the first. Tf dc = four undulations, the spectrum will again fail. If de — 52 it will return, and so on. If the bars are broader than the open spaces, there will. be a spectrum for beni, m being any integral number; until the light is too feeble, or until cd wd, n! being also any integral number. If the spaces are broader than the bars, there will be a spectrum for every integral value of min be==nd until a+b 2 — b ab : If, however, — is not integral, take g— the greatest common measure of a a+b g Put this value of 2 equal to m, and we may say generally that the mth spectrum will fail, and also the mth, m being, as before, any integral number. If @ and é are incommensurable, there could be theoretically no perfect spectra, or spectra of maximum brilliancy; nor would any speetrum absolutely fail: but a near approach to failure would occur for approximate values of g. All these propo- sitions result so obviously from the construction above given, that they require no demonstration. The same construction indicates a simple expression for the deviation of each spectrum from the directio.’ RB, of the radius of the original wave. For rep- resenting this deviation by 0, we have— , (a and 6 standing for the breadths of the spaces and bars severally.) and 6. Then »= will give the number of the first spectrum which will fail. sind=——. [17.| Putting 2 = 1, Aone fifty-thousandth of an inch, the length of the mean undulation, and supposing one thousand opaque lines to the inch, the formula gives us, by substitution, sind—0.02—sin 1° 9’. As the sines of small angles are very nearly proportional to the angles themselves, the deviations of the suc- ceeding spectra will be nearly the double, triple, &c., of this. And as thé de- nominator, a+, is the reciprocal of the number of lines to the unit of measure- ment to which 4 has been referred—in this case to the inch—it is evident that the sines of the deviations will increase directly as this number. With five thousand lines to the inch, the fifth spectrum will have a deviation of thirty degrees. The force of the derivative waves from minute apertures thus appears to be great even at large obliquities, when the obstructing effects of interference are removed. In the above expression for sind, if 2 be put equal to 1, and a6 equal to 4, COLORS OF THIN PLATES. 183 sind is unity, indicating a deviation of 90°. A grating, therefore, in which the number of lines to the inch is equal to the number of undulations in the same space, will produce no spectra. The same is true, @ fortiori, of still finer gratings. The spectra formed in this way by diffraction will easily be understood to form the best of all possible measures of the lengths of the undulations corres- ponding to the different colors. They exhibit very distinctly the principal lines of Fraunhofer; and these lines, as might be inferred as a theoretical necessity, preserve invariably the same relative distances from each other. 'The spectra formed by refraction afford measures, not of the relative lengths of the undula- tions in vacuo, but of those lengths as modified by the media of which the refracting bodies are composed. “App: ently these modifications are not simply proportional to the lengths of the undulations. Mr. Cauchy’s investigations upon dispersion show, as we have seen, that they ought not to be. Light veflected from finely ruled surfaces exhibits colors, as well as that which is transmitted through them. These efiects are produced by interference, and are explained upon principles analogous to those we have been considering. Some substances are naturally marked with sinuosities which produce these effects. A familiar example of this kind is seen in mother of pearl. Sir David Brewster found that an impression of the polished surface of this material taken in wax, exhibited the same colors as the substance itself. The effects produced by diffraction may be endlessly varied, by employing (instead of gratings) reticulations, and groups of apertures, of various figures, symmetrically disposed. Many of the phenomena are exceedingly rich and beautiful. We must content ourselves with the examples which have been given, and which illustrate the general principles on which they all depend. § VI. COLORS OF THIN PLATES. We will now proceed, very briefly, to apply the theory of undulation to the explanation of the colors seen in thin transparent plates ; or, as they are com- monly called, Newton’s rings. These, when scen by reflected light, are caused by the interference of the wave which proceeds from the lower surface of the plate with that which is reflected by the upper. Let us suppose, at first, for simplicity, that the light employed is homogeneous. Where the dark rings occur, there must be a difference of path between the interfering waves, of one- half an undulation. Now the wave which is reflected from the lower surface, passes through the thin plate twice; and that which is reflected from the upper surface does not enter the plate. - The difference of path is therefore twice the thickness of the plate; and this ought apparently to be equal to half an un- dulation, or to some uneven multiple of half an undulation. Let @ represent the thickness, and » any integral number; then— 20==(2n4+-1)x4A: and when n=—=0, 204), or 0= HA. It should seem, accordingly, that the first dark ring should appear, where the thickness is equal to one-quarter ef the length of an undulation. As the thickness increases toward 0=-5/, or diminishes twa 0=0, the light should gradually appear; aud when cither of these values is reached, we should have the maximun of brightness. The centre of the system should then be bright. It is not so, how- ever, but on the other hand is entirely dark. ‘The reason of this apparent dis- Ceetence with theory will be understood, when we recall the circumstance, thus far disregarded, that the reflection at the lower surface takes place as the ray is proceeding from a rarer to a denser medium; while that at the first surface occurs as the ray is passing from a denser and to a rarer. It has been already shown that, in the latter of these cases, the molecular move- ments maintain their original directions; while in the former, these movements 184 UNDULATORY THEORY OF LIGHT. are reversed. But to reverse the molecular movements of a wave is to change its phase half an undulation. Accordingly, at the points where 0=}A, and where the difference of path is $A, the difference of phase is $A+3A=A. This thickness should accordingly give a bright ring, and not a dark one; and so it is in fact observed to do. If there could be any hesitation about receiving this explanation of the phenomenon, it may be entirely removed by considering the following two experiments. My. Babinet having produced, by means of Fresnel’s mirrors, the fringes of interference already described, recived the interfering pencils upon a glass mirror, of which one half was transparent and the other half silvered on the back. The reflected pencils, thrown upon a screen, still exhibited the fringes. When both the pencils were reflected from the silvered part of the - mirror, or both from-the transparent part, the fringe in the middle continued to be bright, as in Fresnel’s original experiment. But when one of the pencils was reflected from the transparent glass and the other from the metal, the middle fringe became immediately dark. "The other experiment alluded to consists in introducing between the two lenses, in Newton’s experiment, a fluid having a refracting power intermediate between that of the upper and that of the lower glass. With a crown glass above, having the index 1.5, and a flint glass beneath, with the index 1.575, the oil of sassafras (index 1.53) or that of felaves s (index 1.539) introduced between will convert the dark rings into bright ones, and vice versa. In this case the rays, at both surfaces alike, are passing from a rarer to a denser medium. When the rings are viewed by oblique light the undulatory theory requires that their apparent magnitudes should be governed by the following law. If MM’ be the upper of two glass plates, with par- allel surfaces, enclosing a lamina of air between them, and if IPQSTVRK be the path of a ray incident obliquely at P, and reflected at the lower surface of the lamina at the point S, this will fall = sS=U jn at T with another, reflected from the upper ne surface at T, whose path is NOTVR. When sy the first is at P the other is at N, in PN, drawn from P perpendicularly to NO. These two have the same length of path in the medium MM’. Their difference of path will therefore be QS+ST_NO, or 2ST—NO. As the angle NPO is equal to the angle of incidence (which put == ¢,) and also KST, we shall have— sin? ¢ z 20 ; rice 28T=— , and aay Tsin:-—20tan:sin:—=20 cos: cose” Eo 1—sin” f Hence 28ST—NO=20 =20coss. But in order that there may be interference, ne difference of path must be a multiple of half an undulation. Henee— AA 20cosc—=nx HA, or 0=n——=nxAA.secr. [18.] cos: In which z is an odd number for the bright rings and an even number for the dark. At oblique incidences, therefore, the thickness at which a given ring appears Is greater than at a perpendienlar incidence, in the ratio of ‘the secant of ineidence to unity, or in the inverse ratio of the cosine of incidence to unity. But this is the law which observation had established before the theory of undulation had indicated its necessity. There is still one point to be attended to before the theory of the phenomenon is complete. The dark rings, as seen by reflection in homogeneous light, are absolutely dark, showing that the interference is total. But the amount ‘of light COLORS OF THIN PLATES. 185 in the two conflicting rays ought to be equal in order to produce this effect. Now, if we assume (what will hereafter be proved) that the amount of light reflected at either surface is in a constant ratio to the amount of light inc ident upon it, when the angle of incidence and the index of refraction are ‘themselves constant, we shall perceive that the ray which emerges after one reflection at the lower surface is feebler than that which is reflected at the upper: for the light incident upon the lower is already enfeebled by the loss at the upper, and the reflected ray is again diminished by the second reflection which occurs at its emergence through - the upper. But the light which is thus turned back at the upper surface is again reflected at the lower, and at its return another portion emerges through the upper. A series of reflections thus goes on between the two surf: 2CeS, each one contributing to strengthen the emergent ray; and the resultant of all these contributions is to bring the ray from the lower surface, in the end, up to exact equality with that which is originally reflected from the upper without entering the lamina. This will appear to be rigidly true if we consider the following statement. ‘lhe intensity of light is measured by the living force which ani- mates the mass of ether in which the molecular movements are going on. Let the masses in the two adjacent strata of the two media which act upon each other be distinguished by the letters m for the denser and m! for the rarer. Now it is true (as will hereafter be proved) that the velocity of molecular movement in a wave reflected from the separating surface of two given media, at a given incidence, bears a determinate ratio to the molecular v elocity i in the incident wave. Let this be represented by the ratio v: 1, the incident velocity being unity. Then the living force of the reflected wave will be mz?, and that whic it passes into the sag me dium and forms the transmitted wave will be m(1—z*). Ae- cordingly ~~ “(le ) is the square of the molecular velocity in the transmitted wave. et it be represented by w’. By reflection at the second surface, w becomes ew, and this, by another reflee- tion of the returning wave at the first surface, becomes vz. From the living force of the wave returning from the second surface subtract the living foree which it loses by the second reflection at the first, and the remainde vr, which is the living force transmitted through the first surface, will be m'vu? (L—v’). 2! And this, divided by the mass m, gives mew (1—v”) for the square of the first m component of the molecular velocity in the wave which reaches the eye from the second surface. In like manner v?« becomes vw by second reflection at the second surface; and v*u becomes v*u by the ieceediae reflection at the first surface. And the expression for the eet of the second component of the mn! molecular velocity we are seeking, will be ~ v8’ 2(1—~*). The next term will m am! ogee be — vu? (1—v*); and from a comparison of these three the law is evident. m By substituting ‘the value of wv, taki ing the square roots of these squares and making their sum, which is the re sultant molecular velocity of the wave emergent from the second surface, equal to v’, we shall obtain— v' =(1—2’) (vt torte... +0"), a pee The sum of the series in parentheses is 7 Hence v/v, or the reflected Uv —_— velocities, and consequently the intensities, of the waves reflected from the two surfaces, are equal. It is assumed in the foregoing that all these components agree in phase. But this is evidently true at the points where the dark rings, as seen by reflection, appear. For at these points the first return wave from the lower surface is in 186 UNDULATORY THEORY OF LIGHT. conflict with the advancing wave, which it meets at the first surface. This advancing wave does not change its phase by refraction, but the reflected part of the return wave does so, and is therefore in harmony with the advancing wave which it joins. The two accordingly conspire from that time forward ; their emergent portions at the second surface producing a bright ring by trans- mitted light, while their reflected portions, returning to the first surface, conflict with the zext advancing wave which they mect there. But at the points where the drzght reflected rings appear, the case is different. The return wave is in harmony with the advancing wave which it meets at the first surface, and its emergent part conspires with the reflected part of the advancing wave. But its reflected part, losing half an undulation, conflicts with the transmitted part of the advancing wave, and thus produces, by subsequent transmission through the second surtace, a ring partial y obscure, but not entirely so, from the great inequality of the conflicting molecular velocities. If we disregard the sucecssive advancing waves, and consider the successive values of the terms vz, v"v, 7u, &e., at these points, proceeding from a single original wave, we shall fiud them alternately positive and negative. Their emergent parts must be so likewise. And since they are decreasing, their sum takes the sign of the first term, which is positive; so that their resultant conspires with the wave reflected to the eye from the first surface. The components, simultaneously reflected to the second surface from the ‘first, form a similar series with signs reversed, and therefore have a negative resultant, conflicting with the wave emergent at that surface.* * This matter may perhaps be made more clear as follows: Calling, as above, wu the value of the molecular movement in the ray transmitted through the first surface, and v the ratio of reflected to incident light, the advancing and returning waves within the lamina will have the successive molecular velocities— 1. Advancing wave, uw, UU, vu, vou, eu, &e. 2, Returning wave, vu, vu, vu, vu, &e. And the squares of the velocities of the emergent components will be— . mi. ee area, eee eee ae uv m , Ist surface, —(v2u*—vtu*), —(v®u?—v*u*), —(vwe—ol?u?), —(vr4u?—vl6y?), &e. Vt mn ae ne 7? it / / Tlie oy ate m SY Fae Meda p MU cere a 2d surface, —(ur—viu2), —(viw—v'u?), —(e8u?—olu?), —(v?ue—v4u?), &c. mn +m m m Consider the movement in the incident wave to be positive. Then if the lamina were without thickness, the successive reflections still going on, the sign of the movement in the diminished waves successively emergent would ke always positive for the second surface, (for which the number of reversals by reflection is always even, ) and always negative for the first, (for which the number of similar reversals is always odd.) By giving greater or less thickness to the lamina, any difference of path may be introduced for either the rays seen by reflection or those seen by transmission. If @ represent the thick- ness, the differences of path which wiil exist, after the several successive reflections, will be 20, 40, 60, or generally 2m0, m being any integral number. If G=2 X $A, or 2O=2n X fA=—nd, a. being also any integral number, it is manifest that 2m$=mn2, being a number of complete undulations, cannot change the sign of the movement, whether 2 be even or odd. But if 26==(2n--1) xX}, then 2mP=m(2n-+1) x 4A will be an odd number of half undula- tions when m is odd, and an even number of half undulations, or an integral number of complete undulations, when m is even. Accordingly, the wave changes its sign for every odd value of m. Hence, if 26=n2, or =n XA, the movement will be negative for all component waves emergent from the first surface, and positive for all emergent from t! he second. Also, for 20=(2u-++1)X4A, or 6=(2n-+1) XFA, the signs will be alternately positive and negative at the first surface, and negative and positive at the second. For the first case, if we take the square roots of the squares of the’ emergent components given above, substituting the value of w, we shall have for the resultant v’ at the first surface, o'=(v2—1).(v--v3-Lv5....ad inf.) Whence v’=—2. The interference is therefore absolute, and the rings formed at these thicknesses will be per- fectly dark. ; For the rays emergent at the second surface we obtain the expression— w/=(1—v?).(1-e2-et....ad inf. )=—08), a, COLORS OF THICK PLATES. 187 In these explanations we have supposed the incidence perpendicular, and have regarded the faces of the laminw as parallel. In the case of Newton’s rings, neither of these suppositions is usually true; and the second can never be so. The inclination of the faces is not, however, great enough sensibly to affect the conclusions. In the case of oblique incidence, it is obvious that no ray reflected from the second surface can return to the same point of the first surface (supposed parallel) at which it entered. But the loss occasioned by this deviation is made good by the reflected component of some other ray parallel to the first, in the plane of incidence and on the other side of it rela- tively to the point of emergence. It will thus be seen that the colors of thin plates, for which, on the theory of emission, it is difficult to assign a cause which does not introduce as many dif- ficulties as it removes, are all necessary consequences, on the undulatory theory, of the simple principle of interference. 'The hypothesis devised by Newton to account for them has not been presented, since it is now generally abandoned, and the limits of these lectures would not allow its introduction. The colors of thick plates, of which some examples were noticed in the intro- ductory lecture, depend on causes similar to those above explained. In the case iustrated in Fig. 8, which we here introduce again for the sake of the explanation, if the light entering at o be composed of rays perfectly parallel, and be reiurned from the spherical sil- vered glass mirror, by a perfect specular reflection, to the perforated screen ¢, placed at the centre of curvature, it will all of it pass through the perforation toward 0, and no rings will appear; or at least only such as might be Fig. 8. due to the diffraction of the aperture, very much enfeebled by the reflection. But if the first surface of the glass be imperfectly polished, the specular reflection will not be perfect, but there will be a reflected cone of scattered light at the first incidence. This has nothing to do with the phenomenon. There will, however, be also a transmitted cone of scattered light, which will become at the second surface a reflected cone, having a virtual apex behind the mirror. Moreover, the light transmitted and subsequently reflected regularly, will, at its emergence after reflection, form a second scattered cone, the rays of which will have a virtual origin behind the mirror, though the apex of this cone is at the first surface. The condition of the light of these two cones is easily seen to be such as to produce interference ; hence the formation of the rings observed in the experiment. That is to say, the brightness of these transmitted rings is equal to that of the incident light. In the second case, the equation for the first surface is, v'=(1—v?).(v—v3--v— 07... .ad inf.) This may be separated into two equations, thus: Put v’=w-+-w’, Also w=(1—v?).(v-+-v°-+-v9-013_.. ad inf.) And w/=(v?—1).(v3--v7-+-vll-+-215__. ad inf.) Then wary) wr ‘vad wep ae ao ine value is positive, and shows that the rings by reflection at these thicknesses will be right. At the second surface, for the same thicknesses, we shall have, u/==(1—v?).(1—v®-+ 0105... .ad inf.). And, by proceeding as before, (1°) 2-2’ =u'/——_ f | ey Showing that the rings scen at these thicknesses by transmitted light are obscure, but not dark, because u’, which embraces all the light transmitted, Las still a value, 188 UNDULATORY THEORY OF LIGHT. In the other case, it will be observed that the rays I and I’ undergo repeated reflections between the surfaces of the plates—a portion of the light escaping and being transmitted at each reflection. If the plates are of perfectly equal thickness and all the surfaces perfectly par- allel, there will be no interference. Suppose, how- ever, that one of them is slightly thicker than the other. Then, if we attend first to the transmitted rays, T’, T’, we shall see that the path of T, after incidence and up to final emergence, is made up of three times the thickness of the first plate, once the thickness of the second, and once the distance between the plates. Put 6 for the first thickness, 0’ for the second, 6 for the distance between, and L for the length of path. Then— Fig. 9. L=36--6!--o. Tracing back 'T’ in the same way, and denoting its length of path by L', we have— L'=0+36'-+6. Hence L’/—L=2(6’—0). And when this value is so small as to be comparable to the absolute thicknesses which produce the colors of Newton’s rings, similar colors may be seen here. If we attend to the reflected rays R and R’, we shall see (employing the same notation as before) that— L==46--20. L'=20+20'+20. Hence L’/—-L—2 (0'—0), as before. It will be noticed that there are other rays, as 7 and ¢, which do not form tints, their differences of path, as compared with R, R’, or with T,'T’, being too great. §. VII —POLARIZATION BY REFLECTION AND BY REFRACTION. We will now proceed to give a physical theory of the phenomenon called polarization of light, and of its production by reflection and refraction. It has already been hinted that the phenomenon itself consists in the determination of the molecular movements in the suecession of undulations which constitutes a ray or beam of light, to one constant azimuth, or definite direction in space ; those which exist in common light being distributed impartially through all azimuths. In order to simplify the problem of the influence of reflection upon molecular movement Mr. Fresnel commenced this investigation by consider- ing first the case of a wave polarized already in the plane of incidence. In such a wave the molecular movements are (for reasons which will appear here- after) presumed to take place in a plane whch is at right angles to the plane of polarization. At the reflecting surface, they are therefore coincident with the surface itself. If the ray is passing from a medium of less refracting power into one of greater, we must suppose that the ether possesses either a different elasticity, ora different density, or both, in the two media. Mr. Fresnel assumed a difference of density without a difference of elasticity. He assumed, secondly, that in the common surface or stratum bounding the media, the movements parallel to the surface are common to both media, so that the components of velocity in the incident and refleeted wave, parallel to the surface of reflection, are together equal to the component of velocity in the transmitted wave parallel to the same surface. Or, if unity represent the incident molecular velocity, o POLARIZATION BY REFLECTION. 189 that of the reflected wave, and w that of the transmitted wave, we shall have the equation, 1+v=w With these suppositions let Ie, Ie be the bounding limits of a mass of the ether, along which an undulation moves, meeting the reflecting ee MN ince. Let ch, eR’ be the nannies of the reflected undulation, and Cc 1 eT’ those of the transmitted undulation. Draw ch, ef perpe ndicular to Je,cT. Let cd be the length of the incident, and ef that of the transmitted undu- Fig. 47. lation. Draw ad, gh parallel to cb, ef, respectively. We may regard the incident undulation as a mass whose bulk is the prism abcd, and de: isity d, impinging upon a mass w hose bulk is efgh, and density 0’. Since the molecular movements in this case are im the the common surface of the media, the dreadths of the prisms, according to the second assumption foregoing, are equal to each other. Their lengths will be A ane A’, and their depths be and ef. Or, putting m and m! for their masses, :m!::bcX2x0: efi’ xd! Now, the wave lengths are proportional to the Gace of progress of the wave in the two media a, (which we may denote by Vand V’.) Hence, if we put + for the angle of incidence, and p for the angle of refraction, we shall have, 4:4’::V: V’:: sine: sinp. Also, ech=:, and cef=p ; from which we derive dc=ce.cost, and ef=ce.cosp. And substituting— m:m':: sintcos:.d : sinpcosp.a’. But, in the propagation of tremors through elastic media, the velocity of pro- gress is directly as the square root of the el: asticity, and inversely as the square root of the density. Or, putting < for the elasticity, v—<, and vem, ee be- 6 ing constant. Accordingly td ‘ 6:6'::=:=5; and, by substitution, : V2 vy? ,_Sin:cost sinpcosp sinrcose sinpcosp cose cosp m:m! ::——— : — 3 : : ; VW Ne ogintt caine: sine ; Bing: Now the living force in the reflected and transmitted waves must be equal to the living force in the incident ; or— mxV?=mxv*+m'xu*; that is, cost Cos cos cos Os oe a ee; or, (1—2?) OFF — CORP sine sine sinp sine sinp” From this, with the equation previously given, z= 1+, we obtain, by elim- ination, sin( — > 2cos:sinp \? ee ae ey [19.] [20.] sin( (¢-+p) sin(¢-+p) If, in order to embrace in the formula only the angle of incidence, we elimi- nate p from the foregoing by means of the equation sins—zsinp, we shall obtan— by 2 ie SEY and v= Tee) PMR V n?—sin2« + cose V n?—sine-+ cose When the incidence is perpendicular, «= 0°, sins = 0, and cos:=1. In this case, vaC— Sj) i and =(5)- The intensity of light is measured by the living force of the molecular move- ments, or by the mass multiplied by the square ‘of the velocity. As the mass 190 UNDULATORY THEORY OF LIGHT. is the same for the incident and reflected waves, their intensities are as 1? and v. When we compare the transmitted with the incident or reflected waves, we B sais cose s ; must consider the masses. By multiplyingv? by ——, and w? by ae, their SSHssint sing ; COS? Laan 5 an sum will be found equal to ——, which is mx 1?, or the living foree of the sine incident. wave. : et cose cos ae : For perpendicular incidence m= a and m!'= = become infinite; but their sine - sing ratio remains finite; and as they are not expressions for the absolute values of the masses, but only of their relative values, their ratio only is needed. By replacing sin: by its equivalent xsinp, we have— ‘1 (HOOBG. 1COSIor ye eOR? m: Mm! 33-——3-—-- 31 -— 1 COse :: COSe: meOSe ; asinp sine 7 which, when cos:=cos0°—cosp=—1, gives m:m'::1:n. And the sum of the intensities at perpendicular incidence is— (x—1)? dn (n+1)? f ——~, 2 == = go l=1xl’, (a+1) (w+1) (+1) which is the intensity of the incident wave. If now we consider the gencral value of v?, given above, we shall see that v increases with the increase of the angle of incidence, and becomes equal to the total molecular velocity of the incident wave, when :—90°. For, at this inci- dence, sin’: —1, and cose=0. Henec— Shae Vv ne—12 = -) == 1 s"and 27 Vv?—1 For intermediate incidence, we may transform the expression thus: a ( V (x? — 1) +c0s*—coss y Ixv?stnaxv’= 9 v= V (ne? — 1)+cos*e+ cose- The value of the radical diminishes with the increase of the incidence; but . . ee . >a > a . . 2 it diminishes less rapidly than cose. For, the form of a binomial square being— q g a+ 2ay+y", if we put 2ay4+y’—= constant, it is evident that as x diminishes, y must increase. Fatting, therefore, cos: in place of a, we shall have— cos’: + 2ycose+ y” = cos (n?—1), or, 2ycost+y’=x’—1=constant ; and as cose diminishes, the other part of the root of the radical increases, so that the value of the entire radical diminishes less rapidly than cose. The numerator ef the expression accordingly increases with increase of incidence, and the denominator diminishes: and both these changes increase the value of ». Hence, the amount of light reflected increases from incidence —0° to inci- dence —90°. It is worth observing that the expressions we have obtained above for the molecular velocities of the reflected and refracted wave, are also deducible directly from the ordinary formule for the impact of elastic bodies. These formule, (employing m and m’‘ for the masses, as above,) are— m—m' 2m 0 and w= Sar ae m+n m—+m If, in place of m and m’, we substitute the values found for the masses, viz : mae, and m'="“, the foregoing formule will be reproduced. sine sinp POLARIZATION BY REFLECTION. 191 Let us next examine the case of a wave polarized in a plane at right angles to the plane of incidence. In this case, the molecular movements are in the plane of incidence. ‘The expressions for the masses will be the same as before ; but the components of the molecular velocities parallel to the reflecting surface are to'be taken, instead cf the velocities themselves. These components are, for the incident wave, 1 Xcos¢; for the reflected wave, v’ Xcose; and for the trans- mitted wave, w/Xcose : and the assumption of Fresnel is— (1+ 0')cose= w/cosp.* * Tn the attempt to apply the theory of undulation to the case of reflection and refraction at the surfaces o: crystalline media, it has been found more satisfactory by Profs, McCullagh and Neuman to employ the following assumptions, viz: I. The vibrations of polarized light are parallel to the plane of polarization. Il. The density of the ether in both media is the same as in vacuo. III. The vis viva-is preserved. IV. The resultant of the vibrations is the same in both media; and therefore, in singly refracting media, the vibration of the refracted ray is the resultant of the vibrations of the incident and reflected rays. On these principles, the case of reflection in the plane of polarization is simp'e. Let the refracted ray be extended backward, and it will divide the angle between the incident and reflected rays (which equals 2c) into two parts, which are, respectiveiy, :++p and c—p. Upon this retroduced line as a diagonal, if a parallelogram be constructed with the incident and reflected rays as sides, this diagonal and these sides will be proportional to the amplitudes, and therefore to the velocities, of the mo'ecular movements which are perpendicular to them severally. Employing then, as before, unity and the symbols v and wu to designate these velocities, we shall have directly— sin(c—p) sin2z == — =, w=... sin(t+p) sin(t+p) In the case of reflection in a plane at right angles to the plane of polarization the vibra- tions are al] parallel, and the fourth principle above gives— 1+-0'=w’. Also the third principle gives (m and m’ representing the masses of the ether put into mo- tion in the contiguous strata of the two media)— m(1—v’?)—m'u'®, These equations lead to the values— m—m' 2m / / v=- . i= mem’ m—en’ The same values may also be deduced from the laws of impact of elastic bodies According to the second principle, the masses m and m‘ ure proportional to their volumes ; and these volumes have been found in the text to be proportional to sinzcose and sinp cosp. Substituting these expressions in place of m and m’ in the foregoing fractions, we shall obtain— 2sin@e C ~ tan(e-+p)’ e ~ sin(i+p)cos(e—p) tan(¢-+p) coszu-+-cos2p) ‘ Comparing these values with those of ihe text, we find those or v alike, but with reversed signs and interchanged—that which represented the velocity of molecular movement nor- mal to the plane of polarization before, now denoting the velocity of movement in the plane, and v.v. In the expressions for the transmitted rays there is a difference which results from the adoption of the second of the principles foregoing, making the densit of the ether in the two media the same, which is not the supposition of the text. Z However strongly on some accounts this view of the subject may seem to recommend itself to our accepiance, it introduces a difficulty (elsewhere noticed) into the theory of double refraction, which has never yet been met, and which scems to have been singularly ignored by many who have engaged in this discussion. 7 hee In order to facilitate the comparison of the values of the several expressions foreroine they may be reduced to a simple form of common denominator, when they become— eee 1. For the case of vibration in the plane of reflection— ,__tan(¢—p) } sin2 ___ sin2(t—p) __ 2sin2vcos(t—p) ~ sin2c+sin2p° ~ sinze-fsindp 2. For vibration normal to the plane of reflection— ,__Sin2i—sin2p ,_____ 2sin2e eee TEA CC eae DES E sin2v-++ sino sin2i-++sindp 192- UNDULATORY THEORY OF LIGHT. Combining this with the equation of living forces given above, and reducing, we obtain ficce results : py ae an(t—p y. ai =(, __ 2cossinp —__ z 3 C entra) nd = ( ea Petes Replacing, as before, the value of sinp by its equivalent derived from the equation sint—=zsinp, we arrive at the following values which embrace only one variable: V 72 —sin®: — n2e0sc)\2 2cOst 2 - = ee) ; and wz? = ——— —). [25.] [26.] V 2 —sin®e-+ n2cose V n2—sin®:-+n2cose The following forms are convenient for discussion : 1. For vibration in the plane of reflection— __ RCOSp—COst ee 2ncost neosp-+-cose ncosp--cose 2. For vibration normal to the plane of reflection— nCOSt—COSp ;__ Sncose ~ neost-Lcosp’ ~ neost--eosp" At a perpendicular incidence cose—=1 and cosp=1. Hence, in both cases, n—I1 2n =——, and u! = ; n+ n+ Thus z and w’ will always be positive, and v and wv’ will be positive when » is greater than 1 and negative when 2z is less than 1. This ought to be so, according to the laws of mpae* of elastic bodies, because, the density of the ether being by hy pothesis the same in both media, the masses iepcting ¢ on each other will be as sine to sinp, or as to iH As the incidence inercases, the variations of the value of v and v’ will be dissimilar. When vib.a.ion is in the plane of refiection and n exceeds unity, the positive term ncosp is necessarily aways meater than the negative term cose. Both these terms diminish as ¢ increases. If they dinumished at the same rate, the value of v would be constant. But as 4 is always giecater than p and neither excee ods 90°, the rate of diminution of cose is more rapid than iha: of cos :p, and the value of v increases with the incidence. The same is true when z is less than unity; only in that case the increasing value of v is negative. When the incidence is maximuni, or -=9L°, x being greater than 1, cose=0 and v=1; that is te say, the reflected is equal to the incident light. For the ainownt transmilicd in the same case, we have, at a perpendicular incidence— . Qn al And for 1=90°, or the maximum incidence, 2 beine greater than I ? Bs Ono ’ u=0. It is also apparent that the amount transmitted constantly diminishes as ¢ increases. When vibration is normal to the plane of reflection, the positive term in the value of 7’, which is neoss, is at fils gieater (2 being greater than unity) or less (7 being less than unity) than the negauve term cosp. But since at the maximum incidence cosi=0, there must be some value of ¢ which wvl give ncosi=cosp, or ncost—cosp=0. Accordingly, at this inci- dence no light wi:l be reilected. The two conditious— ncosi==cosp, and nsinp=sinz, give immediately— sinp=cosl, or 1-+p=90°. The incidence ¢ is the polarizing incidence; and we here sce that it fulfils the law of Brewster. At the maximum incidence, n being ae than 1, v‘=—1. The sign of the molecular movement, therefore, changes at the polarizing angle. The transmitted hight is im this case, at the perpendicular incidence, ) en w= ; n--1 And at the maximum incidence, u'=0, At the polemaie incidence, where, as me have just seen, coso=ncost, NCOSL /— ncosi--ncost POLARIZATION BY REFLECTION. 193 If we suppose the incidence perpendicular, we shall have, as before, Aye BV ate ae ; ‘—_ — ) , and w?=€ - ) . Aft incidence 90°, we have again, a+1 a+1. Ree Vn? —1 a v=) = 1s 9nd w=), Vne—1 The agreement of these formulas with those obtained in the other case, is what ought to be expected, since, at a perpendicular incidence, the direction of molecular movement can have no influence on reflection; and at 90° impact ceases. But if we examine the first value of ov! given above, we shall perceive that it does not constantly increase with the increase of the incidence ; for the denom- inator, tan (t+), becomes infinite when ¢+-+p—=90°; and at this incidence »/~0, or there is no reflection. If then, in the originally incident beam, there had been a succession of waves, some of them polarized in the plane of incidence, and the rest polarized at right angles to that plane, all this latter class of waves would, at this particular incidence, be transmitted, while a portion of the others would be reflected. The incident light, from the mixture of the two classes of waves, would be imperfectly polarized, or not polarized at all: but the reflected light would be wholly polarized in the plane of reflection. In the result just reached, we see a reproduction of the law experimentally established by Brewster, viz., that, at the polarizing angle, the transmitted ray is at right angles to the incident ray, or -+p—=90°. If we now take the case of a wave whose plane of polarization is in any azi- muth to the plane of reflection between 0° and 90°, we may apply the principles already illustrated, by decomposing its molecular movements into components, one of which shall coincide with the plane of reflection, and the other with the reflecting surface. If the given azimuth be a, the azimuth of the molecular movements will be 90°—a. ‘Phe molecular movement in the plane of reflection will therefore be cos(90°—a)—=sina ; and that in the reflecting surface will be That is to say, at this incidence the entire molecular movement normal to the plane of reflec- tion is transmitted. In this case the condition 14-v'=w' is always fulfilled. When vibration is in the plane of reflection it is fulfilled only for the perpendicular incidence. At other incidences the fourth principle of McCullagh and Neuman, quoted above, necessarily involves the truth of Fresnel’s assumption for this case, viz: (1++v')cosi=w'cosp. When x is less than 1, these formule fail for incidences beyond the limiting angle of total reflection. : ; The formule in the text admit of reductions similar to the foregoing. They thus become— J. For vibrations in the plane of reflection— sin2v—sin2p Asinpcose nr Mereteene ip Pexeicay se aa ei ee . sin2c-+sin2p sin2c-+sin2p 2. For vibrations normal to the plane of reflection— . sf SEI Mapp, @ 31a epee Oster pe) ~ sinQe-fsin2p" sin2v+-sin2p And for convenience of discussion: 1, Jor vibrations in the plane of reflection— _____"cost—cosp pas __ 6 COSe neosi--cosp ncosi--cosp 2. For vibrations normal to the plane of reflection— NCOSP—COSL 2COse — / 3 y= ———_ — neosp--cose ncosp--cose ‘The first of these values of © becomes zero at the polarizing angle, and is positive for all higher incidences, 13s {QA UNDULATORY THEORY OF LIGHT. cosa. The living force in the reflected beam (which we oh repuesent by R) will consequently be—the mass ae assumed for conv sin(t—p)\? tan(¢ =P) ls r= ) .cos’a + ) sin?a. [27.] sin(¢+p) tan(¢+ p) ‘The agreement of this result with our previous conclusions may be verified by making @ successively 0° and==90°. In the first case— 2 sln(¢— : tan(¢— Hie ( ( =e) ; and in the second, R= eae ( sy, ; sim(¢-++ p) ‘ ; tan(¢-+p) If a== 45°, sin’a= 4, and cos’*a=4. Consequently, eee (ase A, ey [28.} Ls aa ) cece ‘ 20. “& Asin(¢+ p) tan(¢+) : This might easily be anticipated by considering that, in the supposed oo the incident beam is equivalent to two beams, each having an intensity of 4, and polarized—one in the plane of reflection, and the other in the plane perpen- dicular to it. he reflected beam should contain one-half the force in each plane which it would have done had each intensity been = 1. Let there now be two beams each ==4, incident together, and polarized in the azimuths a and a’. From what has just been said, it is evident that the value of R will be— 9 sin No . is tan(¢—p ia (= a me .(cos?a+cos*a! ) +3{ (= e)y’ sin(¢+p) tan(: +p) In this expression, if a/=90°—a, cos*atcos’a'=1. Also sin?atsin?a’=1. R becomes, therefore, equal to the sum of the intensities of two rays each —$, polarized, one in the plane of incidence, and the other at right angles to it, ne matter what may be the value of a. If, then, any number of waves, in different azimuths, follow each other in so close succession as to blend their impressions upon the eye, and if their azimuths are so impartially distributed that for every value of « there is another = 90°—a, the forces in all these azimuths being equal, then the resultant effect of the whole must necessarily be— sin(t—p)\”__, stan(t—p)\? : lace) +2 ey =a [ 0. But this is the condition of common light. The formula just stated, there- fore, represents the living forces in the two principal planes, in a beam of com- mon light after reflection, the original force being taken == 1. When ¢4-p=90°, the second term disappears. The reflected'beam is then entirely polarized. It we decompose the second term in the value of R, above, into its factors, we shall have (disregarding the numerical coefficient, and omitting the expo- nent)— 0 .(sin?a + sin?a’). [29.] ps ie tan(:—p) __sin(¢«—p) cos(¢+p) [31.] tan(¢-+p) sin(s-+p)" cos(t—p) * ; The molecular velocity of the wave polarized at right angles to the plane of reflection appears thus to be equal to that of the wave polarized 7m the plane of cos(¢-- 0) reflection, multiplied by the factor —— i cos(¢—p) est value it can have) the numerator and denominator of this fraction are equal, with opposite signs. The sign does not concern us at present, as it has no effect upon the value of the living force in the wave. For all values of ¢ less than 902 (y being necessarily less than « when exceeds 1 1) the denominator is greater than the numerator. It follows that in the reflection of common light, a larger amount of living force will, in the reflected beam, be preserved in the movements Wher ¢==90° (which is the great- POLARIZATION BY REFLECTION. 195 perpendicular to the plane of reflection than iv those coincident with that plane; or, in other words, that the refleeted beam will be more or less polarized in the plane of reflection. In order to estimate the amount of this polarization, we must take the differ- ence between the two terms in the value of R. And if we desire to find the proportion of light polarized, we must divide this difference by the sum. Or putting P to represent this proposition : cos*(‘+p)' a ‘ . sin?(:-+p) j __ cos*(t—p)—ceos?(¢t+p) ae ~ sin’(:—p) (1+ cos*( tp cos*(¢—p )reos"( «tp ) [32] cos? t—o gin?((—p sin*(¢ p) (1 sin?(¢+p) Reverting once more to the case of a wave polarized in azimuth a to the plane of reflection, we shall perecive, by the formule, that after reflection it is still polarized, though not in the same plane as before; for the rectangular components of the molecular movement being unequally altered, their resultant must have a new direction. In the expressions, cos*(t—p) tee Soe) sin(t—p) tan(ec—p) . sin‘t—p) cos/t+p —=_| —————.. c08 a, v/==_. cect) Sirgela ee Ry EN +p) sin(e-+p) tan(¢+p) “sin(t+p) cos(t—p) the first is the molecular velocity normal to the plane of reflection, and the second is the same velocity zz the plane of reflection. The second divided by the first is therefore the tangent of the inclination of the molecular movement te the normal; or of the resultant plane of polarization to the plane of reflection. Putting this inclination = a’, we have _ sina. sing eos(t--p cos(¢+ fang == y see) ee B\ py [3334 COSa COs(t—p) cos(t—p ) If the reflected ray undergo reflection from a second mirror parallel to the first, its incident azimuth will be a’; and, after reflection, it will have another azimuth @”, of which the tangent will be , cos/t+tp) cos*(¢+p) tana’—=tana’. +"? =tana,— >. [34.] cos(t—p) cos?(t—p) And, as the law is manifest, we may say that after any number, x, of reflee- tions, the tangent of the azimuth will be tana —tana ( While cos(:-+p) has a value—that is, while :+p is more or less than 90°— tan™a will also have a value; or the plane of polarization of the wave will not be brought, by any number of reflections, into absolute coincidence with the plane of reflection ; but when ¢+p==90°, it will be so by the first reflection. cos((+p) . ‘ When ee is a small fraction, or at least not a large one, the plane of polarization will, after a few reflections, be brought sensebly into the plane of reflection. For instance, let ¢ be 45°, and also a==45°. ‘Then, for glass cos tty will be about 3 In this ey [35.] SSS Sone ov. cos(t—p) (index 1.50) p will be 28° nearly; and : 7: cos(t—p case one reflection wi!l reduce the azimuth to 16° 42’; two to 5° 9’; three to 1° 32’; four to 0° 28’; and five to 0° 84’. 196 UNDULATORY THEORY OF LIGHT. § VIIL—CIRCULAR AND ELLIPTICAL POLARIZATION BY REFLECTION. In all that precedes it has been tacitly assumed that the initial phase of the reflected undulation is a continuation of the final phase of the incident, or of the same reversed ; and also that the virtual origins of the elementary waves of which we suppose the resultant refle;.ed wave to be composed, are in one tiva- riable surface, whatever be the azimuth of the incident molecular movements. If these assumptions are entirely true, the expressions for the molecular velo- city of the reflected wave ought to correspond with observation in all cases. ‘These expressions, nevertheless, fail for the case of total reflection at the second surfaces of denser media, as will be apparent if we substitute the value of x, which, in the cas¢ supposed, is less than unity in the formule. == | —____—. V n2—sin®:-+ cose When sin®: x”, v? and v? each == 1; or the reflection is total. We know, experimentally, that it continues to be total for all higher values of ¢; but the radicals in the foregoing become imaginary. Mr. Iresnel, therefore, concluded that reflection in some manner modities the phase of the undulation. Experi- ment proves that it does so, and also that the degree of the modification depends upon the azimuth of the molecular movements, and upon the incidence. The conversion of plane into circular polarization by reflection in “ Hresnel’s rhombs ” has been deseribed. ‘Che manner in which this change takes place may now be understood. If the plane ray is incident in either of the principal azimuths 0° or 90°, its plane of polarization is not affected by reflection. But if its azimuth be 45°, it emerges from the rhomb after having undergone two total reflections circularly polarized. Now the plane polarized ray in azimuth 45°, is equivalent to two plane polarized rays of half the intensity in azimuths 0° and 90.2 And as these components would singly undergo no sensible change of plane by reflection, while jointly they produce a circularly polarized ray, we infer that one of them has been advanced or retarded upon the other by a quarter of an undulation. If the ray had undergone only one reflection in the rhomb, or if it had undergone three, it would have emerged neither plane polarized nor circularly polarized. If it had undergone four, it would have emerged plane polarized again, with a change of 90° from its original azimuth. Now, all these phenomena are represented by the equation [1] for the resultant of vibrations at right angles to each other, which is as follows : 9 ay 2 z = aS nen a “as ql? ? a V n2—sin2:-+-n2cost ay? +ara’—2aa'xycos0=a" asin". If we substitute for 0, which is the interval between the two compounded ; ; hiss : h ; undulations, the more convenient symbol ans in which 7 expresses the differ- ence of phase as a fraction of an undulation, the equation takes the form, 5 th be es h che h aly’-a'x —2aa'rycosen, =a a'sin2n— ‘ . “a . , . . ; This equation becomes the equation of a circle if we make a—a’, and h A =}, or an odd multiple of 4. It is then a’+y?—=a’. It is the equation of an : ; Leeks. 5 ellipse for any values of 7 if ais nota’. Hence the necessity of the con- dition that the original plane of polarization should be in azimuth 45°, that the components into which the velocity is decomposed in the principal azimuths . . u} . “fp h s may be equal. It is an equation of an ellipse when a=a’, if 7 is not == 4, : 2 , a re or an odd multiple of 4. The ellipse becomes a straight line if {hh or an odd CIRCULAR POLARIZATION. 7% multiple of 4. It is therefore evident that, at each reflection in the rhomb, one of the component waves is accelerated or retarded one-eighth of an undulation upon the other. The restoration of the plane polarization, after four reflections, in an azimuth 90° removed from the azimuth of incidence, may be understood by considering the following illustration. Let the arrow PP’ represent the amplitude of movement in a polarized wave at a given moment. Let this be re- solved into two rectangular compo- nents 45° inclined to it on each side, represented by the arrows QQ! and RR’. Suppose the molecule, at a given instant, to be situated at the point C* of its path. CP’ is the direction in which it is moving, and the length of the line is the extent of its range. By two reflections in Fresnel’s rhomb, or by any other cause, let the component IRR’ be so advanced upon QQ! that, at some future instant, the molecule shall have reached the limit of its range in the horizontal direction, and shall be about to return (as at R in the second system of arrows) when, in the vertical direction it is in the middle point, and going toward Q'as before. This would be in CO’, but for the horizontal displace- ment. In point of fact, it is at It. The vertical velocity, (represented by the dotted arrow Q’Q',) is at its maximum, and the horizontal velocity is zero. ‘The conditions are such as, in the section on vibration, are shown to produce : revolution of the molecule in a cirele. The path of the molecule will accord- ingly be RQ’'R’Q. After two additional reflections in the rhomb, the horizontal movement will be advanced over the vertical by another quarter of its double vibration, and will bring the molecule, in its progress from right to left, to the middle point, C", in the third system of arrows, at the same instant at which the vertical movement, in the direction Q’, brings it to the same point. The velocities are now both at their maximum, and are equal. The molecule takes the mean direction, PP’, between them, and the ray is plane polarized in an azimuth 90° from the original plane. Suppose the eye of the observer to be at E, the revolution of the molecule is dextrogyre, or, as it is also called, dextrorsum. Conceived as viewed in the oppo- site direction, it would be levogyre, or sinistrorsum. In the earlier history of this subject, some confusion arose from the fact that different observers applied these terms in different ways. Since observation, however, is only made upon rays approaching the observer, this is the point of view now universally adopted in naming the direction of gyration. It appears, then, that the advance of the left-hand component, by a quarter undulation, produces a dextrogyration, and vice versa. If the plane of original polarization were P’P’”, then, iv the resola- tion, RR! would be reversed, and the advance of RR’ would be the advance of the right-hand component, producing levogyration. In this case, after four reflections in Fresnel’s rhomb, the resultant plane of polarization would be PP’. If we distinguish, as positive, the azimuths to the right of the plane of reflee- tion, and, as negative, those to the left, we may say that a plane polarized ray in original azimuth —45°, is circularly polarized dextrorsum by passing through one of Fresnel’s rhombs; and becomes plane polarized again in azimuth + 45°, after passing through two. If the original azimuth be +45, the circular polar- ization is sinistrorsum, and the final azimuth of plane polarization, negative. One of these rhombs may, therefore, be used as a polariscope, to detect the direction of rotation of a circularly polarized ray. If two rays, one in azimuth +459, and the other in azimuth —45°, were to be reflected simultaneously in one of Iresnel’s rhombs, the two consequent big. 48. *The letters C, C’, C’’, are accidentally omitted from the diagram. They should be placed ou the dotted Jine at the intersections of the successive systems of arrows. 198 UNDULATORY THEORY OF LIGHT. gyrations, being in opposite directions, would produce a rectilinear resultant. In ; this case, suppose the molecule, M, to be in any part of the circumference in which either of the gyrations would cause it to revolve; it will be subject to the action of three forces: one, MC, directed toward the centre of its orbit, and the other two, represented by P and Q, equal and opposite. The two latter neutralize each other, and the molecule pursues the path MC. When the molecule is at M’, the tangential forces P and Q, which will then have the directions P’ and Q’. will not directly balance each other, but will have a resultant in the direction RC. And for all other points in the path of the molecule, as M"’, M’’, &c., the resultant of the tan- R eential forces will always be in the diameter, MN, of the Fig. 49 orbit. In Fig. 48 we have supposed the arrows PP'and P’'P’” to represent not only the positions of the planes of molecular vibration, but the direction of the move- ments. heir resultant plane is accordingly QQ’. If the direction of one of them, as of P’P”, had been opposite, the resultant would be RR’. If the two were in any equal positive and negative azimuths, greater or less than 45°, their resultant gyrations would be elliptic; but the ellipses, being equal and similar, and similarly situated to the plane.of reflection, while they are opposite in move- ment, would still produce the vibration QQ. And two movements in azimuths equally above and below 909, cither positive or negative, would in like manner produce the plane vibration RR. Now the condition of natural light is such that, for every azimuth of its successive plane vibrations, as PP, producing, by total reflection, a gyratory molecular movement, whether cireular or elliptic, there will always be found another which will produce an equal and opposite gyration. And, although these gyrations are successive and not simultancous, though, therefore, there is never, in this case, any real composition, like that illustrated in Fig. 49, neutralizing, im fact, the gyratory movements, yet the compensatory effects follow each other with such rapidity that, to our instru ments and our powers of vision, they are as if they did not exist. Common light cannot, therefore, be polarized by total reflection. Moreover, common light need not, in any case, be supposed to be made up strictly of plane. vibra- tions. It is only necessary to suppose its gyratory movements to be as impar- tially distributed as we have heretofore presumed its plane vibrations to be. If, however, we suppose a surface which is not a surface of total reflection to possess the power of accelerating or retarding one of the rectangular components of the incident molecular velocity over the other, then the reflected light will, in general, be elliptically polarized. For the two components are never equally efleeted except in total reflection. Now there are very few substances capable of reflecting light which do not possess this power, and, accordingly, ellipticat polarization is the effect most usually attending reflection. As has been else- where stated, it is only those substances whose indexes of refraction are very near to 1.414 that produce a kind of polarization that is sensibly plane. This subject has been very thoroughly investigated, theoretically, by Mr. Cauchy, and experimentally by Mr. Jamin, with results mutually corroborative of each other. In order to clearly understand the experimental methods employed, let us observe that, if a plane polarized wave be supposed to be decomposed into two rectangular component undulations, the curves represent- ing these components will cross the common intersection of their planes in the same points. These crossing points may be called nodes. In the case sup- posed, the nodes of the two components are coincident. ‘The effect of reflection is, in general, (2. e., in all cases except those which have the index of refraction just now mentioned,) to throw the nodes of the components out of coincidence. And the original plane polarization will be restored by bringing back the nodes CIRCULAR POLARIZATION. 199 to their original coincidence, or by encreasing the discrepancy between them by repeated reflections until it amounts to half an undulation. In the first case, if the reflection were total, as at the second surface of glass. the plane of’ polari- zation, after restoration, would be unaltered. In the second case, on similar sup- positions, it would be changed 96°, When the reflection is not total, the resultant plane, after the reunion of the displaced nodes, will differ from the original plane in consequence of the unequal losses experienced by the two com- ponents in reflection. Both those methods have been employed in experimentally determining the dislocating effects of different media, at diiferent incidences, upon the rectangular components of plane polarized light. Many of Mr. eal $ more recent and élaborater -esearches have been made by the method first meationed. The esseatial part of his apparatus consisted in a double prism, formed of two equal acute wedges of rock crystal, cut parallel to the axis, and combined as shown in the figure annexed. The wedge ABC has the edge AB par- iP, LB Pi Fi A allel to the axis, and’ the wedge ADC has the edge DC A i $$ 2B perpendicular to the axis. The surfaces AB and DC are both parallel to the axis. If a plane polarized ray, PQ, C pass at right angles to AB through the middle of this Dipl lipase. a gi system, W here the wedges are equally thick, it will remain Qi plane polarized, and the position of its plane will remain Fig. 50. unaltered whatever be the azimuth of incidenec; the dis- locating effect of the double refraction of one of the wedges being compensated by an equal and opposite effect of the other. But if the system be moved the right or to the left, the two opposite effects will no longer be equal. This being a positive e crystal, the component of molecular movement parallel to AB will be in retardation of that perpendicular to AB, for the position of the ray, P/Q’. and will be in advance tor the position P'Q’. But if the ray has been alr ready dislocated by reflection, some part of the prism may be found which will produce an equal and contrary effect, so as to restore the plane polarization All that is necessary, then, to make this instrument a measure of the dislocation is to connect it with a scale and a screw movement, and to determine the value of the seale divisions. This last determination is easy. since a run which converts a plane polarized ray into a ray plane polarized with a difference of azimuth of 90°, is equivalent to half an undulation. Mr, Jamin’s apparatus accomplished this change in twelve complete turns of the screw. Smaller divisions were measured by the graduation.of the serew-head, of which there were two hun- dred divisions to the revolution. he deli icacy of the contrivance may be appre- ciated from this statement. It is known as Mr. Jamin’s “compensator.” It would occupy too much space to attempt here to give a full account of Mr. Jamin’s interesting researches, or of the methods employ ed by him auxiliary to that just described. The most important results of his investigations are the following : Nearly all transparent bodies produce, by reflection from their surfaces, a difference of phase between the component waves polarized in the two principal planes. All whose indexes of refraction exceed 1.414, advance the phase of the component polarized in the plane of incidence. All those whose indexes are below that value retard the phase of the same component. The difference of phase augments with the incidence from 42 at 0° to 4 at 90°, and becomes #4 at the polarizing angle. The variations are slow and almost insensible for some distance from either 0° or 90°. They usually become sensible near the polarizing angle. ‘The limits are nearer together as the polari- zation under that angle is wreater. Beyond these limits the polarization is plane, but imperfect. Within them it is elliptic. The two limits are nearer to each other as the index of refraction approaches 200 UNDULATORY THEORY OF LIGHT. 1.414. They wnite, for substances whose index has that exact value. Mr. Jamin found but two substances in which this condition is falfilled. They were a specimen of menilite, and a crystal of alum cut perpendicularly to the axis of the octahedron. Water and glass, which under ordinary light appear to polarize perfectly, are easily seen not to do so under the strong light of the sun. In the cases in which the index has the particular value just mentioned, the advance of phase at the polarizing angle is “brusque” from 4A to 2. This is very nearly the case with water and glass. teflection from the surface of metals always produces elliptical polarization. ‘The advance of phase is progressive from incidence 0° to incidence 90°. 'There are, however, very large differences between metals in this respect. § IX. ROTATORY POLARIZATION. We are now perhaps prepared to understand the reason of the rotation of the plane of polarization of a ray transmitted along the axis of a crystal of quartz. We have seen that Fresnel, by an ingenious combination of prisms, succeeded in demonstrating the existence within the crystal of two cireularly polarized rays, gyrating in opposite directions. And we have seen that the resultant effect of two opposite gyrations is to produce a movement in a plane. ‘Phe gyratory movements within the crystal are then not actwal but virtwal—in other words there are forces constantly tending to produce these gyrations, which hold each other in equilibrio or at least nearly so. We must consider these forces as suc- cessively traversing all azimuths within the length of each undulation. If the wave were of the same length for both gyrations, the forces being presumed equal, the molecular movement would be constantly rectilinear, and the plane of polarization would not change. But, as the plane does in fact change, we are led to infer that the undulation lengths for the two rays are ot equal. The annexed figure may serve to illustrate the mutual action of these rays. Suppose MADB to be the orbit in which a force P tends to urge a molecule, M, to revolve around the centre, C, to which it is drawn by the foree MC. Suppose the equal force Q to urge the same molecule to describe the same orbit in the opposite direction. 'These forces holding each other in equilibrio, the molecule will follow the direc- tion of the third force, MC. Now suppose the force Q suspended, the molecule will take the direction of the circle ADB, and will continue te revolve in it so long as the force P (supposed always tan- gential) continues to act. But its movement will impart to the molecule next below it a similar motion, and that to the next, and so on; so that, as these successive molecules take up their movement later and later, there will be a series in different degrees of advancement in their several circles, forming a spiral; and when the molecule M shall have returned to its original position, the series will oceupy a position like the curve MEFLN‘OR. If now P be supposed to be in turn suspended, while the force @ continues to act, the effect of @ will be to produce a contrary spiral, which may be represented by MSKTV. If MD be a diameter of the circle MADB, drawn from M, and DNHN’ be a line parallel to the axis CG of the cylindrical surface which is the locus of the spirals, then, if the undulation lengths are the same for both movements, the two spirals will intersect DH in the same point, the intersections marking the completion of a half uadulation for each. But if these lengths be unequal, the intersections with DH will take place at different points, as N and N’. Let now a plane intersect the cylinder at any distance below MADB, as at INDEX OF ROTATORY POLARIZATION. 901 FE, parallel to MADB. It is conceivable that this plane may be made to pass through the point where the spirals intersect each other. If I mark the point of intersection, and we draw the tangents IP’ and 1Q’ in the plane of the circle LHI, then there will be a molecule at the point I which will be in the cireum- stances of the molecule in Fig. 49 at the point M—that is to say, solicited by three forces, of which two, IP’ and IQ’, are equal and opposite, and the third is directed in the line 1G toward the centre. The molecule will, therefore, move in this line, and not in a circle; and if the plane of the cirele EHIH’ be the bounding surface of the crystal, or the surface of emergence of the light, IG will mark the azimuth of the molecular movement of the emergent ray. But if the plane of KHIH’ do not pass through the point of intersection of the spirals, it must cut each spiral in a different point. ‘The figure is drawn to represent this more general case, the points of intersection with the spirals being severally Land K. By joining LK, and drawing the radius GI perpendicular to it, GI will bisect the angle LGK, and M’, at the intersection of GI and LK, will be the position of the molecule in the plane EHLIK, which, if the tangen- tial force P only were acting, would be at L, and if the tangential force Q only were acting, would be at K. The tangential forces acting at the moment on this molecule will not be represented by IP! and IQ’, but by tangents at K and L, like RP’ and RQ’ in Fig. 49, in which figure the position of the molecule M’ corresponds to that marked by the same letter in the present figure ; but in that figure the resultant of the tangential forces is RO, directed to the centre, and in this it will, in like manner, be IG. Now, as DH, the distance between the planes ADB and EHLI, is a larger art of the length of an entire turn of the spiral MSNK than of the spiral {i LN’, the line GI will fall on the right of GH, the position it would oceupy if the two undulations were equal in length. We may therefore say, as before, that if the plane EHI were the surface of emergence of a ray from a crystal, in which it had been subject to the action of the forces supposed, its plane of polarization, GI, would be turned toward the right from its original azimuth. ‘The plane of polarization turns, therefore, in the direction of the winding of the closest spiral, or of the ray of shortest undulation; but it turns in the direction of the gyration of the ray of longest undulation. This rotation of the plane thus demonstrates that the two rays advance with unequal velocities in the axis of quartz—a remarkable fact which is not true of any crystal which produces plane polarization only. It also enables us to determine the relative velocities, or to ascertain the index of rotatory polarization. For since GI bisects the angle between the points K and L, which mark the relative degrees of advancement of the two rays in their respective rotations, if we take a thickness, 0, which produces a rotation of 90°, we know that the difference of phase is then one-half an undulation. If 4 de- note the length of the longer undulation, and /’ that of the shorter, then— 9 0=mi=(m+ 4)’; or Ze: aonen zie ; A m 2m 0 : ; : As ym and A may be determined by experiments on refraction, the value of mis known when @ is measured. By pursuing this method, Mr. Babinet found the value of —==1.00003; a value which, small as it is, is the largest a known for rotatory polarization. : When light is transmitted through quartz at right angles to the axis, the emergent rays are plane polarized. My. Airy has proved that, for directions oblique to the axis, the polarization is elliptic, the ellipticity increasing from the direction perpendicular up to the direction parallel to the axis, where it becomes circular. 202 UNDULATORY THEORY OF LIGHT. It is dificult to conceive exactly the physical action by which rotatory polari- zation is produced. But there is no difficulty in imagining such a decomposition of the molecular movements ina plane polarized ray, as shall represent the relations which exist after the rotatory polarization has been established. We have seen that when a plane undulation has been resolved into two equal rectan- gular components, if the nodal joints of these components become dislocated by a quarter of an undulation, the resultant will be a movement in a circular orbit. We have also seen that when the left-hand component is advanced by this amount, the motion becomes dextrogyre; and whea the right-hand component is advanced, it becomes levogyre. In order, then, to explain the co-existence of two opposite circular polarizations, we must suppose two sets of equal rectangular components dislocated in these two opposite ways. This was the hypothesis of Fresnel. In order to facilitate the conception, suppose the arrow P to represent, in quantity and direction, the molecular movement, at a given instant, in the origi- nal plane polarized wave. Imagine it to be R aresultant of two other waves, Q and R, one in front of it, and the other behind it, reach at the distance of one-eighth of an un- dulation. ‘these will then be a quarter of an undulation distant from each other. Let yi Q@ and R be again resolved, each into two ‘i equal rectangular components, in azimuths Fig. 52. +45° and —45°; Q, into g and7; and R into g’ andr’. Consider all these four component movements, at the instant supposed, and in the positions represented, to be at their maximum of velocity, in the direction of the several arrows denoting them. Then, if we consider the relative stages of advancement, or phases of: movement, of the pair g and 7, in respect to g/ and 7’, when both are referred to a common plane, it will be seen that the latter, though most advanced in position, are least advanced in phase For, if we conceive the curves of these waves to be drawn, the ascending node of g’ will be found in the plane of gr, and the descending node of q in the plane of q'r’. Hence, at the point where the wave g! begins, the wave g is one-quarter advanced. We have, then, two pairs of plane undulations, g and 7’ and 7 and q’, severally normal to each other, and with nodes dislocated to the extent of one-quarter of an undulation; g and 7 being the members of the pairs which are most advanced in phase. In the case of the pair g and 7’, the right-hand component being that which is most advanced, the resultant movement is a revolution sinistrorsum. In the case of 7 and gq’ the resultant will be a revolution dextrorsum. The values of these several components are determined from the general equation following, which is simply equation [3,] with the symbols changed: P*=Q7-_ RR? 20 eos’: By hypothesis R=Q, and 6—90°. Hence P?==2Q?, and Q=55 i 72 Q ie Again, Q@—=¢7’+7=2¢*. And i sm sue R P Also, R2==q?+47?—2q?. And g!’—=—-—=———-=3P. a: . te v2 vev2 * It appears, therefore, that the molecular velocity in each of the component waves 4,7, q',7', is equal to one-half that of P, as it should be, in order that the sum of their living forces may be equal to the living force of the primitive wave. Since the two circularly polarized rays in the axis of quartz have unequal INTERFERENCES OF CIRCULARLY POLARIZED RAYS. 203 velocities, there must be certain thicknesses of the crystal, which will make the difference of their paths equal to half an undulation, or to an odd multiple of half an undulation. It might be supposed, therefore, that in such cases inter- ference would occur, so that the crystal should naturally exhibit colors. The fact is not so; and if we consider the conditions we shall discover without diff- culty the reasons why it is not. If, in Fig. 52, the two components g a and 7‘ of one of the circularly polarized rays be supposed to advance or ga uin upon g’ and r, the distance between g and q’ will diminish until ¢ passes q’, ‘and the distance between 7 and 7’ will constantly increase. If e¢ represent the amount of advance, the distance of 7’ from the plane of gr in the figure will be c++4/, and the dis- tance of g from the same plane will be c only. Now, since g and q’ are equal, the resultant to which they are equivalent will fall half way between them, (page 167.) The same is true in regard to the resultant of 7 and 7’. But the point half way between g and q! will be situated at a distance frora the plane gr which is the mean of the distances of g and q’; thus— Distance of Tae Dh fin ee deel Distance of q/= wf ean ae dt) = dere In like manner— Distan i : Distance of ace 42 fMOm—Ue+ 4) eth That is to say, the resultants of the components in ec ach plane always coincide in position. We have next to consider their values. From the statements above it appears that the distance between r and 7’ is the entire distance of 7” from the plane gr—that is, —=c+44. And the distance between g and q' is the difference of the distances of g and q' severally from the same plane gr—that is, c— i. Tn the general equation for the resultant of two waves whose molecular move- ments are in the same plane, (equation [3,]) we must accordingly introduce the following values of 0: N Por g and q/, 9=27(5—2). For 7 and 7, 6=2z (5+4). Then putting Pp for the first resultant, and p’ for the second, and remembering that g— q’—=r=.’, the equations become, _ ee aN rah eh Choa Wee sary 78 ie Tey LO 2.805 8 sien O==T 7 err cos2n (eas er —277 sin275—= 2 1—sin2r, : Whence p?+p?=29?+27?—=con-tant. And the intensity of the light is inva- riable. By considering the foregoing values of p? and p”, however, it will be seen that they are severally variable, though their variations are always compen- satory. Ifé be any number of half undulations— P=P+q’ 2+ 2aq' cos: a(5— NS =P+q"?4+2¢q' sinda. — 2¢° (1+sinzc€), c i Sin2z —0 and =? But if ¢ be an odd number of quarter undulations, Sings—1 or—1; and either p?=—0, or p?—0. N Both p? and p”, therefore, pass through a succession of maxima and minima, the increments of the one corresponding always in value to the simultaneous 204 UNDULATORY THEORY OF LIGHT. decrements of the other, and each becoming periodically zero. It accordingly follows that if two circularly polarized rays, whose molecular gyrations are performed in opposite directions, be thrown together in a nearly common direc- tion, and observed by means of an analyzer, fringes of interference may be de- tected in the two principal azimuths, those in one of these azimuths being com- plementary to those in the other. Mr. Babinet made this observation, employing Arago’s prism to produce in- terfering pencils of plane polarized light ; which pencils he polarized circularly by means of “ quarter-wave lamin ”’ of mica placed in their paths. ‘The gyra- tions were made of opposite kinds in the two pencils, by placing the two laminz so that their principal planes should be at right angles to each other. As an analyzer, he employed a doubly refracting prism. ‘The fringes immediately appeared; thus furnishing a very interesting experimental corroboration of a theoretic anticipation. In the year 1845 Mr. Faraday communicated to the Royal Society of London a very remarkable discovery which he had made, of the apparent influence of magnetism upon light. If any homogeneous transparent body be placed under the influence of a powerful electro-magnet, it will possess the property, while the magnetism is maintained, of turning the plane of a ray of polarized light traversing it in the direction of a line joining the magnetic poles, in the same manner as such a ray is turned by quartz, or by liquids possessing the property of rotatory polarization. Mr. Faraday was at first disposed to attribute this effect to a direct action of magnetism on light, but that idea is now abandoned; and the received opinion on the subject supposes that the molecules of the medium undergo some modification during the continuance of the magnetic influence, which assimilates their action upon the ether to that of substances which pos- sess permanently the power of rotatory polarization. ‘The direction in which the plane of polarization was turned in these experiments depended on the direction of the electric currents. When the currents were reversed, the rotation was reversed also. It is impossible in this place to do more than to allude to this interesting discovery. § X. CHROMATICS OF POLARIZED LIGHT. We will now proceed to apply the principles we have been considering to the «xplanation of the colors produced in doubly refracting substances by polarized light. We have seen that double refraction consists in the generation of two waves of unequal velocity and of dissimilar form in the doubly refracting body. We have also seen that the molecular movements in the two waves are at right angles to each other. In consequence of the inequality of velocity the two rays into which a doubly refracting body divides a single incident ray may emerge from a surface opposite and parallel to the surface of incidence in different phases. If not entirely separated by the deviation of their paths, they may thus, so far as phase vs concerned, be in condition to interfere. But we have seen that interference is impossible between waves whose molecular movements are perpendicular to each other. If, then, by any contrivance, we can turn the planes of polarization of two rays which, by double refraction, have been made to differ in their length of path by half an undulation, or by any odd number of half undulations, so that these planes shall coincide, interference will be pro- dueed. It is this which is done in the arrangements which have been described, by which the gorgeous colors first observed by Arago in plates of doubly re- fracting crystals, are made to appear. In the first place, the lamina must be doubly refracting, in order that there may be two rays. In the second place, it must be thin, that the difference of length of path may be small. In the third place, the original light must be polarized, otherwise there will be two systems of interferences compensating each other, and obliterating each other’s effects. CRYSTALLINE PLATES IN POLARIZED LIGHT. 205 In the fourth place, the principal plane of the lamina should, in order to produce the most complete interference, be at an azimuth of 45° to the plane of original polarization—the two rays being, in this position of the crystal, exactly equal to each other. In the fifth place, we must observe the phenomena by means of an analyzer, which allows only the light polarized in a single plane to come to the eye, or which, like a doubly refracting prism, separates the emergent light which is polarized in one plane from that which is polarized in the trans- verse plane; otherwise in this case again we shall have the blended effeets of two compensatory interferences. Finally, the principal plane of the analyzer should, in order to produce the best effect, be at an azimuth of 45° from the principal plane of the lamina. The necessity of this condition may be readily deduced from the law of Malus. ‘The annexed figure may illustrate the changes which take place in the passage of the ray through the system. If the arrow, P, rep- resent the direction of an elementary mo- ter lecular movement of the original polarized ray, this movement will be resolved in the lamina into two movements at right angles to each other, and each inclined 45° to P, as shown by the arrows R, (the ordinary ray) and R, (the extraordinary.) Suppose these rays to emerge, without difference of path, from the lamina, and to be received upon a crystal of Iceland spar whose principal plane coincides with the direction of P. JThen R, will be resolved into R,, and R,,; and R, will be resolved into R,» and R... Ry and R,, will conspire, and Ry, and Ry, will conflict. The first pair, on the supposition we have made, will only be effective. The second will destroy each other. But R, is retarded (in the case of a negative crystal) behind R,. Let the retardation amount to an odd number of half undulations, and the arrangement of the illustrative arrows will be what is seen here. In this case the pair in the prin- cipal plane of the analyzer conflict and are Ree destroyed ; while the pair in the transverse R,- Plane conspire. And this represents what actually occurs, when the thickness of the 7 lamina is such as to produce exactly the peta amount of retardation here supposed. But since the undulations of the component rays of white light are unequal in length, the retardation which will be sufficient to suppress one color, will not entirely suppress the others. The ray R,o+Reo will not therefore be wholly extinguished, but will exhibit a color which will be the resultant of the unsup- pressed tints. Moreover, the retardation which produces perfect coincidence in the ray R,.+Re. for one color, will not do the same for the rest. There will therefore be a color in this ray also, in which the tint suppressed in the other plane will be predominant. It is to be observed, however, that when the plate is so extremely thin that the retardation suffices only to produce a difference of path equal to a single half undulation of the mean ray of the spectrum, or less than this, no color will appear. And the reason will be obvious, if we consider that, though the undulations of the different colors are unequal, their inequal- ities as compared with the total length of the mean undulation are not great. ‘The undulations of the middle violet, middle green, and middle red—the extreme and mean colors of the spectrum—are approximately in the ratio of the-num- bers 17, 21, and 26. A retardation of half an undulation of the ereen would therefore be about the fourth part more than a half undulation of the violet; and a fifth part less than a half undulation of the red. But a retardation of Jive half undulations of the green would be not far from s7x half undulations of the violet or four of the red. ‘The violet and the red, therefore, having in » Vig 53. 206 UNDULATORY THEORY OF LIGHT. this case lost (approximately) an even number of half undulations, will comport themselves, on being restored to the original plane of polarization, as if they had lost nothing at all; while the green, which has lost an odd number, will inter- fere and be extinguished. ‘The tint observed in this plane will accordingly be the resultant of red and violet; which, on account of the comparative feebleness of the violet, will be but a slightly modified red. In the transverse plane, however, the red and violet. will interfere and be extinguished, while the green compon- ents will reinforce each other, and produce their characteristic tint. It will be seen that the planes of polarization of the pairs of rays which pro- duce the complementary effects we have been speaking of, undergo two succes- sive movements. ‘The first movement is from the original plane of polarization. The second movement is, for one pair of rays, similar to this, and for the other, opposite. ‘The opposite movements restore the pair of rays which they atftect, back to the original plane of polarization: the similar movements carry the other pair of rays into the transverse plane. If there were no difference of path introduced in the passage of the lamina, or in the case that the ditference of path produced were always an even number of half undulations, two movements in contrary directions would simply restore the ray to its original condition, and produce no interference; while two move- ments in the same direction would extinguish it entirely. But if an odd number of half undulations has in any case been lost, two successive contrary move- ments will extinguish the ray, and two scmi/ar ones will restore its original con- dition. A single half undulation of the mean ray of the spectrum lost, will pro- duce a total, or almost total, extinction of the light, after two contrary move- ments; and will produce sensibly white light after two similar movements. Plates so thin as to produce a difference of path less than this, will fail to ex- tinguish the light in cither plane; but, as the thickness goes on diminishing, the original: plane will gain and the transverse plane will lose; until, when the thickness is zero, the light will be entirely restored in the first, and entirely lost in the second. It is common to speak of polarized light which has passed in this manner through a thin crystalline lamina, as having undergone depolarization in the lamina: an expression which seems to imply that it is restored to the condition of common light. his, however, is not true. There is one analogy between the cases, which consists in the fact that the vibrations of common light, when resolved into components parallel to two planes passing through the direction of the ray and normal to each other, are equivalent to those of the two rays into which the one original polarized ray is divided by the lamina. But the great dissimilarity of physical condition between the two is evidenced by the fact that in the one case the analyzer produces colors, while in the other it does not. ‘There is a particular thickness of the lamina which produces something more resembling depolarization. It is that at which one ray is retarded behind the other a single quarter of an undulation. In this case the analyzer finds an equal amount of light in both planes, and in fact in all planes; so that, so far as this test is concerned, the light is truly depolarized. But we have already learned that this amount of dislocation of the rectangular components of molecular movement in a plane polarized ray—the components being equal—produces circular polarization. And in fact, the most convenient mode of producing cir- cularly polarized light is to employ for the purpose what is called a “ quarter- wave lamina.” Such a lamina will convert a plane polarized ray, incident upon it in azimuth 45° to its principal section, into a circularly polarized ray. When the lamina which is the subject of experiment is so thick that the difference of path between the two rays amounts to many half undulations, then no color can be totally extinguished in cither plane. For it must be remembered that each color occupies a considerable space in the spectrum, and therefore has undulations belonging to it of many different lengths. The dif- CHROMATICS OF POLARIZED LIGHT—FORMULZ. 207 ferences may be slight, but slight values many times repeated become large values at last; so that two red rays whose phases are for several undulations sufficiently unlike to conflict, may, after a larger number, be nearly enough alike to conspire. If the numbers 21 and 22 represent the lengths of two undulations of green, after a retardation of eleven times the length of the former, the latter will have fallen half an undulation behind it. Thus, after a certain amount of retardation is reached, there will be found undulations of all colors im- partially distributed through all varieties of phase, and the chromatic phenomena above eee will cease. A general expression for all these phenomena may be found as follows: Let PP’ be the plane of polarization of the original ray ; QQ’ the princi- pal plane of the lamina; RI the conjugate plane ; QO’ the principal plane of the analyzer, which we will suppose to be a doubly refracting prism or rhomb of Iceland spar; and EE! its “conjugate plane. Draw PA, PB, perpendicular to QQ’ and RN’; BI, BG perpendicular to EE’,O0’; and AD, AI perpendicalar to 1’, OO’. ‘Then if CP rep- resent the velocity of molecular movement in the original ray, CA and CB will represent its equiva- lent components in the directions RR and Q’Q. If these components be further decomposed in the directions OO’ and ELE’, we shall have the original velocity CP represented by the four elements CG, CH in the principal plane, and CD, CF in the con- Jugate plane of the analyzer. tepresent the original velocity CP by V. Put the angle PCQ—a, and the angle PCO=,. Then the angle OCQ will be a—p. The tri iangles PC_A, PCB give CA=Vsina; CB=Veosa. Andthe triangles ACD = ACH, and BCF=BOCG, give CD= sinacos(a—p) ; ; CK=Veosasin(a—s); CG=Vecosacos(a—p} ; Big. 55: 7) i CH=Vsinasin(a—g). Mien, to find the resultant of CG, CH, the molecular velocities of the two rays emergent in the plane OO’—that is, of the emergent ordinary ray—we recur to the general equation— A? =a" +a" + 2aa' cos6. in which we must substitute for a and a’ the values of CG and CH given above; and for 0 the amount of retardation in phase of one of the rays behind the other in passing the lamina, which, if 4 represent the actual difference in length h ene of path, may be represented by 2 ene. The equation just stated may be con- veniently transformed by adding 2aa’—2aa’ to the second member, when it will become— AV?=@+a?-+ 2aa' —2ad' + 2aa!'cosd. Or A?=(a+a'?—2aa! oe ae —4aa'sin® 40. Substituting now the values of a,a’, and 0, we obtain— Re Ve [ [eosaeos(a—) -+sinasin(a — /) |’— 4sinacosasin(«— /)cos(a—) Which may be reduced to the following entirely equivalent forms: Wes ye [ costs + [cos?(2a—?) — costelsint, | : [37] A?—Y? | cost — [sin?(2a—/) — sin] sints) | , [38.] 208 UNDULATORY THEORY OF LIGHT. And by pursuing a similar course with the values of the components CD, OF, of the extraordinary ray, we shall obtain for its resultant intensity the two values, also equivalent to each other— Alta Vve ‘ee [sin?(2a—/?) — sin?gsin’ | [39.] 2s pen eouae A? —V¥ | sire —[cos?(2a—/3) —costajsintss | [40.] The intensity of the light in either plane is thus expressed in a formula of two terms, one of which is affected by interference, while the other is not. It is from the second that the colorific effects proeeed—directly, when this term is positive relatively to the first, and indirectly when it is relatively negative. This term may therefore be called the chromatic term, and the other the achro- matic. In considering these equations we observe, first, that if we add either value of A’ to either value of A’, the chromatic term disappears. The colors are therefore complementary; and if blended, the resultant is white. Secondly, since A?+A”—V?(cos?@+sin??)—V?, the sum of the two intensi- ties is equal to the intensity of the original ray; as it ought to be on the princi- ple of the preservation of living forces. , : ; ee ’ Thirdly, the chromatic effects being dependent on the factor sin’s for their character, will be dependent not only upon this factor, but also on the coefficient, sin?( 2a—?)—sin’p, or cos?(2a—C)—cos*}, for their guantity. Their greatest values will hence occur when this coefficient is maximum. There being two variables, a. and 8, if we make the first constant, we shall find maxima when cos2(a—?)=0, or cos2(?—a)=0. This gives a series of values for 2(a—) or 2(6—a’‘, which are 90° and its odd multiples. It is sufficient to consider the first, which gives a—P=45°, or 3—a—45°; from which e—6+45°, or a=S—45°. For the higher values we need only replace 45° by the numbers 135°, 225°, 315°, &c., successively. These values substituted in the coefficient all give the same result; hence all the maxima dependent on ? alone are equal; and it is obvious that they are independent of a, since a is not a function of 8. If we find, then, the maximum with reference to a, and substitute in the resulting expression, instead of 2, its value =a-45°, as obtained above, we shall have the maximum of the maxima, or the azimuths of QQ’ and OO’, in which the chromatic effects are the most brilliant possible. The solution gives sin(4o—23)—0. Hence 4a—28=0, or 180°, or 360°, &c. Contenting ourselves with the first value, and substituting for 8, we have 4a—2a490°=0, or a=F45°. Andas B=a+ 45°. we conclude that the arrangement in which the colors will be most brilliant is that in which the principal plane of the lamina is inclined 45° to the plane of polarization of the incident light, and in which the principal plane of the analyzer is in azimuth 0° or 90°—theoretic conclusions already anticipated by experiment. Fourth, attending to the first of the formule for A? and A” we see that the chromatic term in each is symbolically positive. If the term, therefore, is essen- tially positive in itself, the color of the ray is the color which the interference expressed by that term would produce, diluted with such an amount of white light as is expressed by the achromatic term. When the chromatic term in the same formulz becomes essentially negative, the color will be that which is left by subtracting its own color from the amount of white in the achromatic term. ‘That the subtraction will be possible—that is to say, that, when the chromatic term is negative, the achromatic term will always be the greater—will be evident on inspection. For examining the coefficient of the chromatic term within the bracket, it will be seen to consist of a positive and negative element, which elements, CHROMATICS—DISUCUSSION OF THE FORMULA. 209 being squares, have their essential the same as their written signs; but the negative element of this coeflicient is the same as the positive achromatic term. Hence the entire coefficient can never be greater than the achromatic term; and can only be equal to it in the single case when cosine or sine (2a—@)—=0. But h cel the chromatic term has another factor, sin’n, which is always less than unity, except when / is an integral odd number of half undulations. This, therefore, usually still further reduces the value; so that neither of the expressions for intensity can ever become negative. Fifth, if 8 remain constant, the value of the chromatic term will vary with a, and may even become zero when c=3. The force of the color will therefore undergo corresponding variations; and all color will disappear in the case just mentioned. ‘The same also will be true when a=$+490°, B4-180°, &c., &e. But though, in these positions of the lamina white light only is seen, the eolee reappears for values of a intermediate between 2 and 84+90°, 84+90° and B+180°, &c.; and this color is the same as before, since the sign of the chro- matic term does not change. When a is constant and ? varies, the color in like manner rises and descends in brillianey, having a minimum —0, at the values Ba, B=a490° and b=a+4180°, &e. Butas, in passing each of these successive values, the coefficient of the chromatic term, as is evident on inspection, changes its essential sign from positive to negative, or the contrary, the tints observed in the successive quadrants will be complementary to each other. Sixth, when a=0°, 90°, 180°, &c., the chromatic term disappears for every value of 3. In this case the light remains white throughout the entire revolu- tion of the analyzer, and one or the other of the achromatic terms disappears, for the azimuths 8—0°, P—99°, &c. Seventh, if we suppose the lamina and the analyzer both to remain stationary while the polarizer revolves, we shall see that the chromatic term changes its sign in the course of every quarter revolution. For example, since the change of plane of original polarization affects the azimuths of the lamina and of the analyzer equally, if we suppose a revolution of 90° in the negative direction, the coefficient cos?(2a—)—cos’?? becomes cos*(24+180°—90°—/)—cos*\ 90° +/2)=cos?(90°+2a—/)—cos?(99°+/3)—=sin?(2a—/)—sin’?. But, by reference to the two equivalent values of A’, [37.|[38,] we see that cos*(2a—)—cos*é— —(sin?(2a—j7)—-sin?7.) Hence, in the rotation of the plane of polarization through an are of 90°, the coefficient of the chromatic term passes from positive to negative or the contrary. If we suppose a revolution of 180° still in the negative direction, we shall find the sign once more the same as in the original po ee Thus, cos?(2a—/)—cos*? becomes cos?(2a+360°—180°—/)— cos’(180°+2)==cos?(180°+2a—)—cos?(180°+ 8)=-cos*(2a—f)—cos’3. If we suppose the rotation in the opposite direction, the alternations are similar. It is, hence, manifest that unless the light employed in these experiments be originally polarized, no chromatic phenomena will make their appearance. For unpolarized light being made up of successive undulations impartially distributed through all azimuths, those which are embraced within any one quadrant will neutralize the effects of those within the adjacent one, the complementary colors produced by each similarly situated pair succeeding each other with such rapidity as to blend their effects upon the retina. i : lest Ti Kighth, if we consider the factor sin’xs we shall see that, when A==$,, 2A, &c., the value of this factor is unity, which is its greatest possible value. ‘The chromatic effect-is, therefore, greatest when the retardation of one AY upon the other is an odd number of half undulations. If, in this case, ?—=2a, then A’?=Y", and A?—0. If P=2a+90°, A2—0, and A”?—V*. Supposing, there- 14s 210 UNDULATORY THEORY OF LIGHT. fore, the light homogeneous, the apparent planes of polarization of the emergent rays will be in azimuths 2a and 24+90°. h Ninth, if A=A, 2/, 32, &c., sin’ = 0; and the equations become simplified to the forms A’?—V"cosf; and A?—V’?sin’/, which are a reproduction of the law of Malus. 'The interposition of the lamina produces, therefore, no apparent change in the plane of original polarization. Tenth, if h==4/, 3A, 2, &c.—that is to say, an odd number of quarter .undula- : any ’ s tions—sin?x- becomes sin?45°—4. If, then, a—45°, the equations become— Fi 2 7 A?—V{ cos*8+4(sin®@—cos*/) |==3 V?(cos*3+sin?7)—3 V”. A®—V"*[sin?#+3(cos?3—sin’/) |= V(sin?8+ cos"? —=3V*. This result, being independent of the value of f, indicates an apparent depo- larization of the light. But in fact, it is the case of circular polarization, which we have already considered. It will be seen that it is necessary to the produc- tion of the effect that a should be 45°, in order that the two normally polarized rays may be equal to each other. In any other azimuth of the lamina, the polarization will be elliptical. If a lamina of erystal cut at right angles to the axis be employed, then in the direction of the central incident light the two rays are of equal velocity, h e : 2 : ’ and the factor aa No chromatic effects will therefore be perceived in the centre. But the rays which come to the eye converging from points not central, will differ in velocity, the difference increasing with the obliquity. As every plane which passes through the axis is a principal plane, there will be an infinite number of principal planes intersecting each other in the line which forms the path of the central ray, the projections of which upon the surface of the lamina will form so many radii diverging from a centre. And as all planes which are parallel to the axis, however placed, are principal planes also, it is obvious that the planes normal to these radiating principal planes will form cylindrical principal sections having a common axis. The plane ef polarization of the incident light can only coincide with one of the radiating principal planes. For that plane, the value of @ in our formule will be 0°. For the principal plane at right angles to that, the value of @ will be 90°. But we have seen that when a—0° or 90°, the value of the chromatic term is 0. Hence there will be two planes in which no color will appear for any position of the analyzer—that is, for any value of #. But the brightness of the light seen in those planes will undergo variations of intensity, as # varies, according to the law of Malus. For every plane except the two which have just been mentioned, the chromatic term will have a value—very slight in the neighborhood of those planes, and maximum at 45°. Very near to the centre, converging rays will have but a slight obliquity to the axis; and as a difference in length of path of one-quarter of an undulation or less fails to produce color in white light, there will be a central area which will be alternately white and black as the analyzer turns. rom this area will proceed at right angles the arms of a cross, alternately dark and bright, which, from the faintness of the color in the neighborhood of azimuths 0° and 90°, will have a very sensible breadth. At that degree of convergency which makes the amount of retardation for the most refrangible rays $A, will appear the first decided chromatic effect. And as, in a plate of uniform thickness, this convergency must be the same on every side, the color will take the form of a ring. This ring will be bright if the analyzer is crossed upon the polarizer; in the opposite position, dark. In order to observe the phenomena to the greatest advantage, it is best to employ homogeneous light. Then at greater convergencies, corresponding to retarda- RINGS SEEN IN CIRCULARLY POLARIZED LIGHT. 211 tions, or values of A, equal to 32, 3A, &c., will be seen, with the crossed analyzer, other bright rings; while at the intermediate convergencies, corresponding to values of h=A, 2A, 3A, &c., will be seen dividing rings, intensely dark. When white light is\used, the dark rings will be mainly occupied by the smaller rings of the colors whose undulations are shorter than the mean, or the larger rings of those which are longer. Since the retardation depends directly upon the convergency, and the place of a ring of any color depends on the equality of the retardation with the length of a half undulation of that color, it will be evident without further demonstration, that the longer the undulation the larger the ring, and wice versa. Rotating the erystalline plate in azimuth will produce no change in the phe- nomena. Tor in all positions of the plate there will always be one principal plane in azimuth 0°, and another in azimuth 90°. Rotating the analyzer will cause the rings to pass by progressive changes into the complementary tints. In this rotation ? becomes ==a and >a succes- sively for every one of the radiating principal planes which it passes, up to f—90°. The sign of the chromatic term changes, therefore, in every such case. And, as the sign changes also for S=a+90°, 6=a+180°, or @=a+270°, the color in all the quadrants will undergo similar changes simultaneously. ‘Thus, in an entire revolution of the analyzer, the colors will be four times successively reversed ; and for every position in which g—45° or any of its odd multiples they will disappear. The remarkable dislocation of the rings seen in erystals cut across the axis, when examined in circularly polarized light, has been mentioned. By applying the principles we have been considering we shall be able now to account for this singular effect. Suppose the crystal under examination to be a positive one, in which the ordinary ray has a higher velocity than the extraordinary. When a circularly polarized ray falls upon such a crystal, its component undulations, which, as we have seen, are at right angles to each other, with nodes dislocated by a quarter of aa undulation, will advance with unequal velocities, and the amount of their nodal discrepancy will be changed. This would not disturb the symmetry of the rings, if the change were similar in all the quadrants. By attending to the following analysis, we shall see that such is not the case. Let RR’ represent the direction of progress of a circularly polarized wave, of which the component invlecular movements are represented by PP’ and QQ”. The positions of these arrows are those in which the molecular movements of their respective undulations are assumed to be at their maximum of velocity, and the distance between them, upon the line RR’, is to be taken as represent- ing a quarter of an undulation. If we consider the effect of this composition of forces upon a molecule in the plane of movement of QQ’, we shall perceive that 919 UNDULATORY THEORY OF LIGHT. PP’ will there be about commencing the return movement, in the direction denoted by P”, while QQ’ will be in the height of its activity. The actual position of the molecule in the orbit described on QQ’ as a dia- meter will in fact be at M; but QQ’ and P’’ may be taken as representing the directions of motion at the instant supposed. Let ACBD be a plate of the erystal cut across the axis, and let the analyzer (not represented) have the plane of its free molecular movement parallel to AB. Draw CD at right angles to AB, dividing the crystal into four quadrants. As all the molecules in the wave front are actuated by similar movements, it will be sufficient to consider one of them in each quadrant. Let their several component forces be represented by the arrows marked p q, each pair having the same relations to each other as PP’ QQ’. It will be possible, in every quadrant, to draw a radius parallel to p org. Let these radii be drawn. Now, the radii being principal sections of the crystal, that component in each case whose direction of movement coincides with the radius, will (if at all inclined to the axis) be an extraordinary ray, and will be retarded behind the other compo- nent. An inspection of the figure will show that this will happen for p in the first and third quadrants, and for g in the second and fourth. Let the inclination of the rays to the axis be such as to cause a retardation of the extraordinary ray of one quarter of an undulation behind the ordinary. Then, by comparing the positions of the arrows which represent the relations of the components after emergence, it will be seen that the effect has been to bring the planes of maxi- mum molecular movement into coincidence in the second and fourth quadrant, and to increase the distance between them to half an undulation in the first and third. But these changes are just what is required to obliterate the nodal dislo- cations in both cases, so that the waves will emerge plane. The resultant molecular movements in the second and fourth quadrants will be obviously vertical and parallel to AB. At the inclination or distance from the centre, therefore, which produces this amount of retardation, will be seen in these quadrants the first bright ring. Had the incident light been plane-polarized, however, the first ring would not have appeared until after a retardation of a half instead of a quarter undulation had taken place; it would have conse- quently required a greater inclination of the incident ray, and its apparent distance from the centre would have been increased. In the first and third quadrants, the resultant molecular movement may be inferred by referring the two components p and g toa common plane. If qg be referred to the plane of p, for example, then, as the distance between them in the figure is half an un- dulation, the arrow g must be reversed, and the resultant movement will be horizontal. The analyzer will suppress this movement; or, in other words, at this distance in the first and third quadrants will appear a dark ring. In these quadrants there will not appear a bright ring until the retardation is increased half an undulation more; that is to say, to the total amount of three quarters of an undulation. Plane polarized light would have required a total retardation of only a half undulation to exhibit this ring. In the first and third quadrants, therefore, the bright rings are removed outward, and in the second and fourth they are removed inward, from the places they are seen to oceupy in plane- polarized light, for a distance corresponding to a difference of a quarter of an. undulation. | From what has been said, it will be easy to understand why two crystalline laminze, of equal thickness, and cut from a crystal parallel to its axis, or equally inelined to the axis, when crossed upon each other, neutralize each other’s effects. Tor the original polarized ray is, by the first lamina, divided into two which we have represented by R,, R,. In the supposed relative position of the two laminz the ray R, passes without double retraction in the principal plane ot the second crystal, and the ray R, in the conjugate plane. After emergence, RINGS IN CRYSTALS OF TWO AXES. 213 and before analysis, therefore, the two rays may be represented by R,, and Reo, Which symbols show that each has been equally modified in its passage through the system, and hence, that they reach the analyzer without any differ- ence of path. In the foregoing formule, accordingly, A==0 for this case, and the chromatic term disappears. We also obtain an explanation of the effects produced by nclining the lamina to the incident light. In general, the increased thickness of the erystal which the rays will have to traverse at an oblique. incidence, will have the effect to increase the value of /, and the colors will descend, or take the tints belonging to thicker plates. But the new direction of the rays within the crystal may be one in which their difference of velocity is greater or less than that which belongs to the direction of perpendicular incidence. In this case the tints will descend more rapidly by inclining in one direction than they do when the in- clination is opposite; or they may possibly remain stationary, or rise on one side and descend on the other. We suppose here as before that the analyzer is crossed upon the polarizer Crystals of two axes, cut at right angles to either axis, will exhibit elliptical rings, the variations of velocity of the two rays being subject to different laws in the principal plane which contains the two axes, and in two other principal planes co-ordinate to that. When the axes are not largely inclined to each other, a lamina of the crystal taken perpendicularly to the line bisecting the angle between them will exhibit both systems at once. In these crystals neither ray obeys, in general, the law of Snellius. But there are three planes—those just mentioned—in which one of the rays obeys this law. ‘These three planes are, in the first place, that which passes through both axes; and, secondly, both the planes normal to the first, which bisect the angles between the axes. The terms “ordinary ray’ and “ extraordinary ray,” in the sense in which those words have been used, in speaking of crystals of one axis, are inapplicable in the present case. The following equation, deduced by I’resnel from the general theory of double refraction, expresses the relation between the velocities of two rays traversing the crystal in the same direction, but possessing the differing polarizatious produced by its double refraction : pov pola Aap. sagt ini, wey 2 (ae) singsing’. [41.] In this formula, v and 2’ are the two variable velocities; @ and ¢ are the Sne/- lian velocities (constant) in the two principal planes co-ordinate to that which contains the axes; and ¢ and ¢’ are the angles made by the common direction of the two rays with the axes themselves. It may be remarked that the rays whose velocities are here denoted by v and v', cannot be the two rays which proceed from one incident ray, since these two rays do zot pursue the same course within the crystal. This consideration is not important, when the divergence of the rays produced by double refraction is small, (which is the case with most crystals of two axes, and with ad/ for rays in the vicinity of the axes themselves ;) and therefore we may employ this law for the purpose of determining the forms of the colored rings, in plates cut so as to make it possible to observe both axes at once. Putting vv'=ae and v-+v'—=2 Vac, suppositions which are sensibly true near the axes, the formula gives— shining vy? (cay abhi: sya sere en ly.) ——)' —= ——— { —. ~— } sinvsing’ = ——__=— DS very nearly. v4 \ &e sing Bind tae gsing’,, (very ¥ As we propose to confine the inquiry to the immediate vicinity of the axes, where ¢ and ¢/ are small, we may take the angles themselves, or their chords, 214 UNDULATORY THEORY OF LIGHT. instead of their sines. Let these chords be r and 7’. Then the equation be- comes— Va 2 r= (vv), [42.] which, if :—v’ be made constant, is the equation of alemniscaie. 'The annexed figure represents a /em- niscate, or curve whose distinguishing property is that the products of every pair of radi vectores, drawn from two polar points, and intersecting in the curve, are equal to each other, and to a constant quantity. If PQ, the distance between the poles, Kie 87 be bisected at A. and PA made = gq, then the con- é stant value of PRx QR, divided by gq, is called the parameter, and may be represented by p. Put PR=z, QR=7’, AN=za, and RN=y. The construction gives, immediately— P=(q+e)4y; P=(g—2)+y": whence PrP=((q-+a) +9) ((q—2) +97) =P"e- Or P= (PietyyAgr=p¢_. [43.] In the ease in hand, the parameter is the quotient. found by dividing the second member of the equation for the velocities, in its last form, by g. ‘The value of g itself may be directly measured, if the chromatic image be thrown upon a screen, as was done by Sir John Herschel in his study of the forms of these curves; or it may be assumed at pleasure, from a knowledge of the angle between the axes. Thus, if ABUD be the lamina, and aa’, b6' the axes, then, to the eye at E the poles are a and & in diree- tions parallel to aa’ and 60’; and half their distance is the value of g. The rings, however, may be re- ferred to any distance, as EP; and the poles will then be at Qand R. The distance EP and the angle REQ are all that is necessary to determine g, which is now PQ. It must be observed, however, that for a projection on this scale, the value of the constant, or second member of the equation above, must be increased in the ratio of the square of the distance of QR to that of AB from the eye. When the direction in which the rays reach the eye is such that the differ- ence of path of the two rays is half an undulation, there will be seen, in homo- geneous light—the analyzer being crossed upon the polarizer—the first bright rine. When the difference becomes an entire undulation, the first dark ring will appear. The parameter of the lemniscate changes with every new ring. For the bright rings, the parameters will evidently form an arithmetical series, corresponding to the odd numbers 1, 3, 5, 7, &c. Por the dark rings there will be a similar series of values, proportional to the even numbers. The lemniscates are not perfect, (though some of them are nearly so,) because we have admitted some small errors into our assumption. The inner curves also will, in many cases, form ellipses around a single pole. It is obvious that this must be the case when the constant is less than g*. For ¢ is the smallest value that the product of the radii vectores can have; and when the parameter is not equal to g, there can be no lemniscate. i When the analyzer is crossed upon the polarizer, in observing these curves, if the plane of the axes is in the plane of polarization of the incident light, there will be seen a black cross intersecting the system symmetrically; the principal bar of which will coincide with the plane of the axes. The transverse bar will pass at right angles to this, half way between the poles. In these two Fig. 58. DOUBLE REFRACTION. 215 planes there is (in the position of the crystal supposed) no double refraction of the incident polarized ray. The light is therefore transmitted without interrup- tion, and being cut off by the analyzer, shows the dark cross. By rotating the analyzer 90°, the cross becomes bright, as with crystals of one axis. But when the crystal itself is turned in azimuth, while the analyzer remains in one of the principal azimuths, the arms of the cross break at the centre, two of them on each side forming together a curve. At 45°, the two curves present the appear- ance of opposite hyperbolas. To follow these changes analytically would require a larger acquaintance with the physical theory of double refraction than is furnished in what precedes. We will therefore, next in order, turn our attention to that subject. § XI. DOUBLE REFRACTION. We have seen that the double refraction of light is always attended with polarization. It is proposed now to attempt a physical explanation of this phenomenon. Refraction, in general, considered as a’ bending of the ray, is owing to a change in the velocity of the wave as it enters the refracting medium. When the refraction is double—in other words, when a single wave is divided by re- fraction into two waves—the velocities of the two waves must be unequal. It is presumed that this difference of velocities is owing to a difference of elasticity of the ether within the medium. But, inasmuch as the two rays often follow the same track, each with its own determinate velocity, while they remain quite distinct from each other, it is evident that their velocities cannot be determined by the elasticity of the ether éz the direction of their progress. It becomes therefore a necessity to assume that their molecular movements are transverse to the ray, and in the surface of the wave itself. The fact of double refraction is thus an incontrovertible proof of the truth of the doctrine of transverse vibra- tions, independently of the many evidences of the same truth derived from po- larization and the phenomena of interference. But inasmuch as, in a medium in which the elasticity of the ether varies ac- cording to a certain law, the elasticity will usually be different in each of the indefinite number of planes which may pass through a given ray, it follows that if the ray pursue a determinate course with a constant velocity, its transverse vibrations must be confined to some determinate plane. Double refraction in- volves, therefore, as an indispensable condition, polarization; and, as a general rule, plane polarization would secm to be the necessity. Experiment proves that these theoretic inferences are correct; and also that the planes of polarization of the two rays which originate from a single incident ray, in a doubly refracting body, are at right angles to each other. ‘Two ques- tions present themselves, therefore, for solution: First, how is the direction of molecular movement in a polarized ray related to the plane of polarization? and secondly, what cause determines this movement in the doubly refracting body, to these particular directions ? In regard to the first question, we may arrive at a conclusion, by considering the case of a erystal of one optic axis, like Iceland spar. If we suppose such a erystal to be ground to a perfect sphere and polished, a ray ineident perpen- dicularly upon any part of its surface will coincide in direction with the radius of the sphere. Such a ray falling upon a sphere of homogeneous glass would pass undivided through the centre. But with the sphere of crystal which we have supposed, there is but one diameter in which this will happen. ‘This is the diameter coincident with the optic axis; and in this direction there is no double refraction. If the incident ray is common or unpolarized light, (a supposition which is to be understood in all that follows,) the emergent ray will be unpo- larized also. And, as the molecular movements of common light are in all 216 UNDULATORY THEORY OF LIGHT. azimuths around the ray, it is evident that the elasticity of the ether in the crystal is the same in all directions at right angles to the optic axis. The mo- ment, however, that we depart from the pole of the sphere—maintaining still a perpendicular incidence upon its surface—a second ray makes its appearance. The light is now equally divided. A part, which we call the ordinary ray, still follows the radius and passes through the centre of the sphere. The other portion is bent at the surface, and crosses the diameter in which we found no double refraction, above the centre or between it and our first supposed point of incidence; that is, the point which we have called the pole. The deviation will be slight at first, and will go on for a time increasing, as we descend in /atitude; but will afterwards diminish till we reach the equator, when it will become nothing. But though the deviation diminishes, the double refraction increases ; that is to say, the difference of velocity between the two rays becomes greater and greater as we approach the equator, and in that plane attains its maximum. Both rays now pass through the centre; but one is so far behind the other that two images may be seen of any object ‘beyond, at different apparent distances from the eye. If the incidence be xot perpendicular, the ray which has always passed through the centre undergoes refraction according to the simple law of Snellius, in all planes and in all azimuths; but this is not at all true of the other. The inference is that the velocity of the first of these rays is always deter- mined by the same elastic force; which must be that foree which we have seen to be at right angles to the axis, or parallel to the equator of our supposed sphere. And here, in order to avoid error or confusion, let it be observed that the line which we have called the axis of this sphere is not ¢he optic axis of the erystal, but only one of the optic axes. All lines parallel to this are equally optic axes. In other words, the name optic axis is the name, not of a dine, but of a direction. Now if we once more follow, in mind, our ray at perpendicular incidenee, from the pole of the sphere to the equator, we shall see that there is no difficulty in imagining its molecular movements to be constantly parallel to the equator, pro- vided we suppose them perpendicular to that meridian plane (principal seetion) which passes through the ray and the axis of the sphere. The constant velocity of the ordinary ray is thus accounted for without difficulty. The velocity of the extraordinary ray being variable, its molecular movements must encounter a different elasticity in different directions of its progress. Moreover, as its plane of polarization is at right angles to that of the ordinary ray, its molecular movements should be so likewise. We have only to suppose these movements to take place zm the meridian, or principal section, plane, and we shall see that they will turn with the ray itself, as we pass from the pole to the equator: so that, while, in the first position, they are parallel to the equator like those of the ordinary ray, they are inclined to it at increasing angles as we descend in latitude, and become perpendicular to it in latitude zero; that is, when the ray is in the plane of the equator itself. Now this would make no difference in the velocity, provided the ether were equally elastic in all directions. As the velocity 7s variable, in point of fact, the conclusion raust be that the elasticity is variable also. In the direction of the axis we must assume it to be greatest, and in intermediate directions to possess an inter- mediate force. Now the plane of polarization of the ordinary ray (experimentally ascertained) is the principal section of the crystal. And as we have been compelled to con- clude that the molecular movements of this ray take place at right angles to the principal section, it follows that, in plane polarized light, the vibrations are at SURFACE OF ELASTICITY. ore right angles to the plane of polarization. This settles the first of the questions proposed above. ‘The second is less simple. If a polarized ray, whose molecular movements are in the direction OP, in the annexed figure, fall upon a lamina of doubly refracting crystal, whose principal section is MM’, it undergoes double refraction in every ease except that in which OP coincides with MM’ or NN’, the conjugate plane. The effect is the same, in seeming, as if the Jamina allowed no free passage for movement, except in these directions. The im- aginary structure presented in the figure is in ae- cordance with this idea. The undulations of which OP is an element, encountering such a structure, would be necessarily resolved into two movemeute, taking the directions of the open passages; and according to the laws of the resolution of forces, we should have OP? =OQ?+40R?, Or putting I for the total intensity of the light, and a for the angle between OP and MM’,— I= Icos*a+ Isin*a, which is the law of Malus. This illustration is given merely to facilitate the conception of the constant determination of the ethereal vibrations in crystalline bodies to fixed directions. The cause must be one more general than such a mechanical structure could pos- sibly be. ‘The theory of Fresnel, embracing all the cases of double refraction, is founded on the assumption that the elasticity of the ether may be different in the directions of three rectangular axes; and among the conclusions mathe- matically deducible from this assumption, is the proposition that, in a medium so constituted, the molecular movements of an incident ray will be unstable except in two determinate azimuths at right angles to each other. If they are not in those azimuths, or one of them, on entering the medium, they will be instantly ¢wrned into them; and thus the ray will be polarized in planes having different directions in the crystal. If we take a crystal of two axes, and form from it prisms, of one of which the edges shall be perpendicular to the plane containing the axes, while the others have their edges respectively parallel to the lines which bisect the angles between the axes, we shall find that, in the planes of refraction of these prisms, one of the rays follows the law of Snellius; but that the indexes of refraction for these are different. ‘These rays thus obeying the ordinary law are moreover polarized em their several planes of refraction. ‘Their molecular movements are therefore perpendicular to those planes, or parallel to the edges of the prisms, that is to say, parallel (by construction) to three determinate fixed lines in the erystal, each at right angles to the other two. ‘These velocities, then, determine the elasticities in the direction of three rectangular axes. Irom these as constants, Vresnel derived an equation expressing the elastic force in all intermediate directions. The three velocities are distinguished by the Ietters a, & and ¢, in the order of their magnitude—that denoted by @ being greatest. And elasticities being as the squares of the velocities which they generate, the three elasticities are a”, b*, and c?. Now if any line be taken which makes with the directions ot the elasticities a’, 0’, c?, angles represented by A, B and C, and if R denote the velocity which the elasticity in the direction of that line is capable of gen- erating, then we shall have the equation— R?=a?cos?A+07?cos?B-+-c?cos?C. [44.] Giving A, B, and C all possible values, Rt will have all possible directions ; and, considered as a radius vector, its extremity will describe a surface the 218 UNDULATORY THEORY OF LIGHT. squares of whose radii will be equal to the elasticities in their directions. This surface, therefore, Fresnel denominated the surface of elasticity.* The surface, as might be inferred from the principle of its construction, is an ellipsoid, of three unequal axes. Now, it is a point important-to be clearly conceived, that when, in a medium of variable elasticity, the equilibrium of forces is disturbed by a displacement of its molecules in a given direction, the resultant of elastic resistances excited is not generally in the line of the displacement. Were the displacement to take the direction of one of the axes of the surface of elasticity, the resistance would be directly opposed to the disturbance. But suppose it to be in the direction of some oblique radius; and, to simplify the matter, suppose this radius to be in a plane passing through two of the axes. Let then, in Fig. 60, ADBE be the section, passing through AB and DE, the axes of greatest and least elas- i ticity. Let, a molecular disturbance, which we will call 7, take place in the direction CF; and, for facility of conception, let us take the line FC itself to represent the resistance it encounters 7z this direction. AC is a, and DC isc. Now, the displacement 7, if it took place wholly in the direction of a, would develop a resistance proportional to 7a’, or equal to fra”, f being a constant. And if it took place wholly in the direction of ¢, it would develop a different resistance— frc?. But the Fie. 60, amount of displacement in the direction of @ is only reosA. And that in the direction of ¢ is only reosC. Also, as A=ACF in this case, and C=90°—ACF, we have rcosC=rsinA. Hence the resistances developed are fra®cosA, and fre’sinA. Now, the first of these expressions being the horizontal component of the resistance (as the ficure is drawn) and the second, the vertical, the second divided by the first will give the tangent of the inclination to a, which inclination we will call A’. Redes 2 a resin Ue dicks “an Al . [45.] JrvcosA a which is less than tanA —or the resultant is less inclined to @ than FC. A graphic method of determining the resultant, both in magnitude and di- rection, is suggested by this formula. TanA/ is a fourth proportional to a’, c’, and tanA. Calling KC radius (for present purposes) FK=tanA. Draw FR perpendicular to DE, and join RB. Join AL, bisect it in M, and draw MN perpendicular to AE, With N as a centre, describe the are EP. Then CE?= C=AC.OP. And CB=@=AC.CB. Or, @::er: CB: OP. .Draw; there= fore, PY parallel to BR, and QO parallel to AB. Draw FG perpendicular to FC, and the radius CO, through O, to meet it inG. OG is the resultant, and GCA=A’. The resultant force consists, then, of two components—one, equal and oppo- site to CF, and the other FG at right angles to it. This latter force deflects the motion of the molecule in FC, and turns it toward the shorter or longer axis, according as the movement is one of condensation or of rarefaction. And there ean be no stability of oscillation in this place, in any line which is not parallel Then ‘ * This polar equation may be referred to rectangular co-ordinates, by putting x, y, and z for the co-ordinates parallel to a, b, and c, respectively, and substituting the following values: Qo tela oadlee® iy Maio Og the ot Rex? y?-++-2*. CosA=yi cosB= 53 cosC= 5. Whence Rt=a?x?-+-b?y?--c?2z2. Or, (22-by?+-22)P=a2x?-+L 22-0222, which is an equation of the fourth degree, RESULTANT OF ELASTIC RESISTANCES. 219 toaorc. In either of those directions the displacement develops no deflecting force; since, in the former, cosA=1 and sinA disappears; and in the latter smA=1 and cosA disappears. The arrows illustrate the relations and mutual action of these forces, and the corresponding movements of the molecules. During compression the disturbing force is CF, and the movement from C toward F. The opposing component of the resistance is C’F’, and the deflecting component GF. While CE pre- dominates over C’T", the point of the arrow CFf—that is, the direction of the -molecular movement—will be turned nearer the direction CD. But when C’F predominates over CF, as in the return vibration, ©’/F represents the move- ment, and the deflecting force turns the point of the arrow C’F nearer the direction AC. The value of the resultant may be determined by means of those just given for its components, from the right angled triangle CGH. For this gives us, (putting p for the resultant, ) p= f*rra'cos’ A+ f2r*ctsinZ A ; or p=+/r V a'cos?A+c'sin2A- The equation of the surface of elasticity also gives us, for the value of the radial resistance (denoted by p’) P=? fr freco? A+ frb-corB-+ frecos’C. Or, as cosC==sinA, and cosB—cos90°—0, p'=fr(@cos?A+c?sin? A). Hence, if represent the angle GCI’, we shall have p! aco’ A-+e’sin2A a IR? Cosw—=—— - ee 46. e = V @eosA+cisin2A V aicos?A-+cisin2A [46.] c ' This simple ease has been examined in detail, in order to facilitate the conception of the more general one, which will now be attended to. Let a molecular displacement, 7, occur in any direction whatever. Let CF, Fig. 61, be the direction of displacement, and let it be as- sumed as the representative of the force developed in that di- rection. As in the former _ease, if this foree be resolved into three component forces in the directions of the several axes, the resistances developed will be fra’cosA, frb?cosB, A : SrecosC. |? According to the laws of the Fic. 61 composition of forces, these three g. 61. components are in the relation of the three dimensions of a parallelopipedon, of which the resultant is the diagonal. Let CNN/GH, &c., be this parallelopipedon. CG is the resultant expressing the total resistance in both quantity and direction. But R®f;, by the equation of the surface, expresses the total resistance in the direction of the 220 UNDULATORY THEORY OF LIGHT. radius; and if, to facilitate conception and comparison, we conceive it to be the diagonal of another parallelopipedon, CMM/I'K, &c., the three dimensions of this solid will be R®freosA, R*freosB, and R? frcosC. For the sake of symmetry, we will employ for a moment these components, instead of R? fr itself. We will denote, also, as before, the two resultants by p and p’ and the angle, GCF, between them, by ». Then, C Pi suadG V Ricos’?A+R'cos’?B+ Rcos?C hi. R? So ——— i : . pP Jr V aco A+6*c0s?B+c'cos?O V atcos*A+b'cos?B+c'cos?’C, . a’cos’*A+67cos°B+c?cos*C V a'cos*A+6'%c0s?B+c8cos?C Or, coso=-+ [47.] Now the wave front-in which 7, having the direction CF, is one of the move- ments, cuts the surface of elasticity in an ellipse, which may be represented by ADBE. The line CG will not usually lie in the plane of this ellipse. If the resultant, p, be decomposed into two forces, one of them equal and opposite to p’, or CF, and the other GE, perpendicular to CI, this last tends to turn the movement in CIF out of that line, as before. But, as it is not in the plane of the ellipse, ADBE, which is the wave front, in order to understand more clearly its eflect upon the direction of movement in the plane of the wave (which is all that concerns the question of polarization) decompose this force again, by dropping, from G, the perpendicular GH” upon the wave front, and joining HF. 'The component, GH”, being normal to to the wave, can produce no effect in the way of polarization. ‘The other component, H’’F, tends to turn the movement, as in the former case, alternately, in the direction of the shorter axis, DI, of the elliptic section of the surface of elasticity, and of the longer axis, AB. Observe that if the displacement had been originally in the direction of one of these axes, there would have been no deflecting force, H’I*. For this lateral force owes its existence to the inequality of elasticity, or resisting force, on the two sides of the movement of displacement. But, by the law of construction of the surface of elasticity, the squares of its radii are the measures of the elastic forces in their directions; and at the extremities of the major and minor axis of an ellipse the radii on either side of the axis are equal and symmetri- cally disposed. It follows, that whenever a ray of light falls upon a medium of such a nature as we have been considering, all its movements will be thrown into parallelism with the two axes of the elliptic section made by its front with the surface of elastictity. And thus we have a physical account of the polarization of light by double refraction. We have, at the same time, the cause of the unequal velocity of the two waves. For, by the construction of the surface of elasticity, all its radii are measures of the velocities of undulations whose molecular movements coincide with them in direction. ‘The two velocities will, accordingly, be to each other as the major and minor axes of the elliptic section of the surface of elasticity made by the wave front. We have also the cause of the polarization of the two rays in planes at right angles to each other. This is so, because the two axes of the ellipse are in that relation. Since the two velocities are both uniform, though unequal, a plane wave is transformed into two plane waves, by double refraction. Supposing the retract- ing surface to be also plane and of indefinite extent, and that a plane wave enters it obliquely, the intersection of the wave front with the surface will be a straight line, and will advance along the surface parallel with itself, as the wave advances. The refracted waves necessarily both intersect the refracting surface CIRCULAR SECTIONS OF SURFACE OF ELASTICITY. 231 in the same straight line. And if we suppose these refracted waves to be com- pounded of the infinitely numerous elementary waves which may be imagined to originate in the line of intersection, each resultant refracted wave front will be a common tangent plane to all the elementary waves of its own kind thus generated. Though the planes of vibration of the two refracted rays are originally per- pendicular to each other, yet the taking of different velocities slightly modifies this relation. The change is hardly sufficient to be sensible. pix There are two sections of the surface of elas- Lan ticity which are circles. Let, for example, in the figure annexed, the axes of elasticity be OX, OY, OZ, and let the dotted lines represent the contour of one-cighth of the surface of elasticity; OP being =a, OA=d, and OE=c. Upon the same axes, with OA—d#, as radius, let there be con- structed a corresponding portion of the surface , of a sphere, ACB; in which AC, AB, BC are quadrants. Since a is the largest, and ¢ the least cones neo axis, the ellipsoidal and spherical surfaces must sit cut each other somewhere between B and C. Fig. 62. They will also touch at A. Let one point of the intersection be at R, and through R pass a plane, OAR, intersecting the spherical surface in AR. In this, take any point, as N, and draw through it the quadrants BNS, CNQ. Considering N as a point of the surface of the sphere, the radius ON=2, and we have LP—P’ co’ A+4?2cos?B+82c08?C. Considering it as in the surface of the spheroid, ON==R, and R2=a?cos?A+67cos’B+c?cos?C. If both these suppositions are true R°-=2?; whence we deduce (a?’—2l?) co?’ A=(b?—c’)cos*C. If a be put for the are OR, the inclination of the plane, ANR, to the axis a, then, in the triangle CNR, we have Cos?CN=cos?A=cos*NR cos*CR=sin?B cosa. And, in the triangle BNR, Cos?BN=cos?C=cos?NR cos?BR=sin’B sin2a. Substituting these values for cos*A and cos’C in the foregoing, and dropping the common factor, sin’B, (a2’—b?) cos’a=(b?—c’) sin®a a—b? sina And =tan2a. Or, tana=+t b’—c? cos*a the double sign indicating two positions for the section, one in the first, and the 29? UNDULATORY THEORY OF LIGHT. other in the second quadrant—that is to say, indicating that there are two such circular sections. The inclination to a of the zorma/s to these circular sections—that is, of the directions of progress of the waves of which they are the planes—will, of course, have for tangent the reciprocal of the expression just given; or, if a’ represent this inclination, tana! = les fond orl [49.] e— ) If the wave front of the incident light coincide with one of these circular sections of the surface of elasticity, it appears, from the principles already laid down, that the wave can have no determinate plane of polarization. For all the radii of the section being equal, the elastic forees are in equilibrio in every azimuth ; and there will be no lateral force to defieet the molecular movements. if, in the first expression foregoing, we make 6=c, the denominator becomes zero, and the tangent is infinite, or tan90°. The two circular sections then coincide in the plane of be at right angles to a, and the crystal is a negative crystal of one axis. If a=6;:t tana==0, and the two cireular sections meet in the plane of ab at right angles to c, and the crystal is positive. If a=c, then, since @ is the mean axis, all the axes are equal and tana= 5 ; an indefinite value, signifying that the circular sections have no fixed positions; or that all the sections are circular. ; Let us now apply the principles we have been con- sidering to the phenomena presented by crystals cut across the axis of greatest elasticity, or the line inter- mediate between the optic axes. In the accompany- ing figure, let QRQ’S represent one-half the surface of elasticity, in which SC=a, QC=6, RO=c. Let PP parallel to RR’ represent the direction of molecu- lar movement in an incident wave, whose direction of progress is S/S. Let AA represent the direction of free molecular movement in an analyzer with which the erystal is observed. Also let QNOQ’ represent one of the circular sections of this surface. The ellipse QRQ’R’ is the section of the wave with the surtace of elasticity; and the axes QQ’ and RR’ are the directions into which it turns all molecular move- ments in its plane. But PP being parallel to RR’, is already in one of these directions, and hence this wave passes through without modification; but en- countering the analyzer crossed upon it, is suppressed. If, instead of a single plane wave, we suppose many waves more or less inclined to each other, con- vergent toward S, and all having the general direction of molecular movement PP, their intersections with the surface of elasticity will be ellipses whose axes are variously directed. There are two planes, however, 8QQ’ and SRR’, which will contain the axes of all seetions made by waves normal to them. For it is easily seen that, if the plane QRQ’R’ turn about RR’, this lime RR’ will always be the minor axis of the section. If the same plane turn about QQ’, this latter line will be the major axis of the section until the turning plane reaches the position QNQ’, when the section will be circular. Afterwards it will be again elliptical with QQ’ for its minor axis. It follows that all the convergent waves . RINGS SEEN IN CRYSTALS OF TWO AXES. 223 which are normal to SQQ’ and SRR’ will suffer no modification of their molecular movements; and as the analyzer AA is crossed upon them all, there will be seen in the field of view two dark lines, or bars, intersecting each other at right angles in the point C. Every other converging wave will, however, make a section of which the axes are not in the planes SQQ’ or SRR’. Let, for example, the plane QRQ’R’ turn around the line LL/, and let KIX’ be at right angles to LL’ in the turning lance. Then CK gradually increases in length, while LL’ remains constant. When CK reaches the position SO, it becomes the major axis of the section. The original position of the major axis being QC, it appears that, during the turning, it changes its azimuth by the total amount QCK, while the minor axis changes from CR toCL. ‘There is therefore no position in which cither of these axes can be parallel to PP or RR’. It follows that every convergent wave not normal to either of the two principal planes SQQ’ or SRR’ must undergo double refraction ; and, therefore, in passing the analyzer AA, will exhibit chromatic _effects.* lf now the direction of molecular movement in the incident wave be changed to P’P’ or P’b", there will immediately be double refraction in both the prin- cipel planes, or the dark bars will disappear from them. But as, in the turning of the plane QRQ’'H’ round the various diameters LL’, the axes of the section made by the plane turn in azimuth, it is evident that some section can always be fsund which at some inclination will have one axis parallel to P/P’. To take an extreme case, let P/P’ be 45° distant from RO, when it will be eqtidistant between the axes RC and Q’C. The optic axes of the crystal, which are in the plane SRR’, will then be in azimuth 45° from the plane of polarization. Now, since the axes of the section formed by the plane QRQ’R’, as it turns round LL’ or KK’, do not reach LL/ or KK’ until K or L reaches S, if LL’ be parallel to P’P’, no light will come to the analyzer in the planes SLL’ SKK’, without being or doubly refracted. The dark brushes will not therefore appear in the central plane coinciding with, or normal to, the direction of inci- dent molecular movement. There will be other sections. however, which will have an axis parallel to LL’ or P’'P’, or to KK’ normal to LL’. To discover their positions, let us consider for a moment the circular section QNQ’. If at N, in the plane SRN’, there be a plane IL’, tangent to the surface of elasticity, and if, in this plane, the tangent lines ¢¢, and ¢'¢’; be drawn—the first tangent to the elliptic section SNR, and the second tangent to circular section QNQ’—then the angles made by the radius CN, of the surface of elasticity, with the latter, will be right angles; but the angle CN¢ wi!l be greater than a right angle, and the angle CN¢, will be less than a right angle. If the plane QNQ’ turn about CN—say to the position t’¢";—the angle CN¢’ will be greater than a right angle, and the angle CN¢"; will be less than a right angle. The minor axis of the elliptic section made by the plane m this position will therefore fall toward ¢’;, from N. So, it the plane turn toward the position ¢/’¢’’;, the minor axis of the section it makes will fall toward ¢/”, from N; that is, below the circular section in each case. ’ Now, LL’ being supposed parallel to P’P’, and KK’ normal to it, let CH CI be the intersections of the planes SLL’ and SKK’ with the circular section. If the plane QNQ’ tum about CH, so that Q’ approaches L, the minor axis of tue elliptic section it makes will fall to the right of H. But if another Ime, to the left of CH, as CO, be made the turning line, a pesition may be found for it in which, for a given amount of turning, the minor axis of the section, which will be to the right of CO, may fall in the plane SHL. The nearer O is to H, the less the plane will be required to turn to produce this effect. Accordingly there 294 UNDULATORY THEORY OF LIGHT. will be a series of sections, more and more inclined to QNQ’, and also to QRQ’, and whose intersections with QNQ’ will differ in azimuth along the are HON, which will have their axes parallel to LL or P’P’. By considering the effect of turning the plane about CI, we should arrive at a similar conclusion in regard to a series of sections cutting the circular section near the point I, one axis of each of which would be parallel to CK. or normal tu P/P’. The normals to the planes of all these sections are the directions of wave progress, or nearly the directions of ray progress; and if, from a point above AA, the analyzer, lines should be drawn parallel to all those normals, they would indicate the directions in which (no double refraction of the inci- dent polarized ray occurring in them) the several points of the axis of the dark bands or brushes ought to appear. ‘These directions being all more inclined to SC than is the normal to the circular section, it is evident that the pole in this case will be the point of nearest approach of the dark band to the centre of the field of view. It is furthermore evident that the bands are curved. For if they are not so, the normals must all lie in one plane. But they cannot lie in one plane unless the sections to which they are normals have a common inter- seetion—a condition which, from the law of their construction, cannot exist. ‘The plane QNQ/ turns about an axis movable in azimuth, and the surface which is the locus of all the normals is necessarily curved. ‘ The foregoing illustration accounts for only one of the dark bands. The other is produced in the same way, and depends on the other circular section which is not drawn. ‘The analytic investigation of these changes would be extremely complicated. It will be seen that this mode of explanation applies itself to the case of one- axed crystals with great facility. The surface of elasticity for such erystals being’ an ellipsoid of revolution, every section has one of its axes in the plane which contains its normal, and also the axis of the ellipsoid. The loci of the dark bands will, therefore, always necessarily be planes normal to each other, intersecting in the optic axis of ‘the crys stal. The direction of ray-propagation is that of the radius of the wave. When the theoretic wave is spherical, the ray is normal to the surface, but not other- wise. The velocity of wave progress is measured by the normal let fall from the centre of the wave upon the wave front; and this in spherical waves is the same as the velocity of ray progress; but in waves not spherical, ray progress may exceed wave progress. § XII. WAVE SURFACE. In order to determine, a prior, the direction which a ray will take on enter- ing a doubly refracting medium it is necessary to know what is the figure of the wave surface. Tor crystals of one axis we have seen that this problem was solved by Huyghens; but the complete generalization of the theory was reserved for Fresnel. Could a molecular movement be produced, starting from a single point and pro- pagated in all directions in a medium of variable elasticity of three axes, the surface defining the limits of the tremor at any moment would be the wave surface. The same form of surface (sensibly) would be defined by an infinite number of planes tangent to a luminous sphere like the sun, moving outwardly from the body in all directions with velocities such as the law of variable elasticity requires, when their distance from the body becomes very great compared with the diameter of the sphere itself. Proceeding upon this FORM OF THE WAVE SURFACE, 225 supposition, Mr. Fresnel obtained an equation for the wave surface, which is the following : Zy2l pe 2 2 P+ 4Bp[e+ypt+e—(av+e) aE ae [a Tar ( Moldy pte (ed) |Fabe—o. [50.] Or, (a? +b*y?+ 02”) [er +y+2— (a’?+0?+c’) | + ate? + by’ +ct2? + 7h. This is an equation of SN the fourth degree, and ( SS represents a surface of SS two nappes, or sheets, inosculating at four points. Figure 64 is a representation of this surface copied from a drawing made by Mr. Ferdinand Engel, of \ Washington city. In order to exhibit the in- =) terior nappe, two ungu- 7 lae are represented as / cut away; one of the section planes passing through the two points of inoseulation in the visible surface, and an- other through one of them. ‘The form of the wave being known, we may apply, for the determi- nation of the direction of a ray, the principle on which Huyghens founded his construction for spherical and spheroidal waves. Resuming once more the figure employed in illustrating that construction, we may say let CD be the direction of the semi-axis of elasticity a—the semi-axes 6 and ¢ being at right angles to this, and to each other. Upon these axes let the wave surface be constructed in space, with C, the point of incidence, as the centre; the values of a, 6, and ¢ being the velocities of rays moving at right angles to them (and whose molecular movements are therefore parallel to them) when the velocity in vacuo is made unity. If MN be the surface of re- fraction, RC incident ray, and CP the normal to the surface, then RCP is the plane of incidence. In this plane draw CG perpendicular to RC. CG will be in the incident wave front. Make RCze1, draw RG parallel to the refracting sur- face, and cutting CG in G. Draw also GQ parallel to RC. Then when the wave front has advanced to Q it will intersect MN in a line drawn through Q perpendicular to the plane of incidence. If the plane of the diagram be sup- posed to be the plane of incidence, this perpendicular will be projected mto the point Q. Both the refracted waves will intersect MN in the same line; and their planes will be also tangent to the two sheets of the surface. If ADB represent one of these sheets, and HFK the other, then tangent planes passing through the perpendicular projected in Q and meeting these sheets, as at FE. and F, will determine the directions, CE, CF, of the refracted rays. It is to be observed, however, that the points E and F, and therefore the refracted rays CE, OF, 1585 HH u == ae 2 ci 226 UNDULATORY THEORY OF LIGHT. will generally not be in the plane of incidence; nor will the ray or radius of the wave surface be normal to the tangent plane. The three principal sections of the wave surface present each two curves returning into themselves, as shown in these figures :— oe Lia 7 ae x’ D Fig. 65. Fig. 66. Fig. 67. The equation of the section through a 4, Fig. 66, is deduced from the general equation of the wave surface, by putting z=0, when it becomes— (Pi +by)(2+y—(@+ ?) + ase? + by+ab?e—, which may be resolved into the two factors— (aa? + By? —a?b) (a2 ++ y—c?)=0, 151.] being the equation of an ellipse and a circle combined. In like manner, making x nothing, we obtain the equation of the section through 6c, Fig. 65— = (Bpte2—Be)(y+2—a)=0; [52] and making y nothing, that of the section through ac, Fig. 67— . (ee+e2—ae)(a?+2?—b’)—0. [53.] This last section is remarkable, as showing an intersection of the circle and ellipse. The intersection is necessary, because the diameter of the circle is the mean axis of elasticity—=d, while the major and minor axes of the eclipse are the extreme axes of elasticity, @ and c. The points of intersection, shown at N, N’, &c., are the inosculating points of the two nappes of the wave surface. Since the velocity of ray propagation is measured by the radius of the wave surface, it is evident that, along the radii drawn to N, N/, &c., there may be two refracted rays having the same velocity. These lines have a peculiar optical interest. Their inclination to a, or a, the axis of greatest elasticity, (or the angle MCN) may be found from the equation (putting S=MCN,) MN MN , CM NO MN and NO are obtained by making both factors of the equation of the section, just given, simultaneously =0. ‘The values of x and z which render this possible are the values of NO and NM. We have then, g+2—b=0, and aa’+c2’—a'e=0. from which we obtain, by elimination, c(a’—b’) 2? = —._—_——, and 2?= ~o- @—e? a—c MEN) ce. av P—e ; 5A NOM ey gaze ba which differs a little from the value found for the tangent of inclination of the normals to the circular sections. But these normals are the directions of equal wave velocity; and ON is the direction of equal ray velocity. 'These two direc- tions are therefore not coincident, though nearly so. tans—— a’(b’—c’) Whence, PRINCIPAL SECTIONS OF THE WAVE SURFACE. zat The lines drawn through the centre.and the points N and N/ are however the optic axes; for it is equality of ray velocity which makes an optic axis. But it is not true that the two rays whose velocities in CN are equal, can spring from the same incident ray. Herein there is an important difference between crystals of one axis, and those of two. In crystals of one axis, when it is pos- sible for two rays whose planes of polarization are transverse to each other, to have a common path and common velocity, they both proceed, or may proceed, from the same original ray. This is not so in crystals of two axes; and what is more, no single incident ray of common light, in this class of crystals, can give a single refracted one; for there are no common points of tangency, in which both nappes may be met by the same plane. If a tangent plane be drawn to the wave surface parallel to one of the circular sections of the surface of elasticity, it will take the position of AD, DB, &c., in the figure ; and will be tangent at once to the ellipse and the circle in the principal section through the axes.* If, then, (in the same figure,) AB represent a refracting surface, and N’C a ray of common light incident at C, in such a manner as to take the direction CQ’” within the crystal, for the nappe whose section is cir- cular, it will yield another ray, CP’/” for the nappe whose section is elliptical. These two rays will be polarized in planes transverse to each other. The directions of their respective molecular movements, and therefore the positions ‘of their planes of polarization, may be inferred from the following considerations. The circular form of the section QQ’Q”Q", shows that the velocity of the rays belonging to that section is equal in all directions. The molecular move- ments must therefore be affected by a constant elasticity. Their directions must accordingly be invariable. In order that these directions may remain invariable, while a ray moves as a radius vector in the plane QQ’, &c., they must be perpendicular to this plane, or parallel to 6. Accordingly the ray CQ’ is polarized in the plane of the section. The other ray, CP’, is polarized at right angles to the plane of the section. The radius, CQ’, of the circular section is normal to the tangent plane AD. For the angle CQ’ A is a right angle, by the property of the circle. And the wave surface on opposite sides of the plane of the section is symmetrical. The molecular movements of’ the ray CP’ are, therefore, im the plane, which, passing through the ray, is normal to the tangent plane. Or, if we draw a line joining the point of contact with the foot of the normal from the centre, this line will be the direction of molecular movement in the ray. The proposition just stated may be generalized, and extended to all rays. In the case of CQ'’, the point of contact and the foot of the normal coincide; and any line drawn through Q’”’ fulfils the required condition, leaving the direction * The truth of this statement may easily be shown thus: Suppose ordinates to XX’, ZZ’, to be drawn from P’ and Q’. Let x and z represent the ordinates from P’, and 2’ and z’ those from Q’. It is evident that the angle at C, where the tangent BC intersects the axis BC h ae Ce Also, that the same tangent = Put CC=k, BC=k’. Then, by the property of the ellipse, we have— eo Cler beh 2! 02. kiz—a", Hence, k(2’/—x)=b?—c?; and k’(z—z')=a?—b?. Dividing the second of these equations by, the first, member for member, we obtain— ki(z—z') a®—b? >, __v—b? | = ab? meayT rast or tana 5 ; and tana—-} A To But this (equation [48]) is the tangent of the inclination of the circular section of the surface of elasticity to a, the axis of greatest elasticity, which is the axis of x. It follows that a plane which, being normal to the section through the inosculating points of the wave surface, is tangent at once to the ellipse and the circle in that section, is parallel to one of the circular sections of the surface of elasticity. . . . 2 ra of x, which we will put =a, will have for tangent g/—r 228 UNDULATORY THEORY OF LIGHT. indeterminate. We have scen, however, that the direction is, in this case, fixed by other considerations ; and it is furthermore demonstrable, that, as the point of tangency approaches Q’””, the line joining it with the foot of its correspond- ing normal approaches perpendicularity to the principal section; and that, in he limit, when the two points unite, the perpendicularity becomes absolute. In the discussion of the tangent plane AD, or DB, drawn parallel to one of the circular sections of the surface of ‘elasticity, Sir William Hamilton made the remarkable discovery that the tangency is not confined to the points P and () in the principal section ; but that it extends throughout the circumference of a minute closed eurve, sensibly circular, of which P and Q are only two points of the circumference. The point N’ is, therefore, the vertex of a conoidal or umbilical depression; and all the points of the circumference of the circle of contact are equally points in the wave front to which CQ!” is normal, and which is parallel to the same circular section of the surface of elasticity to which the tangent plane is parallel. The annexed figure represents this little circle. As, in this, CQ is the normal to the circular section of the surface of elasticity, and CN* is the optic axis, we have— 2272 B—2 tanQC X—tana’—=+ i Zs se , and fen ee ee 5 a—b ona == =a Whence tana/—=- “tanf. [55.] a In anhydrous sulphate of lime (anhydrite) in which the doubly refracting power is uncommonly great, the ratio of ¢ to a is .9725 to 1. The value of £ is 14° 33/, from which we deduce a/—=13° 41/11”. And P—a’=0° 22! 19". A general expression for the value of 6—a’ may be found thus: Oe / tana a tan—tana'=(* -= 1) tang == c c sing sina’ a—esina! 1 / . . a—c §1na sinfcosa! —cosfsina'—=-—— / a ACOs a é a And sin (f—a’ a—c. cosa’cos8——— sina’cosf c ; “sina! cos. [56.] Tn so far as the variation dependent on the trigonometrical function sine’cos? is concerned, we may easily determine the outside limit. For, since a’ is less than f, sina’ right angles to each other. If QAPA’ be the small a circle of tangeney, Q being the point of contact with the circular section, or the foot of the normal, we have seen that the molecular movement from any other point of contact in this plane must be toward Q; that is, the movement at g must be in the direction gQ, , that at r in the direction 7Q, that at p in the direction hs p, &e. Suppose the direction of molecular move- “ment in the analyzer to be AA, parallel to aQa. The vibrations in the ray at @ have the same direction. The analyzer allows that ray therefore _£ freely to pass; but it is crossed on the ray at P Fig. 70 whose direction of vibration is PQ. The radius, CP, will therefore be dark. Now let the analyzer take a position in azimuth A’A’, parallel to a‘a’, tangent at 7. Draw the diameter 7Cp. Draw Qsq perpendic- wlar to7C. It will be parallel to a’a’, and it will be the direction of vibration, of a ray at g. The analyzer in the position A'A’, is therefore in harmony with the ray g, and it is crossed on a ray whose molecular movements are in Or, at right angles to Qg Jom Qr, Qp. rg. The angle Qpr is equal to the angle Qqr, since both stand on the same are, 7Q. And the triangle vgs is similar to the triangle Qpr, the one being right angled by construction, and the other because it is inscribed in a semicircle. The triangle rgs is therefore similar and also equal to 7Qs, or the are Qg is twice the are Qr. Draw the diameter gp’, and join Qp’. The angle gQp’ is a right angle; conse- quently the molecular movements at p’, being in the direction p'Q, parallel to Cr, and at right angles to gQ, or to a'a' or A'A’, will be suppressed. In turning the analyzer in azimuth, therefore, from AA to A’A’, or through an azimuth measured by AA’=Qr, the dark ray has advanced through an azimuth Pp'=Qq=2Q7, which was the point to be proved. In the equation of the wave surface, if 6 be the mean axis, and we make c=, we shall have, after reduction— (PP? 1PYy+br—eb’) (ey +e—b’)=0. [57.] If 6 and ¢ remain unequal, and we put b=a, the equation is— (P2t+ey+er—aec’)(2+y+2—a’*)=0. [58.} These are both equations of a spheroid and a sphere, touching each other at the poles. The first is that of an oblate spheroid circumscribing the sphere, and answers to the case of a negative crystal of one axis. ‘The second is that of a prolate spheroid circumscribed by the sphere, and answers to the case of a positive crystal. The case of quartz, so remarkable on other accounts, is pe- culiar also in the fact that the two nappes of its wave surface are not in contact anywhere. ‘The ellipsoid is entirely within the sphere, and there is no direction either of equal wave or of equal ray velocity. These equations suggest the geometrical relations between the surface of elasticity and the wave surface. The larger diameters of the one are at right angles to the larger diameters of the other, and the smaller have the same rela- tion. For crystals of one axis, the surface of elasticity is an ellipsoid of revo- lution. If its form is prolate, it generates an oblate wave; if it is oblate itself, the wave is prolate. The causes of varying elasticity of the luminiferous ether within crystals are CONCLUSION. 231 not well understood. They are dependent, in some manner, upon molecular arrangement. This is evident from the fact that variations resembling those which naturally exist in crystals may be produced, as we have seen, in homo- genous bodies, by heat or by the force of pressure, flexure, or torsion. So deli- cate a test does the polariscope furnish of any inequality of temperature, stress, or mechanical force of any kind, that Dr. Brewster has suggested the construe- tion of chromatic thermometers and dynamometers, founded on the principles we have endeavored to unfold, for determining differences of temperature, stress, or pressure too slight to be easily measured by ordinary instruments. CONCLUSION. In the review which we have now taken of the applications of the doctrine of undulation, we have encountered no optical phenomenon of which this doc- trine does not furnish an explanation; we have discovered no legitimate deduc- tion from it which has not found its verification in nature. We have seen, on the other hand, that it has served occasionally to point to facts of curious interest previously unknown, which have been subsequently confirmed by the experiments which it has suggested and directed; experiments which require for their exhibition adjustments so delicate and conditions so difficult to secure, that, but for the clew it has furnished, they would probably have remained forever unknown. This doctrine rises, therefore, above the level of a mere hypothesis; it fulfils every essential condition of « true theory; it explains all known phenomena; it anticipates the unknown, and its predictions are corroborated by experiment. Moreover, the simplicity of the connecting link by which it binds together phenomena the most diverse in their nature, is almost without an example in the history of physical theories. In the words of Fresnel, “in order to caleu- late the so various phenomena of diffraction, those also of the rings produced by thin plates of air or water, or any other refracting medium, refraction itself, in which the ratio of the sine of the incident to the sine of the refracted rays is that of the lengths of the waves in the two media, the colors and the singular modes of polarization presented by crystalline lamine, it is sufficient to know the leneths of undulation of light in the media which it traverses; this is the sole quantity which it is necessary to borrow from experiment, and it is the basis of all the formule. If we attend to those intimate and multiplied rela- tions which the theory of undulations establishes between phenomena the most different, we cannot but be struck at once by its simplicity and its fecundity ; and we are compelled to admit that, even though it had not the advantage over the system of emission of explaining numerous facts absolutely inconceivable in the latter, it would still merit the preference because of the means which it fur- nishes of connecting together all the phenomena of optics and embracing them in general formule.” It is not, indeed, to be denied that some embarrassments still attend this theory. There are physicists to whom the phenomena of dispersion still continue to be a stumbling-block, and the differences of opinion which exist in regard to the true relation between the direction of molecular movement in undulation and the plane of polarization of a polarized ray have been pointed out in their proper place; but these difficulties are such as, it is fairly presumable, the further progress of investigation will ultimately clear away, and are\not sufi- ciently serious to impair confidence in the substantial truth of the theory as a whole. At any rate, whether this theory be received or not as a true represen- tation of the operations of nature in optical phenomena, we are compelled to accept it at present as an instrument for combining and systematizing our knowl- edge of these facts and moulding it into a shape worthy of the name of science; since, if we reject this, there is nothing left us on which to fall back which is capable of rendering us the same service. INDEX TO LECTURES ON THE UNDULATORY THEORY. Page. Aberration, stellar, velocity of light ascertained by means Of..--.-.........--2.cceeeseeeceeeeeee ees 122 Absolute lengths of undulations, how measured; table of.....-.....2.-0c0scceecccanenecc-eceee--e 170, 171 Apate; PeculiaMpropenty Ol ec sate ees aa clocd canae sina Aawletslecielete sresige he te Mee ERO ne eeeeee 132 Airy's Spirals 52. caeeae stiasaasclce~sals -iscin coh i eraasen cee eee ae econ eels ee See Se ee eee Ree eee aoe 136 his: “quarter-wavelamina”. 22... 25. to. Sescs ses anoeemeceesnece Varsha doridea saeco ee eee cee 139, 206 Amountiof light reflected'at any incidence. -< .J2. 222-60 sees sees aealson a2. -becteaceesaeeeenecce ee: 194 polarized at GOs; sadcceelngia acces cee Sescicks sessise os cae emo enee ere 195 Analyzeridefinede: a5. .- Sooo no Se Sacto toticeiecelca siaiemeute 1= a setalnls cnleilo oe we wajeaem ee emieslerel= =e 140 Color‘and'xeiran cibility; mutual relation betweencs co. ccccc ec cence acme soe mnleelesieeeeee ee see ae aie 111 Colorsioftthiniplateste. 222-2052 2 elerlseeccece: Secucsise doe reties tick ccecseeceweseeereneme sein 118-20, 183-87 ORSCHI CK On Gi oe ois coin Sse wig ee meee cee ale ee em lanic tbisis a Siaicictele See eee einer eines aos 120, 187 of cry stallinelaminee:in polarized light. <2 cece cee. ane e's acnen seneaeneeemereere =e 132-34, 205-10 of cryptalsicutiacross the axis:<<: 2222 sila=ascia aes see = seers reece 134-37, 210-15, 222-2 of quartz do. iss See eee Se eee ele niainiat= sis siataetela e ente aetetetee teeta isla lar 135, 211-12 of the Spertrim = case steal Janina bade acsae alate ciel esate wsinia © a aleetelelametetetatsteretatstnin.-((elataie)ei= rate dil Offsuled isurtaceste 22 2i. oa <.2c/ecem mascinain= See se UaRet cee seis ne ee eee 166 of waves normal to each other compounded. ---. <2 seiesce~a--emebemese jesesss acess se 168 Of TemnisCate, CULVES <2ac12 joke c emia sooo ,5 one soe seeeeisianl ae = Se ae oe eee eee oe eee 214 Ether luminiferous... 2.0 2.o:s2 ieee cne~ o= 5 dacwadiawtmeeeeeasaesscee- tens See tee eee ce ceeene 158 Incompressibility, Ofc 2 -- cles sas acre 3s sein seme eee aoe So. > cee eee bee srane as 164 density: off, inidifferentubodies 52... 22.,--...-.qassts sete em esecee emis, eee EE ee eae re 158 elasticity Of, Ansenystalss: o2 5 ooe. nc shee esc emiee és Socelneia 8's 535508, 5,.c SSSR Rees 162, 215-20 Fiuclid,vhis treatise on Opies se 22 S525 oc a2. sania eeicincliscieie sees menace se sciseaieee eee eee eee aeeee 108 Hxtraordinary-TVaysyGODNIMOM a2 ajc < 5.< <.c0:52.2.< -n1e's sisisesisjceisieceselosisineeis stacse seeeees eee as sees 115 Bye-piece; Melezenne!ss. ae 2 oven neces enoe ieee cenaeesieessoow asics aneae-acaa sewer seat eee oes 132 INI COMBS nesta csei5- em cncn sane os eee ne are aac erm eee mies erate stots Sloe ca rate Sieiss le tee ate ee ne 132 HOUPMTALING oe sacs loi oy or0/syars srae ora sob Simin lessee mis siele te jsiotoisy-l=jal=jqyelela.ais|=jale(e 2) eee ee eae 132 Bailure of Fresnel’siformulss:for reflection, case, Of... =< e..cjm onmmmsiace nce, sano cele ancien AOA eee ae 188, 196 Hisures:in selenite, inder polarized light. 2c ...<0 «2-4 scianeigenaneseeec ase cneanaaaceetctaeele cee eee 133 Bixedilines instheispectrums --. <<< 1 .s10..2- <1526,5.5 ce sie aa maceme memecinaisemnictecie ose eetee Be eae 125-27 BRizeau, hisiexperiments on the velocity.ef light .:... <2. ss-<-qaccesenamene ae smpsuae ese Soe eeeeee 122-2: Hluid) elastic, body vibratn gin. <5. ss si5 a Sree oe ses enynsin geese aise Siomininnin sim iarenieinaiajsis alee eet 151 tremors.produced! in. <2 <2 22sec oses aon sa csanceleacaeneceeneseee et eseecs= eee nee 152 undulations generated in. 2 -s-sccscc sc. sosccaamabe Ssnee ee sae womie= th oleae = meee eee 151-53 molecular Movements ins = oA a5 aie.c ere Giaje se webaum sees waeee cee eeee ee eee 157 Bormuls general, tor resultant vibrations. £25..-..0-c/5.-252 eee cee ace sh eeemeeerke a6 cee eee eee 150 TOM GISPETSION ss «ooo ers ase ees else eas apeinie oo a ER a se eee eee ie ae eee 156 for interference frin Ses sao ssc occas cose mwcye'sic soa an cas oe cee Geet eee se Oee ee eeeees 170 for diffraction CO...) 256 oe scineie seach Some ge Sateen a meee ase ease Bees 176 for reflection: andsretracti onesie. <.6<<.5, an.ociese canoe cea oe et ee eae eee eee 189-95 for Chromatics of polarized Jicht. -....4...= -cas~faeceeseerer cecmcisce-se casaenceee 207-08 for lemniscates in ‘two-axed crystals <<... 6 s< ses sscceesecncnsessccsteoneseseceee 214 Morms: ‘primitive; of enystals << oon. c cece oe ok sso eclne a cncins slacwiee seco eee ee ee ee 141 Houcault, his‘experiments:on:the velocity of dight o- - =<. .2s.e—5-e-550cmes-een4s-5seeeee Soeeeeeee 124-25 EBraunhoter: ‘his: discoveries in the spechum: <<. > 6.5 sos ca nsoqastaneateae ees eeneeeenaesc co noeeneeee 126 Nis: measures: of UNGUAONS 52). oe 2S xcjnnaiein serene meee easeeces wapesuisiememajcateneee ee 171 Hresnel; his analysis of light in the axis of quarta. 4... ..2-s esse causes seceseasaateccien eee secant 1.6 hisirhomph for circular polarizations —...cj--sa0cassaanecoenme, disid'eia'winia cate Se onan ee eee eee 137 interference experiment; With, MiVOLS =; =f2.4-)=.0- cc = .)e oes e ee eeeeeecine eeabemest aeons ee 168-69 formuls for reflection, case of failure...........--.--.----..- ih sed ee here ie 188, 196 equation of the wave surface..........--------=- Breese er eee cee eee 225 of, the surface.of, elasticity: << ~j<6 -<.c2.cn serie sess aiainae cls seine 143 Newton, compound nature of light announced by-.--.----------+-----2-- eee eee e ee eee eet eneee dil hisiresearches on icolors.of thin, plates =. 2<--. esecnjon oes ss occ see ee onee ee cc eee ene 150 OL superposed undulations <2 3is.28-e 2) sates aacnce rence onda ea cac eater oae one eee pees 166 of elastie resistances in doable retraction te a=.2— sasceseecsee sce s a2 Baka MeAME eee sepa 6.32 | 5.62 | 4.06 | 5.18 li «14.96 | 4.12 | 13.27 | 19.10 Of the diverse, elongated type of skull, undoubted examples have been re- peatedly recovered from Peruvian cemeteries, both in their normal condition and modified by artificial means. They are nearly all small, narrow, and with a marked predominance of the longitudinal diameter. Several of those meas- ured by me showed the average distance from a vertical line drawn from the external auditory foramen to the most prominent part of the frontal bone to be only 2.7 inches, while from the same line to the most prominent part of the occipital bone it was 4.3 inches. J ully two-thirds of the cavity occupied by ~ the brain lies behind the occipital foramen, and the skull, when supported on the condyles, falls backward. Compared with brachycephalic skulls, the fore- head is low and retreating; the temporal ridges approach near each other at the top of the head, a much larger space being occupied by the temporal muscles, between which the skull seems to be compressed. ‘The zygoma is larger, stronger, and more capacious, and the whole bones of the face are more developed. ‘The superior maxillary bone is prolonged in front, and the incisor teeth are m an _ oblique position. ‘The bones of the nose are prominent, the orifices larger, and the cribriform lamella more extensive; the bony substance of the skull is thicker, and the weight greater. Among the numerous interesting illustrations of Peruvian claracteristies ob- tained by Mr. Blake from ancient cemeteries on the Pacific coast, the most valuable for the purpose now in view are the skulls of two children, both of the dolichoeephalic or elongated type; but the one evidently in a normal condition, while the other betrays manifest traces of artificial deformation. It is impos- sible to examine the former without feeling convinced that it illustrates a type of head entirely distinct from the more common brachycephalic crania, while the latter shows the changes wrought by compression. Figure 3 exhibits the unaltered skull. It is that of a child, which, judging chiefly from the state of the dentition, may be pronounced to have been about seven years of age. It is. PHYSICAL ETHNOLOGY. 251 a well-proportioned, symmetrical skull, unaltered by any artificial appliances, and will be observed to present the most striking typical contrast, if compared with an unaltered juvenile skull of the brachycephalic type from the Peruvian cemetery of Santa, engraved in the Crania Americana, Plate vii. The other elongated skull, exhibited in Figure 4, is manifestly of the same elongated type as Figure 3, but considerably altered by ‘compression. The forehead is de- pressed, and the frontal suture remains open. It is that of a child of about five years of age; so that both examples are long past the age when the form of the head admits of material alteration by artificial means. AW WH AG wy NW M9 a QYaQr lag \ a we wry Wy Las YY \S The following measurements give the comparative proportions of the normal aud abnormal skulls figured above; and of two other children’s skulls, in the Morton collection, figured in the Crania Americana, Plates ii and vii. They are marked, A, normal child’s skull; B, abnormal do.; C and D, the Atacama and Santa skulls of the Crania Americana : A. Be C D Longitudinal diameter ..... UO 6.6 6.1 6,9 5.4 Parietal diameter’)... 20205... paren Setters 4.6 4.4 4.5 5.4 Hronteldhiameter U0 eS ee gOce oul aut, A, Verpreal diameter | 2 0S SI Sn 4.82 4.32 4.3 4.6 From observations carried on in the cemeteries of Peru, Mr. Blake was led to the conclusion that the distinguishing traits thus far noted between two classes of the ancient Peruvians are not limited to the erania, but may be dis- cerned in other traces of their physical organization. In describing those of the rounded or brachycephalic type of cranium, he adds: “'The bones of the latter struck me as larger, heavier, and less rounded than those of the former, (the 252 PHYSICAL ETHNOLOGY. elongated crania,) and in the larger size of the hands and feet they also present a noticeable difference. The remarkable narrowness and delicacy of the hands, and the long and regularly-formed finger-nails of the former, are strong evidence that they were unaccustomed to severe manual labor, such as must have been required for the construction of the great works of which the ruins remain. In all the cemeteries examined, where skulls of the rounded form have been found, those which are elongated have also been obtained.” Remembering, however, that the sepulchral rites of the royal and noble Inca race were commonly ac- companied by the same human sacrifices traceable among so many semi- civilized as well as barbarous nations, it is in no degree surprising that the crania of the two distinct classes, noble and serf, should be found deposited together: in the same grave. After a minute comparison of all the brachy- cephalic Peruvian crania in the Morton collection, it appears to me that these also admit of subdivision into two classes distinguished by marked physiog- nomical diversity. ‘The bones of the face in the one are small and delicate, while the other exhibits the characteristic Mongol maxillary development and prominent cheek-bones. ‘The following table of measurements illustrates the proportions of the Peruvian dolichocephalic skull, as shown in examples brought by Mr. Blake from Peru, and in others preserved in the collections of Boston and Philadelphia: TABLE IIIL—PERUVIAN DOLICHOCEPHALIC CRANIA. Locality. L. D..|P. D. | F. D. | V..D. || iA oT, Ton Hieias eee Ii) Atacaiiais: 4228. 3220523 V2 5.2 3.6 BMT). aR EE ee ee Dai dasa sacs. ciel ieek Wes 4.9 oto AD (lesane Sie. Soe See ae Re BLO sre eis Rt Oe 7.0 Aa 3.2 Bede (|) asec | seats es ee oe Oe Se Ones esc caries soe sa Weill 5.2 See. 5.0 14.1 4.0 15.0 20.0 BAUS WopAncai ss chee sete e 6.9 5H) 3.6 52 14.6 Ae |e arene 19.8 GripReKdescea=e-nese= aoe V2 5S Oe 5.6 14.6 AL (Qat| £5 OS eee 20.0 7 ~Kd62.sesed% -pebtotce 7.0 4.9 3.0 so 14.0 Aly J fesiehay os 19.0 a eee eee Ong SE oe Wee, Bol 35 5.2 s 13.9 Ac Opes bai Soeeeae 20.0 Or OATICR sass a15 ioe ae eee ‘eo Heo 4.3 5.3 14.0 4.3 15.0 19.8 TOSS Atacams Pei see eee ee 5.5 4.4 5.1 14.8 4.1 13.7 20.2 ATA iticaca2t Hs3BHal ew 6.8 5.4 4.8 5s 14.8 Art Sai Se 19:4 12 | Royal Tombs; Festa 6.8 5.2 3.8 5S 14.1 At Onis) 7k E See 19.4 13) |i-Pachacamac.< 522m ee. 6.8 5.4 4.5 5.3 14.7 4,2 14.1 19.5 Mieanss-scscricccee | O60 ble: | ocoUn) eek | 14.36 | 4.10 | 14.45 | 19.71 In an inquiry into the physical characteristics of the Peruvian nation, we are by no means limited to the cranial or the mere osteological remains recoverable from its ancient cemeteries. Like the Egyptians, the Peruvians employed their ingenious skill in rendering the bodies of their dead invulnerable to the assaults of “ decay’s effacing fingers ;” and, like the inhabitants of the Nile Valley, they were able to do so under peculiarly favorable circumstances of soil and climate. The colors on Egyptian paintings, and the texture of their finer handiwork, which have shown no trace of decay through all the centuries during which they have lain entombed in their native soil or catacombs, fade and perish almost in a single generation when transferred to the humid climates of Paris or London. The natural impediments to decay probably contributed, alike in Egypt and Peru, to the origination of the practice of embalming. The ceme- teries already referred to are situated in a region where rain seldom or never falls; and the dryness alike of the soil and atmosphere, when added to the natural impregnation of the sand with nitrous salts, almost precludes the decay PHYSICAL ETHNOLOGY. 253 of animal or vegetable matter, and preserves the finest woollen and cotton tex- tures, with their brilliant dyes undimmed by time. By the same means we are enabled to judge of the color and texture of the hair, the proportions and deli- cacy of the hands and feet, and the comparative physical development of two seemingly different races at various stages, from infancy to mature age. When we pass from the southern continent of America to the seats of ancient native civilization lying to the north of the Isthmus, a different class of evidence, in like manner, enlarges our range of observation. ‘The artistic ingenuity of the ancient Peruvian potter has left valuable memorials of native portraiture, and the Mexican picture-writing, with the sculptures and terra-cottas, the products of Toltee and Aztec ceramic art, in like manner contribute important evidence idustrative of the physiognomy and physical characteristics of the ancient races of Anahuac. Still more, the elaborate sculptures and stuccoed bas-reliefs of Central America perpetuate in unmistakable characters the records of an ancient race, differing essentially from the modern Indian; and the study of their cranial characteristics serves to confirm the deductions derived from those other independent sources. The traditions of the Mexican plateau pointed to the comparatively recent intrusion of the fierce Mexican on older and more civilized races; and various independent observers have at different times been tempted to trace associations between the ancient Mound-builders of the Ohio, the elder civilized race of Mexico, and the Peruvians, whose peculiar remains are recovered from the tombs around Lake Titicaca. The predominant Mexican race at the era of the conquest appears from evidence of various kinds, including the portraiture in ancient Mexican paintings, to have been derived from one of the great stocks of the Red Indians of the northern continent. he features represented in the paintings are thoroughly Indian, and strikingly contrast with those of the older native race of Central America, as illustrated by their sculptures, bas- reliefs, and pottery. No doubt, however, the population of the Mexican plateau in the time of Montezuma included descendants of very different races. All the traditions of Mexico point to intrusion and conquest by successive invaders ; and the cranial evidence, as produced in the following tables, shows that there also, very distinctive types of skull-forms appear to perpetuate the evidence of diverse races, and of a mixed stock intermingling the characteristics of the con- quering and the subject people. ‘The same valuable American collections have furnished the materials for the following comparative tables: . TABLE IV.—MEXICAN DOLICHOCEPHALIC CRANIA. | Locality. TDs Pee De Fee tiveeD I. A Meee | O. B.A. | He G. —_— = se ees WE fu | | WiieMextcor Mee 2. 2. 32/2) teil 5.0 SYS) || KD. Wlesoucses LN ae eReeer 19.8 SAhOtumbsy 4-22) sie 2 See Wal 5.6 | 4.6 | 5.5 15.5 | 4.1 15.0 | 20.2 3 | Cerro de Quesilas ------- Tod 5.%f|| 4:40 |) 5.2 15.9) |.4.0 14.0 | 20.5 4 | Acapacingo, F’....------ 6.9 | 5:2 | 4.2 |:5.4,]) 14.5 |, 4.1 14.0 | 19.2 MPL aACMOa ene = — 22 ao 2. eee 7.1 56) | 4.5) | 9-4 | 915.2 | 4.3 34.2 | 20.0 OUPESE COs. 3 322h- bh. 5 2 2~ Sh G.0F | 5.3 | 4:3) 1-553 14.5 | 4.1 14.0 | 20.0 iipMiexico ye +. 22 235- =<) 2S 7.0 5.4 4.3 5.3 15.0 | 4.1 14.0 19.8 SUM ne te gn ne ah 71, [5.5 [44 15.2 | 15.8 | 4.1 | 14.0 | 20.4 Meat 2 = oan lea mae 7.05 | 5.41 | 4.31 | 5.35 || }16.20 | 4.12 44:17) 9.99 ae Lele tai 254 PHYSICAL ETHNOLOGY. TABLE V.—MEXICAN BRACHYCEPHALIC CRANIA. Locality. 1. Dee Pe Diy |e Ds Gen Da a kee I. L. | 0. F. A. | H.C. tel), Mexico) -.4- 226 ee eee 6.6) 9) 5. Biel S- Ohl peo EUG PONG Ns I P| 20.0 OM COE M ac 2a tae eee rem te 6.6 Det ALOv a2 L482 SLO esac 14.5 | 20.0 Sn) Otumba 2 Seer sweey 6.3 5.3 4.4 5.4 1433 PWS WZ 19.2 4 oges i.e ae Be 6.6 Dio 4.4 5.4 14.0 | 4.0 14.0 19.3 Fl Na Crain .ce yet teal aeietas 6.8 5.5 4.6 6.0 15.6 4.4 14.6 19.9 6 | Sanuliorenzoye se oe ie - 6.4 Dad 4.5 5.4 14.6 4.5 SHS 20.2 7 | Mexico, modern -.-----.- 6.6 | 5.3 | 4.3 |] 5.2 14.6 | 4.1 13.6 19.0 ns Means: S282 ies. 6.56°| 5.51 | 4.30 | 5.55 | 14.69 | 4.25 13.95 | 19.66 | The Peruvians and Mexicans, with the ancient populations of Central America and Yueatan, constitute the Toltecan family of the two great divisions into which Dr. Morton divided his one American “race or species.” The nations lying to the north of those seats of a native civilization were all classed by him into one family of the barbarous tribes, resembling the other in physical, but differing from it in intellectual characteristics. Yet, as we have seen, even Dr. Morton recognized some differences among them; ‘and Professor Agassiz speaks of their tendency to split into minor groups, though running really one into the other. The following tables, however, will show that the differences are of a far more clearly defined nature, and in reality embrace well-marked brachycephalic and dolichocephalic forms; while of these, the latter seems de- cidedly the most predominant. The examples are chiefly derived from the Phila- delphia collection, though with additional illustrations from the Boston cabinets | already referred to, as well as from Canadian collections. Table V1, which illustrates the form of head most widely diverging in proportions from the theoretical type, shows in reality the prevailing characteristics of the north- eastern tribes, and could be greatly extended. ‘The opposite or brachyeephalie eranial formation is illustrated in Table VII. TABLE VI.—AMERICAN DOLICHOCEPHALIC CRANIA. P. D. | F. D. | V. | I. A, Tribe. L. D. I. L. | 0. F. A. | H. € Ie Seminoles a's = tecis.45 Gel 5.6 4.7 5.5 15.0 Al 14.8 | 20.3 2 OL Ae. . te cise eect, 7.3 5.9 4.6 5.8 15.9 4.4 15:3") =2057 3 Nd OR SaSa ae see tos sae 7.0 5.6 4.7 5.4 15.0 4.1 14.7 20.2 4 FOO ene 7.3 5.6 4.2 5.6 15.2 4.7 15.0 20.4 Ps hO0n Agana eee eee 7.0 5.9 4.5 5.8 14.7 4.6 14.2 20.5 Or Cherokee Ho secs eee We2ialr oven | Are i LO 14.5 | 4.0 14.6 | 20.2 Mmoe: Os. et cetera 7.0 | 5.3 4.1 5.4 14.5 4.0 14.0 19.5 NOs sais ois Mee com eietete 7.2 5.3 4.3 5.3 14.1 4.5 14.0 19.1 FN aecion .:, socahur See 72 |5.0 | 42 |55 | 146 | 39 | 147 } 192 Oe alee es eget ota 7.4 5.9 4.6 5.5 1523 4.7 14.2 is POO aIC!< = a2 ere em ea 7.0 5.9 4.7 5.5 15.0 4,2 14.2 20.9 JeCinppewa = ---'-----2-: 7.3 | 5.8 | 4.8 | 5.5 15.1 | 4.6 14.2 | 20.9 ESPEN Ge Eee eee eee 7.2 5.5 4.3 5.5 14.8 4.1 14.6 20.2 14 | Pottowatomic ...... -..- 78 157 (44 |53 | 160 | 40 | 15.8 | 224 TW) MUssissavia ie leeiete lace = 7.0 5.2 4.3 5.2 13.8 4.1 14,2 19.5 HG WW elaware tae sence ce = 7.8 5.4 4.6 5.1 14.4 4.2 14.5 20.0 17 een eieteae ie 2 me@ 5:5) 4.4 6.2 15.6 4.3 16.0 21.5 7.6 | 5.3 4.3 5.5 15.0 4.1 15.5 20.5 7.3 | 5.5 4.3 5.5 14.6 4.6 21.0 14.9 PHYSICAL ETHNOLOGY. 255 TABLE VI.—Continued. Tribe. Ge Ds | Psp a! D. |v. De EA. iW reeqrOs Havse i HE G. INammikeapi ees -[ --.-= 56 7.4 : ‘ f 15.0 : 14.0 at id aD 4.4 5.9 ASS) 40) | eee COR ate ee Ao esate. 6.9 5.0 4,2 Dra 14.3 3.9 14.4 19.8 Aissingboime....2---fch. 7.6 5.8 4.6 Dull 14.9 4.3 14.9 O12 PPE GHEE. soe te BE Wee 50 4.4 ove 14.7 4.6 14.7 20.8 Mandan; tics J... = e'- Goll 5.4 4.3 Hak 14.2 oS 14.6 20.0 Pees ok eit ot ews 7.0 Due 4.1 Has 13.9 As2) 14.1 19.8 pcan oe 2 5 eee 7.0 ‘ah! 4.1 Hil 1335) 4.0 14.0 19.5 IVETE Otero oo ercte spe, Wot Deo 4.5 ey 14.7 4.1 Tass 20.2 Menominee 2s. . 25h a2 oe xe od 5.8 4.1 5.5 14.7 ARC) Realty 20.3 bebe dere coe ect ad We oe a Se a a 1 a tea 19.3 BE AG Oejtin< 26 winds epee Ss 7.5 5.4 4.0 5.5 14.5 ASD app ee! 20.6 Minetart, Hy sess5 92-= <1 ed 4.4 4.4 Dal 14.1 4.1 Na 20.2 Meamlttisas trois 2217-24 | 5.47 | 4.36 | 5.42 14.67 | 4.23 14.62 - TABLE VIIL.—AMERICAN BRACHYCEPHALIC CRANIA. | | | Tribe. | L. D. | P. D. | B.D: || WexD. |e bs As I, Ls, |\:O0..F., As, | He Ge Py Maskogee:: 02 SUN a. 6.8 5.8 4.2 5.6 15.4 4.3 15.0 20.0 SD REN Ofcbarn ctayaters Lye wt af 6.6 Bua 4.5 5:3 15kS 4.5 14.0 20.4 SMW Gh eevee: chart ts eps acs 9 3 6.8 5.4 4.3 Deo 15.0 4.4 14.3 20.1 AM NULY Set esa it ayce oer care | 6.7 5.0 4.2 5.3 14.0 4.1 13.8 19.3 BriMNatiCle ts .2 oo eos | 6.7 bag AL al ad 14.5 4.1 14.3 19.0 GAA Adowees: AS aT | 6.7 5.2 4.3 eo 14.2 3.9 14.1 19.1 Pa WAColmeci-tee ote 6.7 5.7 4.2 5.4 14.7 4.4 13.5 19.8 8 Be eee nee a AR ih 6.8 Eyed) 4.3 5D 15.1 4.4 14.4 20.1 Pea Winer ns aa. 16 6.6 5.4 4.4 4.9 13.7 4.3 13.0 19.1 TOMTOM Fe. oe eee 6.6 5.5 4.1 5.4 15.0 4.4 14.0 19.5 PAPO Lisuss. Ao SPU 6.5 5.5 4.0 5.4 14.8 4.4 14.1 19.3 POR edor ets koeet= Ub aoee's 4 6.7 D0 4.3 Sib Pitre 4.4 14.2 19.6 13-\¢@hetimachee s:4ea%y proved himself the greatest geologist of our epoch.” 368 MEMOIR OF LEOPOLD VON BQOCH. all associated, (so/idazres,) and one never commences until the other has ceased. As, in hands so skilful, the thread of analogy, once seized, is never broken, from the volcanoes of the Canaries he passes to those of the entire globe, and ranges them all under two classes, central volcanoes and volcanic chains. The first form the centre of a number of eruptions which take place around them ; the second are all disposed in line, each following the other in the same direction, like a great rent or fissure of the globe; being, as Von Buch adds, probably nothing else but such a rent. From these isolated points of rock, elevated by fire, transporting his view over the innumerable isles everywhere seattered in the ocean, he combines them all under the generic name of zsles of elevation, thus dispelling the opinion which long regarded the former as the relics of a submerged continent. Scarcely had he returned from the Canaries (about 1819) when some inquiry led him to the Hebrides, whose basalts formed the object of his visit, and thus the giant’s causeway became the route which reconducted him to Germany. There, a new problem hurries him to Paris; and though it is the midst of win- ter, and a bruised arm, the result of his precipitation, threateus to detain him, he takes with him a young relative, and this time travels post, for his impa- tience isextreme. “If,” said he, “ Humboldt should have quitted Paris, the great city would seem a desert to me.’’ He arrives, however, in season, and the two friends meet; but how is time to be found for long conversations ? All the saloons are emulous of Humboldt’s presence. ‘The interviews, however, take place regularly, only they commence at midnight and do not terminate until morning. This strain of scientific excitement, added to the cold, renders Von Buch really ill. M.-d’Arnim,* his young relative, hazards some expressions of blame. ‘True, it is my own fault,” replies the culprit, “the fire of the chim- ney near which we were talking had gone out and I felt chilled; but by making amovement to rekindle it I should have perhaps hastened Humboldt’s depar- ture. I preferred suffermg to being deprived of his conversation, and am well content, for I have gained much by it.” Hitherto Von Buch had presented his leading idea of the upheaval of mountains with the reserve distinctive of the conscientious though bold in- quirer. In 1822, after a new exploration of the south Tyrol, he shows him- self more decided, and in a letter to Humboldt, on that country, has given us his ultimate determination in regard to those great and hazardous questions. Here he pronounces, with an authority which no one as yet had acquired on this subject, that all the projecting masses on our globe owe their present position to an actual upheaval.t In this he finds an explanation of the fact, till then inexplicable, that marine shells occur on the summits of the highest mountains ; not that the seas have risen to those summits,t it is the mountains which have been raised from the bottom of the seas. Never had a graver difficulty, nor one which longer resisted the efforts of ingenious minds, been solved in a sim- *T am indebted to M. d’Arnim for most of the private traits of character given in this nar- rative. + ‘* The pyroxenic porphyries of Fassa owe their actual position toan upheaval. But we must carefully observe that it is not the particular elevation of a rock which is in question, but the lifting up of the whole mass of mountains, and consequently of the entire country.”— Letter to M, de Humboldt, &c. ‘‘It is now many years since I entertained a doubt that the whole chain of the Alps—at least the calcareous Alps—owed its elevation to the pyroxenic for- mation. ‘This formation breaks the strata which oppose its egress. It pierces or upheaves first the red porphyries, then the sandstones, then the calcareous strata.”—Jbid. ¢ ‘* Reflecting on the effects of these upheavals, we shall be less surprised at meeting with petritactions of anomis in the sandstones and calcareous strata at the height of nearly 8,000 feet above the Sasso di Val Fredda. These same petrifactions, which are found at 5,406 feet above the passage of the Caressa, 3,800 feet above Seiss, 2,600 feet above Saint Paul and Caltern, were, perhaps, before the catastrophe of the upheaval, situated lower than the level of the seas.””—Letter to M. de Humboldi. MEMOIR OF LEOPOLD VON BUCH. . 369 pler manner. By reversing the fact and presenting it as it really occurred, the explanation at once presents itself and changes the face of the science. With Von Buch it was inevitable that one discovery should lead to others. Thus, a first view reveals to him the upheaval of mountains and that of conti- nents ; a second, the mechanism of the formation of volcanoes ; a third, the re- lation which connects the displacement of seas with the elevation of mountains. One of his most prolific views, that of the discordance of rocks, disclosed to our distinguished colleague, M. Elie de Beaumont, (a geologist who, by his own labors, has united the researches of Cuvier with those of Yon Buch, )* the first germ of his learned theory of the relative age of mountains. We owe still an- other highly ingenious and novel conception to Von Buch. His explanation of the formation of dolomite,t or, more generally, of the alteration produced on deposited and sedimentary rocks by. the incandescent rocks of elevation which have traversed them, though still subject to some difficulties,t must alw ays be looked upon as an indication of a high order, and as having marked out for modern geology one of its most important objects, the study of the secondary action of fire on the envelope of the globe. After so many brilliant labors, the smiling banks of the Spree, with the re- turn of every autumn, continued to recall this eminent and indefatigable man to the quiet retreat which he had chosen. There, a simplicity, the more charm- ing as it was wholly voluntary, presided over the economy of his daily life. t ‘Cuvier has shown that the surface of the globe has undergone a succession of sudden and violent revolutions. Leopold von Bueh has indicated definite and marked differences between the several systems of mountains which diversify the surface of Europe. I attempt nothing but to bring into relation these two orders of ideas.” —Elie de Beaumont: Recherches sur quelques-unes des revolutions de la surface du globe. t By the formation of dolomite, Von Buch designs more precisely the change of calca- reous shell-bearing stone into calcareous magnesian stone. ‘* How-comes it that the magnesia can pierce, traverse, change the nature of the calcareous beds, which are many thousand feet in height, to make of them a rock uniform in its whole extent? It is a question which I have proposed to myself in all my excursions in the neigh- borhood of the valley of Fassa, without finding a solution. The calcareous stone does not contain magnesia. It comes, then, from another quarter, and it is quite natural to believe that it is the pyroxene which furnishes it, since magnesia is one of the constituent parts of this substance. I think I have discovered, in the environs of Trento, the process of nature in this operation, and this process has appeared to me so evident that at the instant of the ob- servation I experienced the most lively satisfaction which I have ever felt in my excursions across the Alps.””—Lettre @ M. de Humboldt, &c. ‘* We can easily conceive that a mountain rent and fissured must lose every appearance of beds; that thousands of channels are opened for the magnesia to introduce itself and com- bine with the calcareous rock ; that by little and little all the mass must change into rhombo- hedrons ; and it is in this way that compact beds, filled with shells, may change into a mass uniform, white, granular, and saccharoidal, without a vestige of organized bodies or any hor- izontal fissures whatever ”’—IJbid. ‘This splitting recalls the phenomena which may be daily observed in limestone furnaces when the fire is withdrawn from them. In going trom Cortina, in the valley of Ampezzo, to Toblach, in the Pusterthal, one is surrounded, during the whole transit, by peaks of dolo- mite. The aspect of these places is so singular that we might think ourselves transported into the midst of an immense furnace. The fragments of dolomite are traversed by immense clefts; they appear rough to the touch, like all substances exposed to the fire. One is tempted to attribute these extraordinary effects to the high temperature which the pyroxenie porphyry had acquired when it penetrated through the inferior strata, and lifted up the dolo- mite in the form of columns, pyramids, and towers. I am persuaded that this same pyrox- enic rock has converted the compact masses into granular masses, that it has caused the dis- appearance of every vestige of stratification and of organized bodies, and that it has given rise to those fissures which are strewn with crystals. We can no longer doubt that it is the compact limestone, which is constantly found under the dolomite and above the sandstone, that has been whitened, fissured, and transformed into a granulated rock.”—Letire sur la dolomie du Tyrol d@ M. Alois de Pfaundler. t On these difficulties, see the important and ingenious labors of MM. Haidinger and Morlot. [The subject will be found also elaborately discussed in the article on the meta- morphism and crystallization of rocks, by Mr. Daubrée, translated for and published in the Smithsonian report. for 1861. ] 24 8 370 MEMOIR OF LEOPOLD VON BUCH. The necessity of peaceful labor, and, therefore, of silence, had induced him to limit his personal retinue to unity, and when age had relaxed the activity of this one faithful domestic, Von Buch, like Leibnitz, had his food brought to him from without. Often his door was opened by himself. If the stranger was one whose presence seemed likely to be importunate, to the question, “Is M. Von Buch at home ?”’ he would quietly reply, “ No ;” and, closing the door, re- turn to his occupations. ‘The young princes of the royal family were some- times among those who hazarded the experiment, and their admission was due not so much to their rank as to the affectionate relations which existed between Von Buch and his sovereign, who, among other marks of his favor, had made him one of his chamberlains—a chamberlain, it must be confessed, of very slender assiduity in his office. If the interruption was occasioned by the ar- rival of a savant, on the very threshold, and without waiting to bid good day, he would encounter the visitor with some such question as this: “Is the sem- bi-lobate divided ammonite found also in Thuringia ?”’ An unappeasable curiosity had directed our geologists’ inquiries to that part also of the terrestrial envelope which is traceable to the action of water, and which paleontology had recently occupied in its search for the remains of ex- tinct races. Since life appeared on the globe, it has undergone many vicissitudes and clothed itseif with many forms ; Jlifferent species have succeeded one another, and as each has surrendered its Spoils to the cotemporary strata, these relics determine the relative age of the deposits, and the history of life serves to il- lustrate and complete the history of the globe. Von Buch, after Buffon, aptly compares fossil shells to medals, and adds, in terms of his own, that these medals also have their /anguage. In a series of memoirs on the ammonites, the tercbraiula, the productus, &c., he has taught us the means of interpreting that language; the new and difficult art of distinguishing with certainty the species which identify the several strata, by characters on which he had bestowed the most earnest and profound study. Nor were his efforts for restoring the ancient annals of the world limited to shells; to fossil botany he brought the same aid, a precise determination of characters, which he had conferred on fossil geology, so that the expressive epithet which he gave to certain fossil shells and leaves, calling them guzding ones (conductrices), might well be transferred to himself. He has truly proved, in these delicate investigations, a guide to other geolo- gists. But to be an intellectual guide did not alone suffice for this good and emi- nent man. Wherever he could discover young persons whose success seemed only trammelled by the rigors of fortune, he was sure to interpose ; and, as if to compensate for the modesty of his own wants, he acted on those occasions with a regal munificence. Such instances were numerous and were seldom made public. ‘Towards a vessel ready to sail, a young savant was one day directing his steps; his baggage was light, though he had divested himself of his patri- mony to procure the means of pursuing his explorations in America. By the way side a stranger is waiting for him, and says: ‘A friend, impelled by a de- sire to promote the progress ‘of science, begs you to employ this in its service;’ he places a purse in the hands of the traveller, and disappears. Being once at Bonn, Von Buch received a visit from a youthful professor of that univer- sity, who desired letters of recommendation, as he was about to join a scien- tific expedition. Return to-morrow, replied the distinguished savant. ‘The interval is employed in seeking information. At the hour prescribed, the young man presents himself, the letters are ready, they converse ; Von Buch becomes animated, affectionate, gives advice, and finally says to the visitor at taking leave : : “IT have a service to ask of you.” “ Compliance will give me plea- sure,” is the prompt response. ‘‘ Yes, yes,” cries Von Buch, “they all say the MEMOIR OF LEOPOLD VON BUCH. StL same thing, and afterwards complain that I have charged them with commis- sions which annoy them.” ‘The young man protests, cannot conceive how he should be suspected of insincerity and ingratitude. “ Very well,” replies the adroit interlocutor, ‘give me your word of honor that you will not even answer me after receiving my commission.’ ‘The other pledges himself. ‘“« Now that . I have your word,” resumes Von Buch, “here are 2,000 dollars which you are to make use of in your travels.” As the injunction did not extend to silence, the recipient felt constrained afterwards to share the secret with others besides his benefactor. A young painter, tormented alike by the fever of art and the anguish of destitution, was languishing at Rome; there was nothing which singled him out but his talent and his misery. Von Buch charges one of the embassies with the remission of a considerable sum; and that the artist may be restrained by delicacy from attempting to penetrate the mystery, he is to be told that it is a family restitution of an ancient date. As it was one of the chief pleasures of Von Buch’s life to restore hope to the unfortunate, so it peculiarly suited his character to act as a peace-maker between the learned when divided in opinion; before all things, however, it was indispensable that science, his sublime mistress, should be treated with the most exact respect. Just and gencrous in his appreciation of men, he was al- ways zealous in setting forth the merit of the labors of his cotemporaries. A sure and constant friend, though blunt, eccentric, and at times impatient, he was ever ready, if umbrage were taken, to make the advances necessary for con- ciliation. Among intimates he was fond of recounting the ludicrous mistakes which had been occasioned, during his travels, by the grotesque appearance under which he presented himself. He loved socicty, but not what is called the great world. Those who had seen him at court, whither his office, as well as the propricties of his station in life, sometimes led him, might have thought him drawn thither by his tastes, but his resort even there was to the circles in which intelligence supplied the attraction. In these, the graces of language springing from an active and full mind, re-enforced by a surprising memory, gave to his conversation when he was in the vein a peculiar charm. Polished in the company of females, he knew how to appreciate those who in the courteous collisions of which our saloons are the lists, and which we call conversation, furnish by their sprightly sallies often the best, but certainly the most graceful contingent. This admi- ration, however, never trenched upon the liberty which he had consecrated to science. Von Buch never married, but, in return, the family affections exer- cised over him the blandest and most potent influence, and his love for the young, towards whom he could find indulgence for everything but self-suf- ficiency, prompted many of the actions of his life. When far advanced in age, he still quitted his domestic roof with the first breath of spring. “I shall travel,” was his simple announcement, and a walk would conduct him from Berlin to Dresden, to the surprise of his more seden- tary associates in the latter place; thence his course would be prolonged as far as Bohemia or Switzerland. It was when an old man that he sealed the moun- tain ranges of Greece, secking among the extinct populations only those which ally themselves with the real world, and finding more attraction and instruc- tion in the chronology of a shell than in all the brilliant fictions which ani- mated Parnassus and Hymettus. In 1850, a German university having summoned naturalists to a congress intended to celebrate the memory of Werner, Von Buch was present, and of course became the centre of all regards, a tribute which, with an affectionate simplicity, he studiously referred to his early master. “ As for myself,” he pleasantly said, in allusion to the only official title which he had ever adopted, “ Tam nothing more than the oldest of the royal pupils of the kingdom of ° Prussia.”” His return from this reunion conducted him through the country of an MEMOIR OF LEOPOLD VON BUCH. his birth, and the view of those fair scenes which he animated with the memo- ries of his youth, plunged him into reverie. It was observed that he passed a long night in deep meditation, in which he seemed to address to the places he was regretfully leaving a touching and silent adieu. He came once more, however, to visit France, whose genius he loved, and to sit in that Academy to which he prided himself in belonging. He left Paris only in the last days of 1852, and peacefully breathed his last in the spring of 1853. Von Buch, who had qualified himself for the direct contemplation of nature by always and everywhere pursuing her indications, has left us an example of one of the noblest of scientific careers. He had the happiness to consecrate a long life and a penetrating genius to the profound and unwearied study of one of the highest questions of natural philosophy. Descartes had suspected the igneous origin of the globe ;* Leibnitz had inferred its incandescencet from the traces everywhere apparent of a vast pristine fusion; Buffont had demonstrated the existence of the primitive fire, still subsisting, and more and more concentrated in the interior of the earth; Dolomieu§ finally had pro- nounced before this Academy the words adopted by Lagrange:|| ‘ ‘This elobe, at first incandescent and fluid throughout its whole mass, is still so in its interior, and has nothing solid but its crust ;’’ but no one more contributed than Von Buch to prepare the vast and sublime generalization which dares to place in this profound and central fire, of which, however, he himself has nowhere pronounced the name or fully admitted the idea, the first and sole, the potent and terrible cause of all the revolutions of our globe. The author thinks it his duty to acknowledge the assistance he has derived, in preparing the above memoir, from the eloquent and learned Nofices of the ereat geologist, published in Germany, by MM. Geinitz, professor of the Poly- technic School of Dresden ; Cotta, professor of the School of Mines of Frey- berg ; Dechen, director of mines at Bonn; Noggerath, professor at the Uni- versity of Bonn, and a fifth, anonymous, pronounced April 6, 1853, before the Geological Society of Germany. * “Tet us suppose that this earth on which we reside has been once a star composed of matter of the first element absolutely pure, so that it differed in nothing from the sun except in being smaller.”—(Descartes: Les Principes de la Philosophie, LV part.) + ‘It seems that this globe has been once on fire, and that the rocks which form the base of this crust of the earth are scoria remaining from a vast fusion.’’—(Leibnitz : Proto- @a, &e. zi t oe internal heat of the globe, still actually subsisting, proves to us that the ancient fire which the earth has sustained is not yet by any means entirely extinct; the surface is more cooled down than the interior. Conclusive and repeated experiments assure us that the entire mass of the globe has an inherent heat, altogether independent of that of the sun. This heat we recognize in a palpable manner as soon as we penetrate into the interior of the earth, and it augments in proportion as we descend.””—(Bufton: Epoques de la Nature.) § ‘ While insisting on facts which seem to me of great importance, and again repeating that the unknown cause which produces the fluidity of lavas appears to me to exist under the consolidated envelope of the globe, I should add that it is not without design that I em- ploy the expression consolidated envelope ; for if I cannot doubt that our globe has once been fluid, there is nothing to prove to me that there can be anything consolidated about it but a crust more or less thick; nothing to show that the consolidation, which has been necessarily progressive, has yet attained the centre of this spheroid. Iregard the general opinion which ascribes a solid nucleus to our globe as a gratuitous hypothesis, and the opposite hypothesis appears to me much more probable, since with it we can explain a multitude of important facts which, without it, are inexplicable.”—(Dolomieu: Rapport fait al Institut national sur ses voyages de Van V, VI.—Journal de Physique, 1798.) | ‘*The suffrage of the illustrious Lagrange is of too great weight and too flattering not to be insisted on when one has had the good fortune to obtain it. It was not without much timidity and circumspection that I hazarded this hypothesis before my colleagues, when the celebrated geometer, warmly seconding my opinion, asserted that it was not only highly tenable, but that to him it appeared the more probable inasmuch as there seemed to be nothing in direct opposition to it.”—(Dolomieu: Ibid.) MEMOIR OF LOUIS JACQUES THENARD. By MF DOURENS. PERPETUAL SECRETARY OF THE FRENCH ACADEMY OF SCIENCES. TRANSLATED FOR THE SMITHSONIAN INSTITUTION BY C. A. ALEXANDER. Alchemy, the offspring of man’s love for the marvellous and proneness to credulity, and therefore almost as old as the world itself, was introduced into Europe by the Arabs. It promised riches and health: no wonder it was re- ceived with general homage. Its immediate object was that mysterious sub- stance the philosopher’s stone, by means of which it proposed to effect the transmutation of all metals into gold, to cure all diseases, secure an indefinite term of life, and open for men an intercourse with spiritual beings. Thousands of ardent adepts dedicated their lives to this chimera, one of whom has thus described his fellows: ‘An eccentric, heteroclite, heterogeneous, anomalous sort of men, possessed of a strange and peculiar taste by which they ingeniously contrive to lose their health, their money, their time, and their life.” I'rom the midst of the darkness, however, leaped some vivifying sparks; these indefati- gable seekers bequeathed us several enduring acquisitions; it is to them we are indebted for gunpowder, alcohol, the mineral acids and antimony. Roger Bacon, Arnaud de Villeneuve, Raimond Lully, Valentine, Paracelsus, Van Hel- mont, Becher, are the representatives of this heroic age of chemistry, which recognizes them as its authors. Absurdity long shackled the progress of the new science. Saint Simon gravely tells us that the Duke of Orleans, “who diligently cultivated chem- istry, had used all its resources to get a sight of the devil, but without success.” That elder age of the alchemists, which had failed in supplyirg the means for getting sight of the devil, had been followed by one which did succeed in getting sight of the Arabian remedies, an achievement, according to Gui Patin, of just as little value. “I have made enemies, he complains, of all the Ara- bian cooks who, with antimony alone, slay more persons than the King of Sweden has done in Germany.” He describes the physician of Cardinal Mazarin as one who “piques himself on three things which no wise man ever did—a knowledge of chemistry, astrology, and the philosopher’s stone; it is not with such fine secrets as these that maladies are to be cured.” One of these fine secrets, however, was destined to make its way in the world. Lemery, arriving at Paris in 1666, attached himself to Glazer, then demonstrator at the Jardin du Roi, as the best source of experiments and analyses.‘ Unluckily,”’ says Fontenelle, “he found that M. Glazer was a true chemist, full of absurd ideas, and jealous even of these.’”’ Quitting him, therefore, Lemery entered himself as master apothecary, inseparable then from the character of chemist, and opened a course of public lectures. ‘‘ His laboratory,’ Fontenelle tells us, ‘was less an apartment than a cavern, which might have been taken for a magi- cian’s, lighted as it was only by the glare of furnaces. Yet the resort to it was so great that the operator could scarcely find room for his exhibitions.” This course was printed, and as it professed to divulge what was then called the ote MEMOIR OF LOUIS JACQUES THENARD. secrets of chemistry, the book sold, adds Fontenelle, “like one of gallantry or satire.” It is true that, by using intelligible language and precise ideas, Lemery cleared away much that was mysterious and gave an important impulse to chemistry. But a science only acquires consistency when known facts are united by acommon bond. This the German physician, Stahl, attempted to effect in regard to the great phenomenon of combustion, and his explanation of that phenomenon, by the disengagement of a principle which he called phlogiston, held learned Europe in thrall for fifty years. This system was overthrown by a Frenchman who, though idly charged with being too much of a financier for a savant, and too much of a savant for a financier, made his own epoch the great epoch of chemistry. Lavoisier began with teaching us that air, the medium in which we live, is composed of two gases, one of which, oxygen, serves for respiration and combustion, while the other, azote, is unsuitable for those purposes. He showed that an animal immersed in oxygen breathes therein with more energy than in common air, but dies if immersed in azote. He demonstrated that combustion can never take place without oxygen ; that metals, in calcining, increase in weight, and that they acquire this i inevease because oxygen nite with them. This theory of combustion, by the decomposition of air and fixation of the oxygen, seemed to leave nothing wanting when the illustrious chemist further evinced that this same oxygen was also the principle of acidification. Nothing could be more simple and satisfactory than this chain of discoveries. Under the impetus thus given the progress of chemistry became a series of marvels. France must ever mourn the sacrilege which prematurely terminated the life of her gifted son, but the interests of chemistry did not languish in the hands of the Berthollets, the Fourcroys, the Monges. Illustrated every day by some new application, this science rapidly advanced toa popularity which none of its sisters could emulate. The story is told us that a boyish herdsman one day exclaimed, “Were I Emperor, I would tend my cows on horseback.” “And I,” rejoined his com- rade, “would eat meat three times a week.” «For my part,” cried the third and youngest, “If such a thing should happen to me, I would be paid thirty farthings a day, that I might give twenty of them to my mother.’ Animated by some of these primitive and better inspirations, which find no echo in our large cities, three vigorous lads of Champagne were traversing, on a fine morn- ing in spring, one or the great routes which lead to the capital of France. With swelling hearts and light purses they had quitted the paternal roof and the village of La Louptiere, near Nogent sur Seine, and had turned their faces towards ‘Paris: not with a view to mnie their fortunes there, but from an ambi- tion to add something to the stock of knowledge which they had gathered from the lessons of his reverence, the curate, and father Bardin, then the oracle of the department. One of the three looked forward to nothing less than being physician of his parish; the others proposed to occupy the same field, as apothe- caries; the most enterprising of the three thought of adding something to the profits of the laboratory by a small trade in groceries. What justified the more avaricious projects of the latter was ‘hen circumstance that his parents, honest tillers of the soil, had lost some moderate resource through the undis- tinguishing violence of the revolution, and were burdened besides with the support of five other children. The one now departing, moreover, had been ever the ambitious hope of his mother; what more natural than that he should form plans for her gratification. As our young adventurers neared the great city, the centre of so many illu- sions, it occurr aT to the most cireumspect of the party that it would not be amiss to scrutinize the resources of their budget. Scrupulously told, the con- tents could by no dexterity of computation be ‘br ought to authorize an outlay of more than sixteen sols (eightpence) a day for each of them. This considera MEMOIR OF LOUIS JACQUES THENARD. B72 tion determined them to direct their steps to the furthest recesses of the Latin Quarter, and even there it was only in the highest story of one of the build- ings that they found the refuge of a common chamber. Under the same roof there happened to be then domiciled a family of those hardy natives of Auvergne, who, that they may some day possess a rood or two of land and be enabled to die among their mountains, distribute for thirty years water and charcoal among the inhabitants of the capital. With the maternal head of this family the young financier, whose thoughtful foresight has been already sig- nalized, opened negotiations for himself and his comrades, and although the difficulties of the situation were avowed with the ingenuousness of seventeen, and the worthy dame could not but feel the risk she incurred in undertaking to provide for the demands of three young stomachs on such scanty resources; although it was now the epoch of “ninety-four,” and she a mother, or rather perhaps for that very reason, she agreed to receive them as boarders. Thus were physical needs provided for ; ° Food and a shelter; who could ask for more? It remains to say that the conductor of this negotiation, one of the most critical of his life, who thereby secured himself a footing in Paris, was Louis Jacques Thenard, born May 4, 1777. Once or twice in the beginning of this engagement it happened to him to be too late for the culinary arrangements of mother Bateau. ‘The trying abstinence which such a lapse of attention imposed left its lesson. ‘I acquired from it,”’ he said in after life, “a habit of punctu- ality from which I have never deviated, and which adds to the claims of that excellent woman to my grateful remembrance.”’ Two eminent men were then engaged in teaching chemistry. Fourcroy, by the clearness of his intellect and a ready and learned method, had achieved a success which secured him universal reputation. Vauquelin, less brilliant but more experimentative, had amassed by incessant labor the materials with which he has enriched science. Our young champagnard, all eyes and ears, lost not one of their lessons; he listened and still listened; at length conscientious self- examination satisfied him that he comprehended nothing. At this mortifying discovery, one which the incapable never make, he arrived on a sincere scrutiny of the obstacle at the conclusion, that in a science not purely speculative it is necessary to begin by a practical initiation. Vauquelin, who was then poor, gave admission into his laboratory to such of his scholars as could pay a fee of twenty francs a month, but with such a condition Thenard had no means of complying. Yet here alone could he see any resource, and therefore, taking courage, he presented himself before the professor, candidly disclosed to him at once his penury and his inclination to labor, and entreated to be received, if even on the terms of a domestic assistant. Wauquelin had, however reluctantly, before discarded such offers; the analogy of his own situation at one period did not prevent him from beginning to frame a refusal, when happily the interposing voices of his own sisters, who had entered at the moment and were touched by the mortification, the intelligence and even, through sympathy, by the provin- cial accent of the young candidate, came to his succor. “Ah, do not send him away; observe how modest, how docile he is; he would not only be useful in the laboratory, but would mind our pot of soup, which most of your dawd- lers suffer to spoil by overboiling.” ‘Thanks to this lesson in practical chemistry, ‘Thenard was accepted. ‘I have never been so ungrateful,” he used afterwards to say, “as to forget that a pot which is allowed to boil can make but indifferent soup.” His rapid intelligence and accommodating nature soon made him a favorite with the youth who frequented the laboratory and procured him at the same time the means of extending the circle of his studies and developing his singular dexterity. ‘Three years now passed by without bringing any marked alleviation of his 376 MEMOIR OF LOUIS JACQUES THENARD. condition, but without any abatement on his part of heart or hope. Vauquelin at length procured him a tutorship in an institution, and Thenard, though look- ing but remotely to the exigencies of a lecturer’s chair, felt the necessity of reforming an accent and gesture which reflected the impressions of his native province. For this purpose, as well as from a very decided taste, he attended the theatre as often as his stomach would compromise for an abstinence suth- ciently long to justify an expenditure of thirty sols. One morning Vauquelin said to him; “I am summoned to Rouen; my course has commenced; you must occupy my place.”’ Unavoidable deficiencies could not but make them- selves perceptible, at the first lecture, to the new professor as well as to his audience, but each succeeding one was marked by so much improvement that, at the fifth, Thenard ventured to cast his eye over the throng and discovered Vauquelin and Fourcroy, in a corner, smiling at his efforts. “At the sight he precipitately abdicated the chair. But from that time those eminent men labored in concert for his advancement, and succeeded in securing him an assist- ant professorship at the Polytechnic School. ‘The carliest accession of a little ease and leisure was but a signal to Thenard for the institution of original researches. Beginning with 1799, when his first Memoir was presented to the Academy, that body has known him, for more than half a century, to lay before it, several times in each year, the results of inquiries which have formed the basis of striking improvements in science, the arts, and industry. Summoned, one day, unexpectedly and not a little surprised, into the presence of the min- ister of the interior, the latter said to him: “There is a deficiency in the supply of ultramarine blue, which is, besides, always scarce and very dear, and Sévres stands in need of a material which can resist an intense fire. Here are fifteen hundred francs; go and find me a blue which will answer the required condi- tions.”’ WiionanaK began to stammer an excuse. “I have no time to lose,’’ said Chaptal, the minister in question, in a petulant tone. “Go and bring me my blue as soon as possible.” In a month from that time the rich tints of the beautiful fabrics of Sévres bore witness to the success of the chemist. In 1803, Thenard had shown that the supposed zoonic acid was but an impure acetous acid, and although Berthollet, then in the zenith of his reputa- tion, was the discoverer of this acid, the circumstance produced no change in the generous appreciation which the latter always manifested for his young competitor. Nor was this the only occasion on which Thenard, firm in the expression of his own convictions, was called upon to contravene so imposing an authority. When occupied with the oxidation of metals, he unhesitatingly maintained the idea of oxides in fixed proportions in opposition to Berthollet, who denied it. Thenard devoted much attention to organic chemistry, and although later inquirers have advanced beyond him, there still remains to his share the merit of having clearly conceived and indicated the relations which connect chemistry with physiology. This science of life rests on an art in which chemistry is pre-eminent, on the high and delicate art of analysis. It was this art which, in its higher and more subtle applications, Condillae first introduced into phil- osophy, and Lavoisier tells us that he himself derived it from that acute thinker. In 1807 appeared researches of great interest on ethers. ‘These, it was known, are formed by distilling certain acids with alcohol, and this was all that was known. Thenard announced several new ethers; and, yet more, laid a foundation for the theory of these agents, which have already revealed to us some of their surprising effects on life, and doubtless hold in reserve others more surprising still. During this period, of engrossing application, Thenard was, early one morn- ing, surprised by a visit on V auguelin. ‘Up, in all haste,”’ cried the visitor, “and apparel yourself handsomely.”’ Thenard, scarcely awake, asks an explana- tion. “The law respecting pluralities forces me to resign my chair at the Col- MEMOIR OF LOUIS JACQUES THENARD. i ’ lege of France, and I require you to go at once and apply for it.” Thenard feels a delicacy. ‘Come, come,” rejoins the professor; “be quick; I have taken the cabriolet by the hour and you ruin me with these delays.” The necessary visits being made, Thenard readily secured the position which con- duced so much in the end to his extraordinary popularity. The students seemed to attach themselves with peculiar enthusiasm to one raised by toil from their own ranks and wholly unchanged by his elevation. Vauquelin, who con- tinued to watch over his interests, and who greatly admired in Foureroy the charms of delivery which he himself neglected, would fain have invested his favorite pupil with this additional attraction, and Thenard readily lent himself to the attempt. It was perhaps the only experiment in which he ever failed. In vain did he seek for models in society, counsels from his friends, instructions from our great actors, Molé and T'alma; the cham ypagnard was destined to bear to the end the original impress, somewhat rough perhaps, but thoroughly French, which definitely consigned him to a type well recognized and not a little vaunted by our national self-esteem, A few years only separated Thenard from the period when foreign invasion had made it necessary for France to improvise nearly all the resources incident to war. ‘To this end, none had contributed more efficiently than Monge and Berthollet, who afterwards accompanied Napoleon to Egypt, and were often consulted by him when subsequent successes had placed him at the summit of power. ‘Tell me,’ he said one day to Laplace, “why it is that I see at present so little of Berthollet?’ ‘My friend,” replied Laplace, “has become embarrassed through his undertakings for the advancement of industry, and is chagrined that it should be so.” ‘Tell him to come and see me,” said the Emperor. Soon after, seeing his old Egyptian at the extremity of the saloon, he goes directly to him and extends his hand. “ Berthollet, you are unhappy, and you do your friends the injustice of not confiding your cares to them: name the sum you require, and think no longer of anything but your researches.” Berthollet was then initiating in these researches a young man whose zeal and intelligence rendered him an invaluable assistant in the laboratory. Gay Lussac, in his earliest memoirs, gave evidence of that precision of thought and accuracy of¢judgment to which in the sequel chemistry has been indebted for so many important services. An analogy of position soon induced between him and Thenard relations of confidence and co-operation, while both were so fortunate as to enjoy the advantages of the scientific retreat which Berthollet had created for himself at Arcueil, and which Laplace often animated by his presence and patronage. About this period a great sensation was produced in the scientific world. Berzelius had just revealed the power of decomposition exerted by the voltaic pile upon compound bodies. Davy, availing himself of more powerful appa- ratus, had succeeded in decomposing the two fixed alkalies, which till then had been considered simple bodies: in potash and soda he found, united with oxygetl, two metals to which he gave the names of potassium and sodium. He after- wards undertook the analysis of the alkaline earths, each of which afforded a peculiar metal, while in all, oxygen presented itself as a common principle. Proceeding still further, he disclosed, in a paper full of original views, some of the profound relations which connect chemical with electric forces, affinities with electricity. With generous enthusiasm, the Institute of France awarded to this paper the grand prize founded for the progress of galvanism; and though war was raging between the two countries, the English savant was invited to come and receive it in person. This was an act of justice nobly accorded. “Will you tolerate this triumph of the English ?”’ impatiently demanded Napoleon of Berthollet. A gigantic pile was forthwith constructed by the Kmperor’s order, and confided to Thenard and Gay Lussac, who soon after 378, MEMOIR OF LOUIS JACQUES THENARD. were able to announce to the Academy that by means of the ordinary affinities they had succeeded in obtaining new substances more abundantly than by the pile. By employing potassium and sodium, they effected the isolation of a new and simple substance, which they named boron. Davy recognized the superiority of the chemical method for the extraction of metals; but he claimed this boron as an element which had come to light through his own investigations. This Thenard and Gay Lussac would by no means concede, and they were right; but they maintained at the same time that sodium and potassium, so far from being simple bodies, were combinations of alkalies with hydrogen, or hydrurets. Their English rival justly answered that, if they adhered to this theory, it would follow of course that their simple principle of boron was but a hydruret of boric acid—an argument which re- mained unanswered. ‘This, however, was the commencement of a discussion which, with profit to science and credit to both countries, continued for not less than five years, and which marks the epoch at which the basis of existing ideas respecting simple bodies was definitely fixed. In one of the memoirs in which they rendered an account of the different aspects of their controversy with the English savant, Thenard.and Gay Lussae had said: “The conjecture is not inadmissible that oxygenated muriatic acid is a simple body.”? It was not without having first tested this acid with potas- sium, and strenuously sought to extort some evidence of oxygen, that they gave expression to such an opinion. For, if oxygenated muriatic acid were ad- mitted to be a simple body, a new principle of acidification would be disclosed, and “a serious breach be thus made in the theory of Lavoisier. Recoiling from this consequence, and restrained moreover by the immovable opposition of Berthollet, they hesitated to pronounce more decidedly. Hence the recog- nition which they evaded passed to the credit of England. Davy admitted the oxygenated muriatic acid as a simple substance, giving it the name of chlorine or chlorium, but at the same time he generously resigned to his two rivals the first indication of the new principle. Thus the grand theory of Lavoisier was subjected to modification, though without forfeiting its title ta be considered one of the noblest contributions of French genius to science. The two friends, whose resources and reputation had been constahtly increas- ing with their labors, had, during this whole controversy, been so completely identified in effort and responsibility, that the learned abroad were disposed to confound them in a single individuality ; and indeed the part borne by each remains to this day undetermined. When, in 1809, a course of instruction was opened at the Sorbonne, both were called to participate. Here Thenard pro- posed to conduct an elementary course, without discontinuing, however, his more abstruse labors at the College of France. So great was the concourse of pupils that space for accommodation was often deficient, and many who had waited long were forced to retire. This suggested to Thenard the propriety of pub- lishing his lectures. They appeared accordingly in four volumes, the first edition in 1813, the sixth in 1836, each edition costing much labor, as the author continued to intercalate the discoveries and doctrines of successive periods. This work maintained an exclusive ascendency in the schools for more than a quarter of a century, so that it may be said that almost all Europe has learned chemistry of Thenard, and doubtless most of the great chemists of the present day, French or foreign, would take pleasure in acknowledging their obligations to his clear and comprehensive method. When the Institute lost Fourcroy, numerous competitors disputed with Thenard the honor of succeeding him. His friend Gay Lussac had the satis- faction of completing, by his first vote, the unanimity of voices with which his comrade was called to a chair. On this occasion the first impulse of The- nard was one which sprang from his heart. “When I once -felt assured of success,” he said, “I immediately set out for Louptiére, full of the joy which MEMOIR OF LOUIS JACQUES THENARD. 379 I should communicate to my mother. To crown my good fortune, I carried with me a book which she had asked me for: The Imitation of Jesus Christ, in large letters, such as she could read without spectacles. When this copy, so rarely to be met with, fell into my hands, I had regarded it as the happiest of my discoveries.” At the maternal fireside, the simple habits of his child- hood were resumed and old associations cordially refreshed. Here he again listened to the tender counsels of his mother, who, at the moment of parting, said to him: “It is now time for you to marry.” This admonition fell on no unwilling ears. From the time when he first received ithe patronage of Vauquelin, Thenard had formed the acquaintance of a young chemist, named Humblot, to whom birth and fortune had opened a path as smooth as his own was rugged. In order to sustain the courage of Thenard, Humblot had often cited to him the instance of his own father-in-law, who, at first simply a laborer in a convent garden, had contrived to evince his talent as a painter, and by the opportune development of other talents in the service of his country during the Revolution, had achieved for himself both distinction and fortune; so that it was said of him by a great man, whose confidence he had won: “Conté is capable of creating the arts of France in the midst of the deserts of Arabia.” Received into the intimacy of this family, Thenard, whose origin and mediocrity of fortune were well known to them, met with warm sympathy in all his successes ; yet was it left to the sagacity of Madame Humblot to divine, which as » daughter of Conté she was well qualified to do, that he was silently waiting for some still greater success in order to acquire the boldness to ask for her daughter—whom Thenard confessed to be for him only too fair and too rich. This obstacle not proving insurmountable, our savant married; and as he was a man who ordered affairs with judgment, and knew how to enter into the details of practical life, he began from that time to build up the large fortune in which were blended the results of his labor, his alliance, and his skilful management. The constantly increasing success of his lectures had become, with Thenard, the most sensitive test of his self-love. At each of them he seemed to put forth all the ardor of a general on the battle-field ; leaving nothing unprovided for, and making but a limited number of experiments, he required them to be exact and striking, and to be presented at the precise moment. The slightest inadvertence or misapprehension on the part of his assistants drew upon them sharp reproofs, and they must have had a hard time of it but for the prompt return of good nature and the acknowledgments which followed. “In a lec- ture-room,” insisted Thenard, “it is the students alone who have a right to be considered ; professor, assistants, laboratory, ought all to be sacrificed to them.”. Before an auditory which had witnessed one of his outbursts, he soothed the not unreasonable susceptibility of him he had maltreated by saying, «Fourcroy has often done the like to me! It produces promptness of appre- hension.”’ It was this same promptness of apprehension which supplied Thenard with one of those penetrating insights which open new horizons to science. The discovery of oxygenated water is recounted by himself in the following terms: “Tn 1818 I was delivering my first lecture on the salts at the Sorbonne : ‘in order that the metals should unite with acids, I was saying it is neces- sary that they should be oxydized, and that they should be so only toa certain point; when the quantity of oxygen is too great, the oxide loses a part of its affinity.’ Asan example I was about to cite the deutoxide of barium, when the thought suddenly crossed my mind that the experiment had not been made. As soon as I re-entered the laboratory I called for oxygenated barytes ; I diluted chlorhydrie acid with ice, adding it in such a manner as to have a liquid at zero. I hydrogenized the barytes and reduced it to the state of paste. I then made the mixture; when, to my great surprise, the barytes 380 MEMOIR OF LOUIS JACQUES THENARD, dissolved without sensible effervescence. So anomalous a fact could not fail to arrest attention. When I returned for my following lecture, I perceived small globules attached to the sides of the vessel, like those which are seen in a glass filled with champagne wine; bubbles of gas were escaping from the liquid, though quite slowly. I then took a tube closed with the lamp at one of its extremities, and, pouring in some of the liquid, heated it. The bubbles were now rapidly disengaged and gas accumulated in the part of the tube which remained free ; I introduced a match and it kindled—there was oxygen present. The hour for my lecture had arrived and I went through with it, but the preoccupation of my mind must have been deplorably apparent.” Thenard had fallen on the traces of a new fact; at first he was disposed to believe that he had made the discovery of suroxygenated acids, but he soon satisfied himself that these acids had no existence. Was it, then, water itself, simple water, which was oxygenized? The idea had scarcely entered his mind before it was proved by experiment, and oxygenated water was thus added to the acquisitions of chemistry. A new and suggestive fact had been reached by Thenard, the report of which soon spread through scientific Europe. Foreign chemists came to assist in the experiments, and the arrival of Berzelius, at this time, in the French capital, seemed appropriately to welcome the recent discovery. Calling with- out form on Thenard, the Scandinavian philosopher saw him for the first time ; yet these eminent men at once recognize each other, and find themselves, as if in virtue of the law of affinities, converted on the instant into old friends. “TI come,” said Berzelius, “to gather ideas in the domain of French chemistry, which you have so much aggrandized and enrichéd. You will, of course, let me see the oxygenated water.” The conversation turned on Gay Lussac and: his iodine, the new element which that chemist had so distinctly identified; as well as on his cyanogen, a compound substance which affects, in-its combina- tions, all the characters of simple bodies. ‘ We must not forget,” said The- nard, “the admirable theory of definite proportions which we owe to you, and which, revealing the immutable laws by which bodies combine, has become the torch of chemistry.” ‘I admit,” rejoined Berzelius, ‘“ that I have been fortu- nate. Do you know,” he added, “that your recent labors and those of your friend have given Davy occasion to say, ‘Thenard and Gay Lussac apart are stronger than Thenard and Gay Lussac united?’ ”” From this conference 'The- nard proceeded directly to the Sorbonne, and was conducting his lecture with his usual facility, when his eyes casually wandered to a corner of the apart- ment, and he immediately showed signs of discomposure. ‘The audience, in turn, became uneasy, but Thenard, promptly recovering himself, exclaims: “Gentlemen, you have a right to know the cause of my embarrassment ;” and, pointing to a remote part of the amphitheatre, ‘Gentlemen, there is Berzclius.” At once the crowd rises, and a respectful circle surrounds the illustrious stranger with long and rapturous applause. Moved by such proofs of enthu- siasm, and forgetting his usual phlegm, the Swede exclaims, as he is borne unresistingly to a seat near the chair: “ With such pupils it is impossible to be other than a good professor.” He afterwards observed to Thenard, “I had promised myself to verify, in entire secrecy, whether all that fame had taught me respecting your talents as a professor were exact. I find it even below your real merit.” Thenard was now investigating the properties of oxygenated water. One of them is extremely singular; Berzelius named it the catalytic force. Many bodies decompose oxygenated water without undergoing any chemical alteration, without seeming to act otherwise than simply by their presence. The phe- nomenon, therefore, depends not on the ordinary affinities ; nor yet on electricity, MEMOIR OF LOUIS JACQUES THENARD. 381 so far at least as was apparent, for the most subtle examination had failed to discover the least sign of electrical action.* Is it due, then, to a new force? So Thenard thought and said. The catalytic foree, he believed, would furnish the theoretical bond of a whole class of facts, some of which were already known. As the fear of mistake is always associ- ated, in a practiced mind, with the pleasure of discovery, he called to his aid the counsels of a friend, a bold and sagacious chemist; and the views of Dulong, after mature consideration, coinciding with his own, he might with confidence leave his conclusions to the judgment | of after times. Thenard, associated in 1810, as professor at the Polytechnic School, with the eminent men who shed so bright a lustre on that model institution, thoroughly identified himself with its progress and its benefits; each generation of pupils which he instructed seemed to afford him a new pledge of the perpetuity of his fame. In addition to this appointment, he received in 1814 that of member of the Committee of Consultation for Manufactures; in 1815, he became a member of the Legion of Honor; in 1821, Dean of the Faculty of Sciences; in 1825, he was created Baron by Charles X. Learning that he was about to receive this latter distinction, he demanded, with visible emotion, “Why is not Gay Lussac also named? He deserves it at least as much as I do.” At the moment he forgot, perhaps, that he had once been a courtier, and a skilful one: it had been at the promptings, however, of a kind heart. Few had admired more than he those superb paintings in the cupola of the Pantheon, in which the pencil of Gros has so admirably imbodied the legends of our national history. The enthusiasm of his cotemporaries seemed to guarantee to the artist the admiration of ages to come, when, at the expiration of only a few months, stains of different shapes and colors made their appearance on the surface of the nave, and it became evident that, from moisture having pene- trated the stones, this great work of genius was hastening to decay. The mortification of Gros eouli be consoled neuer by the public sy mpathy nor the real concernof the sovereign, who saw with regret the threatened ruin of a monument, in which a conspicuous place had been allotted to himself. Thenard, between whom and Gros there existed a sincere friendship, no sooner heard of the exiastrophe than he commenced in secret a series of experiments, by which he ewas led to the discovery of a means of rendering the most porous stones imper- meable to moisture. Once sure of the result, he repaired to the cabinet of the artist and inquired whether he would repaint the cupola if satisfied that the colors would stand. ‘Away with you,” roughly replied Gros, “and let me hear no more about it.” Fourcroy, it will be remembered, had, in the words of 'Thenard, often done the like to him, so he tranquilly withdrew to his labor- atory to await the coming of Gros. This was not long deferred; the door presently opened and the artist inquired, in a voice of anxious emotion, if what had been spoken of were practicable. That evening Thenard was summoned to the ‘Tuilleries, his method explained to the satiatncron of the royal personage, Darecet ‘at his own request was united with him, and he was dismissed with the promise of a grateful requital. *See on this subject a very remarkable note of M. Becquerel, Annales de Chimie et de Physique, t. XXVIII, p. 19, (1825), entitled: ‘‘On the electro-dynamic effects produced during the decomposition of oxygenated water by different bodies.”” The following is an ex- tract: ‘‘M. Thenard discovered that the metals, with the exception of iron, tin, antimony, and tellurium, tend to decompose oxygenated water; that those which are most oxidizable become oxidized, while those which are not so preserve their metallic lusture. It has been observed by M. Beequerel, that during the decomposition of oxygenated water by the sponge of platinum, gold, &c., electrical effects are produced simiar to those which would take place if those bodies were chemically attacked by the oxygenated water. He inferred that the de- composition and the chemical action proceed from the same cause; a conclusion which strongly eR M. Thenard.’’ [See on this subject the prize essay from the Holland Academy of Sciences, published in the present Smithsonian report. ] 382 MEMOIR OF LOUIS JACQUES THENARD. That requital our savant was convinced he should never solicit; but who can count upon anything? One day, at the exit of the students from his lec- ture, the door is found to be guarded by a force of the police, whose suspicions involve the whole assemblage. Certain fugitives from a popular tumult which had just been quelled had found means to make theiz way into the hall, and confound themselves among the audience. In the clamor which results the professor is drawn to the spot; the students are at once quict, but the po- lice refuse to surrender the prisoners. The most that he can obtain is, that those found with notes shall be liberated as students, and others are enlarged on satisfactorily answering some scientific interrogatory which he propounds to them. Fifty, however, of the more unlucky are conducted to prison. At seeing them led away, the heart of Thenard is touched ; he hastens to the minister of the interior, but is badly received; to the prefect of police, with no better success. Suddenly a thought crosses him: “They promised me so much on account of the cupola!’ Immediately his steps are turned to the 'Tuilleries, and with difficulty obtaining an audience, he states the case respectfully but warmly ; they are his cherished pupils, his children ; he will be responsible for them. ‘Yes,’ replies the king, with a smile, “but those who are ignorant of chemistry have been put in prison. See my minister, however; the case has not been provided for.” At midnight the gates of the prison open before Thenard. ‘Gentlemen,’ he cries, ‘you are at liberty ;” then pausing a mo- ment on the threshold, he adds, ‘On one condition, however—that you will learn chemistry.” Appointed counsellor of the University in 1830, “Thenard,” says M. Girar- din, “not only rendered to science the great services expected of him, but proved himself an admirable man of business. Severe against abusesand neg- ligence, no one lent himself with more lavish facility to all true reforms. Much as he had to be proud of in this world, I have never known him prouder and happicr about anything than the right conduct of the state colleges.” For four years he occupied a seat in the Chamber of Deputies, and as he had ac- cepted it with reluctance, so he left it without regret, saying, as he repaired to the scene of rejoicing for the election of his successor, “I am going to assist in celebrating the restoration of my own liberty.’? His declaration that “he did not meddle with anything but what he thoroughly understood,” may be held to have been the rule of his public life. When a member of the higher cham- ber he moved a revision of the laws of instruction, a reimpression of the works of Laplace, and the national protection of the widows of learned men ; he gave also a profound consideration to some of the questions relating to public indus- try. ‘The spirit of party exercised no dominion over him. Swayed by reason, he sct no value on administrative parade, preferring to all other authority that which he exercised as an undoubted master in the domain of science. During an Academie career of forty-seven years, he constantly yielded a zeal- ous support to whatever views or undertakings appeared to envelope.a germ of progress, and there was scarcely one of his colleagues who was not indebted to him for the suffrage of an applauding voice. It was natural that he should cherish a profound regard for the Academy where his fame, his services, and, above all, his habits of conciliation, assured the highest authority to all his expressions of opinion. In private life he cheer- fully accepted the obligations of his eminent scientific position, and his house, open to merit of every description, was the abode of amenity and grace. A certain vestige of its rustie origin, a simplicity which recalled the character of our central populations, gave to this amiable household only a new and pecu- liar charm. In person 'Thenard was large and vigorous, bearing erect a head covered with a redundance of black hair, with features well marked and animated by an eye of lively intelligence. It was impossible not to recognize in him one of those organizations on which nature has lavished all the elements MEMOIR OF LOUIS JACQUES THENARD. 383 of a complete existence. That attachments, both of a public and private nature, should gather about one thus constituted, was inevitable ; complaisant and just, to him all was easy and simple; neither reproach nor ill-will ever troubled a heart which, more than once, was agitated by the expressions of grateful acknowledgment. During his lectures at the Polytechnic School, it happened, on one occasion, that something essential to the demonstration was wanting. Thenard impa- tiently calls for it, and while the attendant runs to seck it, lays his hand, as if to gain time, on a glass, and carries it, without examination, to his lips Having swallowed two mouthfuls, he replaces it, and with entire self-posses- sion observes, “Gentlemen, I have poisoned myself; what I have drunk is corrosive sublimate, and the remedy is the white of eggs; bring me some.” The students, to whom his first words had conveyed an electric shudder, pre- cipitate themselves through doors and windows, ransack the neighboring stores and kitchens, and, as each one brings his contribution, soon an immense heap of eggs rises before the professor. In the mean time, one of the students has flown to the Faculty of Medicine, and, interrupting an examination, exclaims, “ Quick, a physician! Thenard has poisoned himself at the school in delivering a lecture.” Dupuytren rises, seizes a cabriolet on his passage, and rushes with breathless haste to the scene of the accident. But, already, thanks to the albumen, the life of Thenard was saved. Dupuytren, however, insists on the use of a probe, in order to be sure that none of the corrosive substance is absorbed by the stomach. An inflammation of the organ is thereby produced, and Thenard, saved from the poison, is put in danger by the remedy. During his illness, the students of all the schools manifested the most poig- nant anxiety ; with affectionate zeal they watched around his house night and day, in order to avert every possible cause.of disturbance, and listened in un- easy silence for tidings from the interior. Every morning exact bulletins were posted in all the principal establishments, without its being known who were the authors. When Thenatd reappeared in his chair at the Sorbonne, the de- light manifested was proportionally great. Every one sprang to his fect with- out seeming to know in what way to express his joy, and the professor for once confessed himself overwhelmed by a torrent of profound and grateful emotions. It might now have seemed that long years of happiness were in reserve for Thenard, but his fortitude was destined to terrible trials. By a succession of bereavements he lost almost all which could sooth the decline of life : first, his mother-indaw, the early friend who had propitiated his happiness; then the devoted wife who had been its chief dispenser, the latter escaping, by her sudden removal, the pain of secing their last child expire in the bloom of youth; a brother, a sister, and a nephew followed. When one only and tenderly be- loved son remained, the afflicted father exclaimed: “I dare no longer believe in his existence.” The counterpoise which he opposed to these often renewed sorrows was the suggestion of a benign and wise compassion; the foundation of the Soczety of the friends of Science seemed an inspiration from his memories of the past. After bequeathing it a considerable legacy, and associating with it all his friends, Thenard expired June 21, 1857, showing by his latest words that his solicitude still dwelt upon the cherished “Society.” “I trust,’ he said, “that I have formed a union which nothing will ever break. I hope that those who cultivate the sciences, those who are occupied with their application, and even those who only recognize their value, will continue united for their protection.” Let the orphan, the widow, the indigent aspirant, salute with grateful accents the tomb of the excellent man whose last thoughts were for them. MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE, BY M. DE 'QUATREFAGES. 4 “From the Bulletin of the Imperial Society of Acclimatation.—Translated for the Smithsonian Institution. ] Isidore Geeffroy Saint Hilaire was born the 16th December, 1805; and on the 10th November, 1861, he sank under an illness whose insidious progress had set at naught all the efforts of scientific skill and devoted affection, before he had completed his fifty-sixth year. What this short life had been has already been related by those whose eloquence was heightened by grief and friendship, and I have myself said a few words on this subject. What the man was has thus been declared, but the appreciation of the savant required a little more development. It is for this reason that I return to the theme. I wish to sketch, at least, the principal features of that scientific existence which was cut short at the moment of bearing its finest fruits. A child of the museum, Isidore Geoffroy took, as we may say, his first steps in that collection founded by his illustrious father, in those galleries which had grown, as if by magic, under the united efforts of the Brogniarts, the Cuviers, the Geoffroys, the Jussieus, the Lamarcks. This daily spectacle would have inspired even an ordinary mind: judge, then, of its effect on an intelligence of early thoughtfulness. To this influence add that of family traditions*—the example and inspiration of a father like Etienne Geoffroy, the lessons of a mother, whose firm and affectionate heart the most bitter trials have never shaken, and whose elevated judgment has always been recognized by some of the greatest minds of our timet—and it will be seen that few men have entered on their intellectual career under more favorable auspices. Isidore Geoffroy profited by these gifts of Heaven. He was but nineteen, when, in 1824, he made his debut as a zoologist, by the publication of a memoir on a new species of American bat, (Nyctinomus Braziliensis.) He afterwards returned at different times to this group, which had first been disentangled by Etienne Geoffroy, and which for that very reason attracted his special attention; but in 1826, at the age of 21, he laid aside for a time these descriptive labors, to turn to a subject much less restricted, and which at once revealed the secret of studies of deep and long continued interest. He published in the Dictionnacre Classique @ Histoire Naturelle, and soon afterwards in the form of a volume, General Considerations on the Class of Mammifers. Let us dwell a moment on this early work, the first in which Isidore Geoffroy presented a grand general view of facts and ideas. We shall find in it almost all the germs which were to obtain a rich development in his subsequent works. * One of the branches of the Geoffroy family gave, in the 18th century, three members to the Academy of Sciences. +Madame Geoffroy Saint Hilaire, (Pauline Anois) belongs to a family of the magistracy, which still adheres to its old traditions. Her father, M. Briere de Mondetour, was successively Receiyer-général des Economats under Louis XVI, Maire of the 2d arrondissement of Paris, and deputy of the corps legislatif, under the Empire. In all these situations, he knew how to merit the esteem of the sovereigns and the respect of the public. In 1804, Mademoiselle Briere de Mondetour married Etienne Geoffroy, who was already celebrated. She survives her husband, the twin daughters, and the son, who were the fruit of this union. ~ MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. 385 In the description of species, our young naturalist had shown that he could discern and describe with exactness and clearness the most minute characteristic traits. These qualities, so necessary to the zoologist, are seen in the work of which we speak. Already he had shown a sort of innate tendeney to ascend from the details to the whole, to connect isolated facts with general principles. For example, in speaking of the-caudal development of mammalia, the author does not content himself with noting the very considerable variations presented by the number of vertebrae which compose it. He aims to take account of them, and for this purpose ascends to the phenomenaof their first formation. He reminds us that in the human embryo, the coceyx, until the end of the second month, is quite as long as the tail of the dog of similar age. He agrees with M. Serres in attributing to a retreat about the upper part of the spinal marrow, the arrest of development which in the human species intercepted the appendage so prom- inently developed in the dog. He compares these facts with those presented by the tadpoles of the frog and the toad, and concludes by saying: “Thus the mammal is metamorphosed like the batrachian, and all the changes which surprise us in the latter are not even anomalies ; they take place equally in the mammal, and in man himself; and are the general phenomena of embryogeny.”’ All the:anatomical and descriptive part of the work is executed in the same spirit. ‘ The hairy coating of mammalia, the variations of color that distinguish races, the influence of domestication on external characters, the result of the crossing of species and races, likewise conduct Isidore Geoffroy to general considera- tions, the greater part of which had escaped his predecessors. In several passages we see the dawn, more or less advanced, of a great number of ideas which, ripened by reflection and continued study, served as tlie basis of the great work of which we shall speak hereafter. An order of considerations which occupies an important place in this work, and which we cannot pass without notice, is that which embraces zoological geography. From the philosophic point of view where the son of Etienne Geottroy had placed himself at twenty-one, the grandeur and truthfulness of the conceptions of Buffon on this subject could not escape him. We can see that he has been deeply impressed with them ; that already he has been seeking to verify them by ficts; and that if he undertakes the defence of his illus- trious predecessor, it is with a full knowledge of the subject. This enlight- ened conviction, which Isidore Geoffroy shared with his father, is evinced in many of his other writings. Ifthe unjust prejudices inspired by the Linnzan doctrines, imperfectly understood, have been partly dissipated; if, in our day, naturalists admit Buffon to be still greater as a savant than as a writer, it is certainly in great part due to the efforts of these two penetrating minds, so well formed to comprehend, ‘develop, and inculcate a right appreciation of what had too long been misunderstood in the genius of their predecessor. The complete list of the works of Isidore Geoffroy, already published in this bulletin, renders it unnecessary for us to enumerate here several treatises of different kinds which succeeded each other rapidly until 1832. We shall merely point out the tendency, more and more marked in their author, to sub- ordinate facts of detail to complete views, and to attach himself to general and philosophic zoology, such as had been comprehended, though from dif- ferent points of view, by Buffon, Lamarck, and Etienne Geoffroy. These prevailing ideas were manifested officially, as we may say, in a course of lectures given at the Athenzum in 1830, which turned entirely on the funda- mental relations of the animal species among themselves and to the external world. By this course of lessons, which had no precedent in public instruc- tion, Isidore Geoffroy began to assume his special place in the phalanx of those who followed the same banner with himself, and was not long in placing himself in their foremost rank. Two years later appeared the first volume of 25 386 MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. The General and Particular History of the Anomalies of Organization, (1832.) This time it was no longer a simple memoir, nor a resumé enlightened by new ideas; but a work sufliciently new in substance and in form to found, at once, a whole branch of natural science. It is well known how much the anomalies of organization, designated by . the name of monstrosities, have, at all times, struck the imagination of the vulgar and excited the curiosity of the learned. Long regar dod! as prodigtes,* they became afterwards freaks or errors of nature. They were viewed as proofs that the laws governing the formation of living beings might suffer exceptions and infractions. Later, it was understood that physiology was deeply interested in the study of these supposed abnormal beings. But it had required the great progress accomplished during the first years of the present century in anatomy and embryogeny, to demonstrate the extent of the services which the study of monsters was to render. Etienne Geoffroy had often in- sisted on this. Resting partly on the doctrines of his predecessors, but espe- cially strong in his own, he had been the first seriously to take account of the perfectly natural conditions under which these alterations are produced. Isidore Geoffroy followed his father in this track. As he says himself, he proposed to make anomalies better known, to trace their characters, their mode of pro- duction, their relations, their influence, and thus to lead*to the more perfect knowledge of the normal order.t A single fact will show how completely this multiplex aim of the author has been accomplis shed. These beings, so various, so complex, which had been considered the product of as many special infractions of general rules, have conformed to all the exigencies of the classification invented for normal beings. Isidore Geoffroy has divided the slightest deformities as well as the greatest monstrosities, those characterized by excessive complication, as well as those resulting from defective parts, into classes, orders, families, and genera, as had been done with the mammals or the birds. And this classification has re- mained unchanged. Some new genera have been added to it, some new species described, but all have fitted naturally inito the framework so skilfully traced out by the author between his twenty-sixth and thirtieth year. The importance of this work was immediately understood. The first vol- ume, which appeared i in 1832, was a guarantee of those which were to follow. This consideration decided the Academy, and on the 15th April, 1833, Isidore Geoffroy, at the age of twenty-seven, took his seat beside his father in the section of zoology § The History of Anomalies was completed, and other labors and Es succeeded. Of these we can notice only a few. We must first point out the views which Isidore Geoffroy frdggriewly put forth relative to classification. It is well known what importance has justly been attached, since the time of Linneus, to,the forms for the arrangement, in an order determined beforehand, of the numerous beings with which naturalists *The Greek and Roman Jaws condemned to death every child affected with certain organic deviations. In the middle ages it was nearly the same; and even in the 17th century Riolan thought himself very bold, and really was so, in maintaining that they need not be put to death ; that it was enough to shut them up. t Analytical Notice of the Zoological, Anatomical and Physiological Labors of M. Isidore Geoffroy Saint Hilaire, 1853. } The third volume of the History of Anomalics appeared in 1836. § M. Delaunay has preserved the remembrance of an incident which marked this election. Our confrére has recalled, in happy terms, that Mr. Gay Lussac, president of the session, af‘er having counted the votes, yielded the chair to Eftenne Geoffroy, then vice-president, in order to give him the happiness of verifying the triumph of his son himself and proclaiming his election. M. Delaunay has well depicted the emotion of the Academy in witnessing the verification of the vote.—(Funcral of M. Isidore Geoffroy: Discourse of M. Delaunay in the name of the Faculty of Sciences.) MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. 387 occupy themselves. We know that these groupings, at first purely methodic, became.systematic in the hands of Jussieu for vegetables, and of Cuvier for animals. But the latter had deeply felt how incomplete are our classifications when we wish to represent the multiplied connexion’ of living beings.* Isidore Geoffroy had also felt the same, and he tried at least to diminish the imper- fections. ’ Linear classifications, however arranged, never place a- being except between two others, that which precedes and that which follows it. Thus they repre- sent only direct affinities ; they are powerless to represent, even imperfectly, collateral affinities or zoological analogies. Now the latter have, in a general view, an importance which must naturally have attracted the special attention of our author. He soon perceived, like some of his predecessors, that the primary zoological groups may be divided into secondary groups, composed of species which correspond to each other, as it were, term by term. He thought, with reason, that these series ought to be represented, and he was thus led to that parallellic classification which he has applied especially to the mammifers. However, Isidore Geoffroy, no more than Cuvier, regarded his classification as presenting all the relations of beings with each other. He only saw in it a less imperfect representation of what exists. He has several times expressed himself very clearly on this point, regretting to see his ideas presented ina manner too absolute, by some pupils who had not half understood them. Here, as elsewhere, the master was more cautious than his disciples. We can only name-the volume entitled Essays on General Zoology, (1845.) It is less a book than a collection of memoirs on distinct subjects, connected only by the common thought indicated by the title. We shall refer to some of them hereafter. To construct a general system of zoology was, in fact, the constant object of Isidore Geofiroy. It betrayed itself everywhere, and even his public instruc- tion served to manifest it. At the museum, and still more at the Sorbonne, several of his special courses of lectures were partly devoted to the exposition of ideas connected with this purpose, which never quitted him, even when he seemed farthest from it. . But these ideas, as they ripened by incessant study, expahded more and more. He perceived that in general questions, living and organized beings cannot be isolated. ‘Even at the limits of the animal kingdom, the application of the method remains incomplete, the demonstrations for the most part unfin- ished, the synthesis only partial.”t Thus he was led insensibly, and, as it were, in spite of himself, to publish, not a general zoology, but a General Nat- ural History of the Organic Kingdoms. The first volume of this book, which was to be the epitome of the labors of a whole life, appeared in 1854; the second in 1859. The first half of the third volume was published in 1860. ‘This is all that Isidore Geoffroy has been able himself to give to the public. What pious hands have collected will, perhaps, complete this volume and the second part of the work; the rest is forever lost.t It is especially for this reason that the premature death of Isidore Geoffroy *The formal declarations inserted by Cuvier in one of his last works on the essential dis- tinctions between the classifications and the method, has too often been forgotten.—( General History of Fishes, by MM. Cuvier and Valenciennes.—( Introduction by Cuvier. ) tGeneral Natural History of the Organic Kingdoms, preface. ¢This first part extends from Chapter VILI to Chapter XI, inclusive. Besides, the family have tound four sheets, entirely corrected and ready for the press; two partially corrected ; three sheets in the first draught, and a manuscript reaching to the end of Chapter XLX. We may then expect that the third volume will be completed, and that there will, perhaps, only be wanting’ the definitive conclusion which an author sometimes reserves till the last moment, till he has reviewed and reconsidered his work. But for the latter parts, the most original of this great work, neither notes nor fragments could be discovered. All was in the head of the author. 83888 MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. is a real misfortune to science. During twenty-six years this man, of the first order of mind, had in view, in all his works of detail, in ali his lectures, the development of a class of ideas of the highest importance. We have said already, and repeat here, who shall take up the work? And even though some one should step forward to replace him, can it be hoped that his successor will lay hold of this immense problem with the materials and ability which Isidore Geoffroy had at his command ? As if to increase-and justify our regrets, the author places at the head of the first volume an analytic programme of what his book was to be. He divided it into six portions, and we have seen that the second part, at most, will appear. Two-thirds of the work will be forever known to us only by this epitome, the whole of which, representing at least five or six volumes, hardly occupies three pages. Unfinished, or rather only commenced as it is, the General Natural History of the Organic Kingdoms has rendered essential services. Isidore Geoffroy had time to pronounce on some questions which touch on the very foundations of biological sciences, and it is of importance that his judgment on the greater part of them should be known. Heir of Buffon, Lamarck, and of Etienne Geoffroy, having constantly held aloft the banner of the philosophic school, no one can less be suspected than he of having sacrificed to considerations foreign to science. His opinions are the most formal condemnation of certain very ancient doctrines, which some have lately sought to revive in the name of science and philosophy. é Such, for example, is that which puts in doubt the reality of species, by admitting that plants and animals may vary indefinitely, and bring forth series of individuals so distinct as not to be confounded. No one can pronounce against it more clearly than our author. Hedoes more. He shows that in spite of theoretical ideas, a// serious naturalists have arrived at the same conclusion on this question, as soon as they abandon the vague ground of hypothesis to place themselves on that of facts. He has said, and he could say with reason, that in spite of the profound difference of their general doctrines, Lamarck and Cuvieragreed on this fundamental question. Both, in this, contradicted some of their abstract principles; each had to take some steps towards the truth in an inverse direction. The one had to abandon the theory of iadefinite variability; the other, that of absolute fixity. hus they met in the belief which was that of the better years of Buffon, that of Isidore Geoffroy: the belief in the limited variability of species, the result of which is, that the forms and certain functions may sometimes be modified within very extended limits, while the essence of the being remains unaltered. In Buffon, no more than in Geoffroy, was this belief the result of mere hypothetical views; in both it was the result of a deep study of facts. ‘The former, before reaching it, had passed through the extreme doctrines indicated above; the latter, enlightened by this example, and taught by what he had under his eyes in the menagerie of the museum, saw the truth from the first, and supported it by new proofs. Man could not escape the study of the savant who embraced the whole of the animated creation. He was a prominent object of the researches and medi- tations of Isidore Geoffroy. As early as 1842, in a short article of the Dic- tionnaire Universel des Sciences Naturelles, the author rejected the views gen- erally adopted on the authority of Blumenbach and Cuvier, as to the subject of the relation between man and the lower animals. He insisted that the order of bimana should be struck out, as removing us too far from the monkeys, if we see in man only the material being ; and bringing us too near them if we regard the whole of human nature. Ata later period, in his lectures,* and in his * Lessons on Anthropology, given at the Faculty of Science, and summed up by M. De- vaille, 1856. MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. 389 General Natural History, he repeated the same criticism, and contended strongly for the admission of the human kingdom, first proposed by a Frenchman, the Marquis de Berbengois,* and since adopted by a number of eminent men in Germany and France. oe Is this kingdom, like the others, divided into groups distinct and, to a certain degree, independent of each other? Does it contain a, great number of species which may be compared to the animal and vegetable species, or else does it include but one, namely, man?t We know that this question is still agitated, and even with redoubled ardor. The answer of Isidore Geoffroy is that of Buffon, Cuvier, Etienne Geoffroy Saint Hilaire, Miller, Humboldt, and others, He pronounces in favor of the unity of the human species.} The General Natural History of the Organic Kingdoms stops at the funda- mental principles of biology. he author proposed to present, in the third part, the general facts relative to organized beings, considered in themselves or in their organs ; the fourth was to be devoted to the general facts relative to the instincts, the habits, and, more gencrally, to the exterior vital manifestations of organized beings; the fifth, to the general facts relative to the successive and present dis- trib..ion of organized beings on the surface of ,the terrestrial globe; in short, the sixth was to comprise the expositions of what the author calls xatural phi- losoply. There he was to show the convergence of all science towards philo- sophic unity ; to explain his views on the totality of organic nature; to show in the perpetual changes of the details and the permanence of general laws, whence results unity through variety; the harmonic succession of individual and general phenomena, which produce progressive harmony. Certainly no one ean glance over this magnificent programme without a feeling of bitter regret. The History of the Organic Kingdoms will remain like one of those unfinished edifices whose factitious ruins sadden the mind by merely giving a glimpse of what the edifice would have been, by revealing the grandeur of the plan and the genius of him by whom it was conceived. There is an additional proof of the intellectual worth of Isidore Geoffroy. Profoundly devoted by sentiment and conviction to the doctrines of Etienne Geoffroy, he had to guard against a very natural inclination to tread too closely in the steps of this venerated guide. While he retained his filial regard and erected monuments of it|] to his father, no one can mistake him. Isidore Geoffroy was like one of those eminent artists who, after having been a docile pupil of a great master, after having copied his manner, have created one in their turn; have conceived and executed works stamped with their own * Journal de Physique, 1816. M. de Barbengois had called it the moral kingdom.—(See General Natural History of the Organic Kingdoms.) tA polygenistie belief had sometimes been attributed to Etienne Geoffroy Saint Hilaire. In the work which he has devoted to the memory of his father, Isidore Geoffroy has warmly protested against this assertion.—(Life, Labors, and Scientific Doctrine of Etienne Geoffroy Saint Hilaire, 1847.) ¢ According to the lectures reported by M. Delvaille, Isidore Geoffroy, in 1856, only pre- sented this doctrine as having in its favor the largest share of probability. To judge by the conversations I had with him less than a year before his death, his convictions on this point had become much more decided. Unfortunately, he did not reach this part of his work. § Abstract of the Analytic Programme placed at the head of the first volume. || It is well known thatthe son of Butfon caused to be placed at the town of Montbert, where his father had worked, a column which bore this inscription: Excelsa turris, humilis columna, Parenti suo filius Buffon. (1780.) Isidore Geoffroy conceived the nobler thought of raising to his father a more durable mon- ument by publishing the work entitled Life, Labors, and Scientific Doctrine of Etienne Geoffroy Saint Hilaire. The General Natural History of the Organic Kingdoms has asa dedication this verse of Dupoty: “Méme etait fait per moi, cet ovrage est le tien.” (Even though done by me, this work is thine.) 390 MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. genius, and have thus taken rank beside their teacher. We have pointed out what our author was as a man of pure science; it yemains to show him under other relations. But here we may be more brief. His labors of practical science are more generally known, and what is important to point out is the filiation, too often unperceived, which unites them to the preceding. To every one who applies his mind to general questions of zoology, the do- mestic animals have an importance of the highest order. The extent and number of modifications presented by each of their species at once raise and resolve a crowd of problems which touch on the most delicate questions of physiology, even on the history of man himself. Thus they early attracted the attention of Isidore Geoffroy. We find the proof of this in the article Mammifers, in the Dictionnaire Classique, which we mentioned above, and still more in the Essays on General Zoology. We find, amongst others, a memoir relative to the possebility of elucidating the natural history of man by the study of the domestic animals.* 'The author examines at first the analogy which exist between the variations of the domestic animals and those of the human races, and points out the close connexions presented by these two orders of facts. ‘Then he shows how the determination of the original country of a domestic species may throw light on the history of the migrations of a people. These ideas were to be afterwards extended and completed.t Inthe same volume we find a treatise on the domestication of animals,t which was the first step in a path in which the author was so greatly to distinguish himself. This simple memoir furnished the basis of labors more and more mul- tiplied and important, and was transformed into an octavo volume of more than five hundred pages, entitled Domestication and Acclimatation of the Useful Animals. We know, also, that the ideas put forth by the author of this book have assumed a concrete form, and have been reduced to practice by the foun- dation of the Society of Acclimatation and the creation of the Garden of Accli- - matation. These two establishments are truly the works of Isidore Geoffroy, and should rank amongst his best. If, in their beginning, they excited some distrust and some raillery, the first of these sunk under the conciliating and pru- dent direction of the founder; the second disappeared before established facts. Thus their progress was rapid, their future soon assured. Isidore Geoffroy thus left, beside his books, two institutions not less durable than his fame; and if his loss excited uneasiness in the minds of those who had adopted his plans, it was soon dissipated by the choice of his successor.§ The results of the publications of Isidore Geoffroy on: practical zoology, in the foundation of the two organizations which I have just named, deserve to be pointed out no less for their immediate and visible effects than for the influence which they have already exercised, and which must continue to be more and more felt. Hitherto the natural sciences, zoology especially, had. been some- what despised by those who claim the title of practical men. They were merely considered as a species of knowledge calculated to amuse the mind, but without practical utility. For this cause they were rejected, as were chemistry and geology by the metallurgists and miners of the last century. Thanks to Isidore Geoffroy, and to the movement which he originated, these prejudices begin to be dissipated; they may, perhaps, disappear slowly, but certainly it will be at, length understood that zoology has also its applications; that it ought to be to the breeding of animals, and to all that we procure from them, _ * This treatise, an abstract of which was communicated to the Society of Natural Sciences in 1835, had been read to the Academy in 1839. It figures in the Reports. + General Natural History of the Organic Kingdoms. {This work had appeared, but less complete, in the Encyclopédie Nouvelle. » § It is known that this successor is M. Drouyn de l’Huys. +. ¢ . MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. Doaie that which the physico-chemical sciences are to operations upon brute matter. . It is true, Buffon, and especially Daubenton, had acted upon this idea; but, less fortunate than their sutcessor, and perhaps beginning too early, they left no real impress on the minds of the people. It will not be so with the work of Isidore Geoffroy ; and this is one of the special results of that life so well occupied. Here, as everywhere, pure science appears the mother of practical science—a mother fruitful in proportion as she is exact and elevated. In speaking of the works of Isidore Geoffroy, M. Milne Edwards has said: “ All display a profound erudition and bear the stamp of a mind wise, elevated, and generalizing, and the purity and elegance of the style enhance their merits.’’* In speaking of his colleague’s public instruction at the Faculty of Sciences, M. Delaunay expressed himself in a similar manner: “‘M. Isidore Geoffroy,” says he, “was a most distinguished professor. He had an easy elocution, and ex- pressed himself with graceful simplicity, without any pretension to eloquence, and captivated the attention of his audience at once by the clearness of his explanations, and by the art with which he could group isolated facts around the principal ideas which he sought to illustrate.’’} These appreciations are just, and they characterize well the eminent man of whom we speak. His lucid mind embraced at once his whole subject; conse- quently his ideas arose logically one from the other, and, as it were, co-ordered themselves. His words translated faithfully his thoughts, clearness of expression only reflecting clearness of conception. Thus his speech kindled at times, and he never wanted striking images and happy comparisons to render the most comprehensive or profound ideas, becoming thus an orator without effort. His lectures were always as well attended as his works were widely read. It was at the museum, in 1829, that Isidore Geoffroy, at the age of twenty- four, first appeared as a professor. He was then an assistant to his father, and took ornithology as the subject of his lessons. The following year he delivered, _ at the Athenzeum, the remarkable course of lectures of which we have already spoken. Having been appointed, in 1837, assistant to his father at the Faculty of Science? in Paris, he soon quitted this temporary chair to go to Bordeaux, with the title of dean, to organize the Faculty of Sciences created in that city, (1838.) But this task finished, he returned to Paris, and in 1840 was named inspector of the Academy, and charged with the duty of inspector general of the University. At the same time that he fulfilled these high functions, in which civil administration is so closely connected with the best interests of science, he replaced his father at the museum, the latter being struck with blind- ness, as had been Lamarck and Savigny before him. In short, in 1841, this position having been made permanent, the veteran of science yielded the place to the young soldier whom he had trained ; and Isidore Geoffroy received, during his father’s life, the succession which, for a long time previously, he had in great measure administered.t In effect, from 1824, the youthful savant had discharged the duties of assistant naturalist at the Jardin des Plantes. In this office he had to superintend and direct not only the colleetions of mammals and birds, but also the menagerie, founded by Etienne Geoffroy, (1793.). He had devoted himself, heart and soul, to this double task; but he became, perhaps, still more eamest in it when he was made the official chief of this very important part of the museum. All those who have seen him at work know with what steady ardor he labored to “Funeral of M. Isidore Geoffroy Saint Hilaire. Discourse of M. Milne Edwards, president of the Academy of Sciences. t Funeral of M. Isidore Geoffroy Saint Hilaire. Discourse of M. Delaunay, in the name of the Faculty of Sciences. {In 1844 he became titular inspector general, and he exercised the functions up to the pie ae he, replaced M. de Blainville as professor of zoology at the Faculty of Sciences, (1850. 392 MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. enrich these collections of dead and living animals. The galleries soon became too small to contain all that Isidore Geoffroy procured for them; sometimes by using the slender resources which the too scanty fifhds of the museum placed at his disposal; sometimes by availing himself of the authority of the establish- ment and his own personal influence.* Ata time when it was the fashion to find fault with all that concerned the museum, objection was often made to the crowded condition of the cases, and the professor who had the administration of | this portion of our riches was reproached for neglect. It was forgotten that this was the most striking proof of his exertions, for had he been less indus- trious, the localities sufficiently capacious for his predecessors would have sutliced for him. . What we hae just said of the galleries applies equally to the menagerie. But could it be otherwise? The number of living specimens collected in the parks of the museum was tripled in twenty-five years,t while the disposable space remained almost the same. What minute and constant care did it not require to utilize this ground so parsimoniously granted to the first scientific menagerie ever formed ; to struggle against conditions often deplorable; to meet expenses constantly i increasing , even when the budget was restricted in conse- quence of political events. It was in the midst of such difficulties that Isidore Geoflroy succeeded in developing the noble creation of his father, and in making it serve the advancement of pure as well as practical science. Some of the first acclimatations attempted in our age have been produced in this menagerie. I need only recall the Egyptian eooset It is known that this fine species, brought to France by Etienne Geoffroy, and since then almost constantly reared in the museum, has furnished, for the first time, a race truly European, characterized by an increase of size and a change of color, but especi- ally by a delay of about four months in the time of laying its eggs—a delay which brings the mother and her young into harmony with the new climate to which they are subjected. We may also mention, in passing, the yaks, three of which, arriving at the museum in 1854, have increased to a herd of more than twenty head, without the death of a single one, young or old. But lect us dwell a little on the part which the menagerie, often considered as only fit to satisfy a useless curiosity, has furnished to the scientific labor of Isidore Geoffroy. This collection of living animals was to him a field of con- tinual experiment, and he owed to it the solution of some of the most delicate questions of physiology and of general zoology. It was by means of it that he was able to vanquish the greatest, one may say the last, difficulties opposed by Cuvier, Blainville, and Ae naturalists, to the opinion of Guldenstiidt and Pallas, as to the filiation which connects the jackal with our domestic dog. It was from it that he sought instruction on the fecundity of metis and hybrids. It is to the facts collected in this enclosure, and appreciated with rare*clearness of judgment which none could fail to recognize in him, that he was indebted for avoiding, in the solution of such delicate questions, the opposite exaggerations which have alternately reigned under the sanction of great names in scicnce. The museum, with its its galleries and its menagerie—the Society of Accli- matation and the garden of the Bois de Boulogne—formed the world in which *In 1828 there were at the museum 7,500 stuffed birds and mammals; in 1885, 11,750; in 1861, 15,500. Besides the magazines contained at the latter period, 12,000 skins in a perfect state of preservation. + In 1524 the menagerie possessed 283 birds or mammals; in 1842, 420; from 1850 to 1861, 900, on an average. tThe Egyptian goose lays naturally about the end of December. Those reared at the museum for some generations laid, in 1844, in February; in 1846, in March; and since then, in April. (Acclimatation and Domestication of the Useful Animals. ) Itis one of the most striking examples that can be quoted of the influence of the surrounding medium. MEMOIR OF M. ISIDORE GEOFFROY SAINT HILAIRE. 9893 the life of Isidore Geoffroy was passed; a world very small, to judge by its extent, but very large to him who could see in it an epitome of the living crea- tion; and our lamented compatriot found it extensive enough to exercise all the faculties of his mind and the peculiarities of his character.* The books of which we have sketched the tendency and the results attest the activity of his mind, while his character was not less seen in the mixture of firm- ness and gentleness with which he exercised his functions. At the institute and the museum his word had always a real authority over his colleagues. At the Society of Acclimatation and elsewhere many thought they followed the inspi- ration of their own minds when they only yielded to an influence that could hide itself, the better to reach a desired end. Everywhere—and this is not his least praise—his subordinates cheerfully obeyed his orders, always clear and precise, or accepted his decisions, dictated by kindness and justice. Isidore Geoffroy had known all the joys of the heart, and he had felt, too, all its sorrows. Account of. {2220 l.oe e be o ces ke 3 Comets. iiveshigationsyrelative toms 5 seul eeeee ee ef ee ee: 82 Conchology. Smithsonian publications on.... 2... 2... -c0.neos cone cone cccccccces 21 442 INDEX. Page. Congress. Appropriation by, for care of collections ..... MEE MUO sin tesaetee a 77 Contact, phenomena of. Memoir on....--..---- +--+ +--+ 20+ + eee eee eee eee eee 395 Contributions to knowledge. Contents of vol. XIII.-..---.----------------++---- 17 Correspondence. Extracts from...-...----------+----+- ++ 2-+ reece cere ee eens 80 Cycladide. Prime's work on ..--...-.----+++--+2---- eee eee ee erence reer eee 23 Daa, Louis Kr., museum in Christiania, Norway--.-.-.--------------------------- 85 Darlington, Dr. Wm. Work presented by..-------------+----++ +--+ +-+--2----+- 383 Death, Of 5 stesso store sivstetie le Srey ol = olen a la se She aoe elie 83 Davis, Hon. G. Appointed regent, to succeed Mr. Pearce ....---.---------------- 78 Deaths of meteorological observers - ------------ ---- +--+ +--+ -2ere+ eee ee rere eee 69 Dille, I. Letter of, relative to archeology .....-----------------+---------------- 86 Disinfectant, made for hospitals .----------------------+---+----------+-++-------- 38 Distribution of specimens. Rules for-.-.---.------------++----+-+-----+--+------- 35, 36 Donations to the museum in 1862. -....-----------------------+----------- +--+ eee 57 Eaton, Daniel C. Letter relative to ferns -----..------------------------ eae eee 97 Egleston, Th. Arrangement of rocks and minerals by, and list of species .-....---- 36 Engelmann, Dr. Geo. Heights of mountains --....--------------------+-------- 81 Entomology. Smithsonian works on ---.-.----------------++++--++-----+----+---- 24 Specimens referred to collaborators ------.---------++----+---+-++-++++-- 37 Estimates for 1863 .----------- ----- +--+ = ene ee ne ens ce een nne corte ne cone ceeeee 77 Ethnology. Lectures on, by A. Morlot..-...-------------+----------- ae eee 303 Lectures on, by Prof. D. Wilson -....------------------------------ 240 Eulogy on Hon. James A. Pearce, by Prof. Bache -.--------------------+--+----- 100 Exchanges. Literary and scientific. -...-.--.------ +--+ + +++ +++ e+e esse eee cree eee 4} Exchanges. Statistics of..---..--------- +--+ -- +--+ ee ce eee ree cree eee cece eee ee 47 Expenditures of the Institution during 1862 .-..----------------+ +--+ 22-2 reese aT Explorations for the Institution. ...----..--.-------- +--+ +--+ 2-2-2 ee eee eee eee 39, 55 Ilachenecker, Geo. Letter relative to Sheyenne Indians ....-....---------------- 95 Fladgate, Clarke & Finch, attorneys to collect remainder of Smithsonian fund in Buigland. 2.22. 3-502 -22 ooe Steno eee ney e one ae ie ae Sone oe ia arte 15 Force, W. Q. Meteorological system, in charge of....--...---.---------+------+-- 32 Observations on temperature of hydrant water -.--------------------- 30 Foreman, Dr. BE. Setsof Unionidee, by -----..----..---2- --2--- e222 epee 56 Flourens. History of Academy of Sciences of Paris..-.----.--------------------- 337 Memoir ‘of Leopold Von Bach’ 1l 2. oi. oe icc ee ewes sence 358 Memoir of Louis Jacques Thenard -:- 2-22.22 0 od ees anes 373 French, B. B.- Grounds under the care of. ......------------ 2252+ oes eee eee 38 Gallery of art. Additions to-.----------------------- +--+ +--+ 0-222 eee ee eee eee 42 Gibbs, Geo. Letters on philology and ethnology .--..-.-----.----------- 87,89, 91, 92, 93 Gill, Theo... Examination of fishes. ..--2----2-0 02-22 see ee een e eee deeb eee eee 56 Girard College. Prof. Bache’s observations at-....-..--.----5--------------- Rect 17 Government. Aid rendered to, by the Institution ..---.-...----------------+----- 14 Gray, Dr. A. Arrangement of plants, by--------.-2-- --- 222+ sense see ose eee ones 36 Gray, Dr. J. E. Identification of bat .------+-+- +424, ses2 +e 2s eee ee cee eee see e ee 96 Guyot, Prof: A. Extension of tables of. .....----. -+-----2++ t2-222 e222 ee ese eeee 3] New. physical tables. ... .-.<- s<--2=js6 0 cnnisenmesen-4--he-h- ies -=-- 25 On. Parry’s, mountain measurements.» —j.2,-r\- = =)-on ae aie ee <== 82 Relation of standard barometers, established by ..---.----------+----- 31 Hammond, Dr. W. A. Interes# of, in meteorology....-» ------ «----- «=- -oanee 107 Som Inage.; « Naming shells; sry ss iscs.cccscccasancae sos acleneetw eoasr ee ements tee 36 Mectutes:.. Accountiol, durine 186162 52s sce sceressninwe ni oamecilsceseaa eee cici= sa 43 Rules G0) POVEIN, 555. 2.23 -ns- Sees win wale siesioteinee aciels aecimienen essere 44 Mist of delivered 1862635202 .sssaeersacistees eS ee eeeisctu ns oe 45 On the study of high antiquity, by A. Morlot ..:.2.. 00.52. 22. s.sece- 303 Onvethnolocy; by, Professor DANWWilsOne ase acne ae sine eee ole eeiciere soak = 240 On the undulatory theory of light, by F. A. P. Barnard..........-..-- 107 Wesley, coun 2. “Onithe classification of books: -: .- 2. - occ Soc oas once seicccstacess 416 MER ULET Steen SOCIOL Yai O.ONOTCSS taal pate ainin'ny ctniiniarel sae eens ninis ott aleteleyalcie/otete a lehelale a2) 3 Chancellor and Secretary to.Congress:. 055.2. oso jcc Sie cote wwe 4 H. Sibley, relative to telegrams of weather. ......-.-2.. -.-- 22-02 e--0 81 G. Engelmann, relative to Dr. Parry’s barometrical measurements... -.--. 81 J.S. Hubbard, relative to observations of Biela’s comet.....-...----- 82 William Darlington, relative to notices of men of Chester county, Penn- 83 T. Lyman, relative to Schlagintweit’s collections........-.-.--------- H. de Schlagintweit, relative to collections of ethnology, &c., for sale... 84 Louis Kr. Daa, relative to ethnological museum at Christiania, Norway. 85 I. Dille, relative to archeological remains ........--2-2s2e-s.e---+ 20s 86 Dr. Aq. Ried, relative to Atacama mummy........-.-.---- (ensote 3 acs fe 87 George Gibbs, relative to philology and ethnology....-...----..-.---- 87, 93 J. G. Shea, relative to Indian vocabularies.----- s.25 cee. eke 94 E. A. Watkins, relative to dictionary of Cree Indians..-....-.-..-..... 94 G. Flackenecker, relative to Sheyenne Indians...-...---...-....----- 95 W. H. Pease, relative to natural history, &c., of Sandwich Islands: ---. 95 Dr. H. R. Wirtz, relative to herbarium captured from confederates. - - --. 96 Dr. G. Mettenius, relative to ferns of Brackenridge’s collection....-.-.-. 97 DC. Eiston; relative: fo-ferns. seemathean ary 3 62 System, much deranged by the Warsewe<0satenwieoansinds- sem app sano nin 14 Mettonius, GC... Wetter-relativ.e: to. femnsi-.-ceiserssela esis ante LAdalsed = Canale So cepa ets 97 Minerals,, . Examination Of... o0disccas cancavecdacqebedes sis sasps tp te. .aee 33 CH OTEd LOY BELO) a aie aces wend met nape tas galas Haein aap, Sedera Ene. ee faye 98 Miscellancons.Collections.. . Account .0f .2.< cian oewn'dswnss von ot od ese SUh oes ate 21 Comienta/ of rst. f0Ur VOlumes's 00min tas waco u ielsie Geb ta wan 61 Moon. « Mapmotic. IniUenCecOf—., 2a 0 lee astias) ale = 8 ota alate Salo eae oot aietals amiotette Ree siete ise 20 Moarlot;A.. .bectures on study. of high antiquity s.2. se aecet i> ace wloeal selec ene Lr ous MinimiGs Tom Pata g OMe sae slg etm als emt gene ale hte caret ae fo eiclaime beetle ara apne ee 426 Museum... “Accdunt and‘ objett of... 2.26 coc seek cancers tence. meee 34, 37 ATTEN OMent OL SPECIMENS I< ain.cm asa aimsatem iain ia sfalele ela fere a helm Sener teeye 56 Instron Gonanions to; Tdi SG Cee we stealec oe aterm stem eee meeete| = ate o7 National Institute. Property transferred to the Smithsonian.........-...-.--.----- 16 NOrwepridn MiUussuint, Cede Olen aass oe lam o-5.-8 2 aide sects mc clceiaieelomio sete ete ara 85 Oiicers, of the Sthithsonian Institatipn. ss i oe ee Sechaba ces some 5 Parry, Dr. Barometrical measurements of mountains -.......-.2. 200222 sce eee ee 81 Patagonia. . Account of buna venainy Mometects-6 tc el. Gece. scenes ce. am eons -~ 426 Irbarce, Tdi, J? At Onno eyaGne A Sess Oe ce 2 setciare oo aiactere elatictaare Ania. 100 Resoltitious Telstive tothe death Or 0s ose ee etal. ates stale Adie ie aa = 78 Pease, W. H.. Letter relative to Sandwich Islands-..20 220. oe kes 95 Phipson, T. L. The catalytic force, or studies on the phenomena of contact... ..-- 395 Pierce, Professor B.”.. Doctrine of probabilitiesue s!5 a se clsas wale Moe atala Le eletale lana « 19 Politics excluded’ from’ operations of Institution. so.) tes ne aso lee se. oo ee 44 Biime; \."" Naming shellatbin S222 35So Sa e tree tana Cares winnie one ae ete Sintes le fetes 36 On gland so eee cee easel Pate Ode aka e baemrewasien yomerane cae 23 Printing by the Institition dhting 1862) 50.8 6 IS. iad ls. see te duce de aswel cameuk 46 Frize questions by scionite adtietles sis Sosa Paes ea elecelaaeees ee 430 Programme of organization ‘of the Institution... 20.5 22.2 5.05 22c eben i. eee t Of stiontific societies vss el aan ae ace reter Came omen es a eee 430 Provincial Society of Arts and Sciences of Utrecht. Prize questions....-.-..-..-.-- 434 Publicstions. ”.Tist of, during Weses7ers eat eee mevionce cases chen aseainoed 60 ACCOUNT Of ions Ho. cavcce BRS soe cae marets cores eeictene creenetne elena eee 16 INDEX. 445 Page. Quatrefages. Memoir of Isidore Geoffroy St. Hilaire. .... 2.2.2.2... -22- cee e ene eee 364 Keceipts and expenditures during 1862: 2: Ce 2s2es oe ee OS ee ee oe aid 15 Hegents-of the Smithsonian Institution <== 2: .S20sb2 i027. 2 pee. a 5 Repister Onvisitors =< 2s52ssssssesseegreees esse eet OEE, Ee OU RAG 8 38 Reid, Dr. A. Account of human remains from Patagonia.......----..----------- 426 hetter,-withAtacamta mummy: = 2252222255 225225-53 2222S. 586 Ae Se 87 Eeport-of Regents for 1661, contents-of :22552:2225522525255; Soe 27 Executive: Committees sais 222 cn2 nese, Sh 8s S759 A Fe 75,79 secretary; Prof.» Henrysess 02545, ceeteeere Pee. Be. 13 Eixtrercopies ordered 4-+2.:25.s22tseeteces tPA Gus JO gre 3a 27 ‘Hules:for distubution’ of yer sseeaw ae eee ele cee eeee Sores ee ee 28 Resolution of Senate ordering report to be printed... .......---2----- 22+ --0----- 2 Reselutions of Regents relative to appropriations. .....,----------+--------------- 12 Komero; M.~ “Letter pranting facilities to Rantus +02. los. cc cecs cccces oeae core 99 Royal Danish Society of Sciences. Prize questions..-.....2... 222222 -222-- ccecee 436 Royal Society of London. Systematic Index prepared by .----..----------------- 42 Saint Hilaire, Isidore Geoffroy. Memoir of, by Quatrefages...--.........--.------ 384 pausary wonnmission, ~ SciciiiicIHbUrs df -2522%.--.-0-2-~-oc- as-5 eoee roe oe cone 14 Saussure, Henry de. Letter relative to works on Hymenoptera, Orthoptera, &c .... 97 Schlagintweit, Hermann de. Description of collections of ethnography, &c., for sale. 84 SCHEME HAS. Ay) SAONCHC SUTVENS; DY ccssse soc. «nccmecceeccip= cere aewepcercces 20 Shea, J. G. Leiter relative to Indian vocabularies... -- 2.22. 2-2. oe one cw ee en cece 94 Shells of North America. Smithsonian works on ----.--.....-2..-2--0---ee--esce 21 Ebley, urem.. Ueleprapnic 'C0-OpelailOl.: -.s< canes etn eicanionecincpemdemecswnms 80 Silliman ioe reseritiote PUBL Olee. “eat acta as naan cae ee cnlocenesenenic teen ene 43 Sleckam Dr ee Catalooteror: Monkeys, DYeeaaioc\-( ate iemn cn iinieisiacnsvenee cecm|ose sieeacee 55 Squier, E. G., on aboriginal monuments of N. Y. Review of -......-.-....--.-..- 318 Bameiine avis WOVIOW OL =< sccm occ sacue sneer ee cee aa te on eee on ee oieaetetesters 318 eager, 8.0, Lelectanis of weatler {f0M - . =< aap ariein nico cop epeehecsecs