HARVARD UNIVERSITY. LIBRARY OF THK MUSEUM OF COMPARATIVE ZOOLOGY. (oocoWv 'OjvJv/s^i^o^ — ^yLuiu^^ /^03 TRANSACTIONS OF THE ACADEMY OF SCIENCE OF ST. LOUIS. VOL. XII. JANUARY 1902 TO DECEMBER 1902. PUBLISHED UNDER DIRECTION OF THE COUNCIL. A 'ST. LOUIS: NIXON- JONES PRINTING CO. ■^ MAR 4 1903 CONTENTS. PAGE. Table of Contents iii List OF Members. Revised to December 31, 1902 v 1. Patrons. 2. Active Members. History OF THE Academy (Abstract) xiii Record. January 1 to December 31, 1902 xvii Papers Published. January 1 to December 31, 1902: 1. Alexander S. Chessin. — On the true potential of the force of gravity. — Issued January 29, 1902 1 2. K. K. Mackenzie and B. F. Bush. — The Lespedezas of Missouri. — Plates I.-IV. — Issued March 19, 1902 11 3. Alexander S. Chessin. — On the motion of gyro- scopes. — Issued May 13, 1902, 21 4. J. B. S. Norton. — Notes on some plants of the Southwestern United States. — Plates V.-VIII. — Issued May 14, 1902 35 5. C. F. Baker. — A revision of the Elephantopeae. — I. — Plate IX. — Issued May 20, 1902 43 6. B. F. Bush. — The North American speeies of Chaero- phyllum. — The North American species of Tri- odia. — Plates X.-XI. — Issued June 9, 1902 57 7. K. K. Mackenzie and B. F. Bush. — New plants from Missouri. — Plates XII.-XVII. — Issued June 9, 1902 79 8. J. B. S. Norton. — Sclerotinia fructigena. — Plates XVIII.-XXI.— Issued August 25, 1902 91 9. Alexander S. Chessin. — On some relations between Bessel functions of the first and of the second kind. — Issued November 24,1902 99 10. Title-page, prefatory matter and index of Vol. XII. — Record, January 1 to December 31, 1902. — Issued February 9, 1903. List op Authors , 109 General Index 110 Index to Genera Ill CORRECTIONS. P. 82, line 27. — For Jackson Country, read Shannon County. PI. VII. — For erythrosperma, read rhodosperma. MEMBERS. 1. PATRONS. Harrison, Edwin 3747 Westminster pi. 2. ACTIVE MEMBERS. Adkins, James Park and Vandeventer avs. Alleman, Gellert* Swarthmore College, Swarthmore, Pa. Alt, Adolf 3036 Locust st. Andrews, William Edward* Taylorville, 111. Bain, Robert Edward Mather 900 Locust st. Bailey, Liberty Hyde* Ithaca, N. Y. Baker, Carl Fuller* .Stanford University, Calif. Ball, DavidC* 27 William st.. New York City. Barck, Carl... 2715 Locust st. Bartlett, George M 215 Pine st. Bauduy, J. K 2810 Olive st. Baumgarten, Gustav 5227 Washington av. Bean, Tarleton Hoffman* Administration bldg., World's Fair. Becktold, William B 212 Pine st. Bernays, A. C , 3623 Laclede av. Biebinger, Frederick W 1421 S. 11th st. Bixby, William Keeney 13 Portland pi. Boeckeler, William L 4441 Laclede av. Bolton, Benjamin Meade 4160 McPherson av. Boogher, John H 4034 Delmar boul. Brannon, Melvin A.* University, N. Dak. Brennan, Martin S 1414 O'Fallon st. Brimmer, George G 6900 Michigan av. Brookings, Roberts 5125 Lindell av. Brown, Daniel S 2212 DeKalb st. Brown, Willi 3526 Pine st. Bryson, John P , 209 N. Garrison av. Budgett, Sidney Payne 1806 Locust st. Burg, William 1756 Missouri av. Burnett, E. C University Club. * Non-resident. Ti Trans. Acad. Sci. of St. Louis. Busch. Adolphus 1 Busch pi. Busch, Aug. A Busch pi. Bush, Benjamin Franklin* Courtney, Mo. Calvert, Sidney* State University, Columbia, Mo. Carpenter, George O Russell and Compton avs. Carter, Howard* Webster Groves, Mo. Carver, George Washington* Tuskegee, Ala. Chaplin, Winfield S 3636 West Pine boul. Chappell, W. G 3810 Westminster pi. Chase, E. C Oriel bldg. Chauvenet, Louis 5501 Chamberlain av. Chessin, Alexander S Washington University. Chouteau, Pierre 912 Security bldg. Chouteau, Mrs. Pierre 912 Security bldg. Compton, P. C 4156 Washington boul. Comstock, T. Griswold 3401 Washington av. Conklin, Harry R.* Joplin, Mo. Cramer, Gustav "/o G. Cramer Dry Plate Co. Crandall, George C 4287 Olive st. Crunden, Frederick Morgan Public Library. Curtis, William S.. St. Louis Law School. Cushman, AUerton S.* Bryn Mawr, Pa. Dame, James E 2353 Albion pi. Dameron, Edward Caswell* Clarksville, Mo. Davis, H. N 56 Vandeventer pi. Davis, John D 421 Olive st. Diehm, Ferdinand 1834 Kennett pi, Dodd, Samuel M 415 Locust st. Douglas, Archer W °/o Simmons Hardware Co. Drake, George S 64 Vandeventer pi. Duenckel, Frederick William 2912 EUendale av. Duggar, B. M.* 202 Hitt st., Columbia, Mo. Eggert, Henry* 1001 Collinsville av., East St. Louis, 111. Eimbeck, August F.* New Haven, Mo. Eliot, Edward C 5468 Maple av. Eliot, Henry W ,.2635 Locust st. Engler, Edmund Arthur* 11 Boynton st., Worcester, Mass. Engman, Martin F 2608 Locust st. Erker, Adolph P 608 Olive st. Members. vii Espenschied, Charles 3500 Washington av. Euston, Alexander 3730 Lindell boul. Evers, Edward .....1861 N. Market st. Ewing, Arthur E 6024 West Cabanoe pi. Favor, Ernest Howard* Box 842, Columbia, Mo. Fernald, Robert Heywood Washington University. Fischel, Washington E 2647 Washington av. Forbes, Stephen A.* Urbana, III. Fordyce, JohnR.* 2223 Louisiana st., Little Rock, Ark. Forster, Marquard 2317 S. 13th st. Francis, David R 4421 Maryland av. Fi-ench, George Hazen* Carbondale, III. Frerichs, Frederick W 4608 S. Broadway. Frick, John Henry* Warrenton, Mo. Fruth, Otto J 3066 Hawthorne boul. Fry, Frank R 3133 Pine st. Funkhouser, Robert Monroe 3534 Olive st. Gazzam, James Breading 514 Security bldg. Geeks, Frank , 3453 Magnolia av. Gerling, H. J 4320 Cook av. Glasgow, Frank A 3894 Washington boul. Glasgow, William C 2847 Washington av. Goetz, Victor 129 Market st. Goldstein, Max A 3858 Westminster pi. Goodman, Charles H 3329 Washington av. Graham, Benjamin B 5145 Lindell boul. Graves, William W 1943 N. 11th st. Graves, Willis Nelson 2813 Lafayette av. Gray, Melvin L 3756 Lindell boul. Grebe, E 3839 Russell av. Greeley, Arthur W Washington University. Green, John 2670 Washington av. Gregory, Elisha Hall 3525 Lucas av. Gregory, Elisha H., Jr.* Medical Dept.,Univ. of Pa., Philadelphia, Pa. Grindon, Joseph 4546 Laclede av. Gundelach, Chas. H 3900 Westminster pi. Gurney, James Tower Grove and Magnolia avs. Guy, William Evans 4380 Westminster pi. VIII Trans. Acad. ScL of St. Louis. Haarstick, Henry C Main and Walnut sts. Habermaas, Albert 3109 S. Jefferson av. Hambach, Gustav f 1319 Lami st. Hardaway, W. A 2922 Locust st. Hartmann, Rudolph 2020 Victor st. Held, George A International Bank. Henske, A. A , 1504 St. Louis av. Herzog, William 3644 Botanical av. Hirschberg, Francis D 3818 Lindell boul. Hitchcock, Albert Spear* U. S. Dept. Agriculture, Washington, D. C. Hitchcock, George C 3877 Washington av. Holman, M. L 3744 Finney av. Holmes, Joseph A Mines Dept. La. Purch. Exposit'n. Holzinger, John Michael* 207 W. King st., Winona, Minn. Homan, George ...323 Odd Fellows' bldg. Hough, Warwick Circuit Court, Room 1. Hughes, Charles Hamilton 3860 West Pine boul. Huiskamp, John E 5554 Cabanne av. Hume, H. Harold* Lake City, Fla. Hunicke, Henry August 3532 Victor st. Hurter, Julius 2346 S. 10th st. Hyatt, Robert J U. S. Weather Bureau. Ives, Halsey Cooley Museum of Fine Arts. Johnson, J. B 4244 Washington boul. Johnson, Reno De O.* Desloge, Mo. Jones, Breckinridge 4010 Lindell boul. Keiser, Edward H Washington University. Keyes, Charles R.* State School of Mines, Socorro, New Mexico. Kinealy, John H.* 1108 Pemberton bldg., Boston, Mass. King, Goodman 78 Vandeventer pi. Kirchner, Walter C. G 1211 N. Grand av. Kline, George R 215 Pine st. Kodis, Theodore* Schadow, Kowno, Russia. Krall, George Warren Manual Training School. t Elected a life -member January 3, 1882. Members. ix Lackland, Rufus J 1623 Locust st. Langsdorf, Alexander S Washington University. Leavitt, Sherman Washington University. Lefevre, George* State University, Columbia, Mo. Leighton, George Bridge 803 Garrison av. Letterman, George W.* Allenton, Mo. Lichter, John J 5305 Virginia avi Loeb, Hanau Wolf 3559 Olive st. Ludwig, Charles V. F 1509 Chouteau av. Lumelius, J. George. 1225 St. Ange av. Lyon, Hartwell Nelles.. 3910 Russell av. Mack, Charles Jacob, 113 N. Broadway. Mallinckrodt, Edward 26 Vandeventer pi. Markham, George Dickson 4961 Berlin av. Marx, Christian William* University of Cincinnati, Cincinnati, Ohio. Maserang, Joseph, Jr Washington and Leffingwell avs. Mason, Silas C* Berea, Ky. Matthews, Leonard SOON. 4th st. Meier, Theodore G 3938 Washington boul. Merrell, Albert 3814 Washington boul. Meyer, John F 1739 Pennsylvania av. Michel, Eugene H 2721 S.King's Highway. Miller, Charles F 1751 Missouri av. Monell, Joseph T.* Flat River, Mo. Monroe, Lee Ernest* Eureka, Mo. Moore, Robert 61 Vandeventer pi. Morton, Isaac W .....°/o Simmons Hardware Co. Mudd, Harvey G 2604 Locust st. Muegge, Aug. H Grand av. and Hickory st. Mueller, Ambrose* Webster Groves, Mo. Nagel, Charles 3969 Washington boul. Nasse, Aug 209 N. 2d st. Nelson, Aven* Laramie, Wyom. Niedringhaus, George W 3745 Lindell boul. Nipher, Francis E Washington University. Norton, J. B. S.* College Park, Md. Oglevee, Christopher Stoner* Lincoln, 111. Olshausen, Ernest P 1115 Rutger st. Olshausen, George R.* Armour Institute, Chicago, 111. X Trans. Acad. Sci. of St. Louis. O'Reilly, Andrew J 326 City Hall. O'Reilly, Robert J 3411 Pine st. Outten, W. B Mo, Pacific Hospital. Overstolz, Herman 100 N. Broadway. Palmer, Ernest Jesse* 321 S. Allen st., Webb City, Mo. Pammel, Louis Hermann* Ames, la. Pantaleoni, Guido 415 Locust st. Parker, George Ward 417 Pine st. Parsons, Charles 2804 Pine st. Pauls, Gustavus St. Louis Altenheira. Pettus, W. H. H 4373 Westminster pi. Pfeiffer, Egmont 4247 Castleman av. Pike, Sherman B 5881 Cates av. Pitzman, Julius 1900 S. Compton av. Poats, Thomas Grayson* Clemson College, S. C. Post, Martin Hayward 5371 Waterman av. Preetorius, Emil "/o Westliche Post. Prewitt, Theodore F 4917 Berlin av. Primm, Alexander T., Jr "U J- Kennard & Sons. Pulsifer, William H.* The Grafton, Washington, D. C. Quaintance, A. L.* Experiment, Ga. Randall, John E 1910 Olive st. Ravold, Amand 2806 Morgan st. Reverchon, Julien* Box 229, Dallas, Texas. Richter, Phil. George 2424 S. 18th st. Rieloff, F. C 3837 W. Pine boul. Robert, Edward Scott 1105 Union Trust bldg. Robertson, Charles* Carlinvllle, 111. Roever, William Henry* Cambridge, Mass. Rogers, Herbert F =/o Provident Chemical Works. Rolfs, Peter H.* Tropical Laboratory, Miami, Fla, Rosenwald, Lucian* Las Vegas, New Mex. Ruf, Frank A 5863 Cabanne av. Runge, Edward C Supt. Insane Asylum. Russell, Colton* , 325 S. Bunker Hill av., Los Angeles, Calif. Ryan, Frank K... 2725 Lawton av. Sander, Enno, 2807 Lawton av. Sargent, Charles Sprague* Jamaica Plain, Mass. Members. xi Schmalz, Leopold 2824 Shenandoah av. Schneck, Jacob* Mt. Carmel, 111. vonSchrenk, Hermann Mo. Botanical Garden. Schroers, John 1730 Missouri av. Schrowang, Otto Holland bldg. Schwab, Sidney 1 2602 Locust st. Schwarz, Frank 1520 Lafayette av. Schwarz, Henry 1723 Chouteau av. Schweitzer, Paul* Coluaibia, Mo. Scott, Henry C .64 Vandeventer pi. See, Thomas Jefferson Jackson*. ..Naval Observatory, Washington, D. C. Selby, Augustine Dawson* Wooster, O. Senseney, E. M 2829 Washington av. Sheldon, Walter L 4065 Delmar av. Shepley, John F 60 Vandeventer pi. Shoemaker, William Alfred 4383 Westminster pi. Simmons, E. C 9th and Spruce sts. Simmons, W. D.. 9th and Spruce sts. Sluder, Greenfield 2647 Washington av. Smith, Arthur George* 422 N. Dubuque st., Iowa City, la. Smith, D. S. H :j646 Washington boul. Smith, Irwin Z 87 Vandeventer pi. Smith, Jared G.* Honolulu, Hawaiian Islands. Soldan, F. Louis 3634 Flad av. Spiegelhalter, Joseph 2166 Lafayette av. Starr, John E.* 258 Broadway, New York City. Staudinger, B 3556 Lindell boul. Stedman, John Moore* Stale University, Columbia, Mo. Stevens, Charles D 1749 S. Grand av. Stevens, Wyandotte James 4043 Juniata st. Stocker, George J 2833 S. King's Highway. Stone, Charles H 5562 Clemens av. Strauss, Julius C 3516 Franklin av. Stuart, Jame3 Lyall .5346 Maple av. Sutter, Otto 3035 Bell av. Taussig, Albert E 2647 Washington av. Taussig, William 3447 Lafayette av. Teichmann, William C 1141 Market st. Terry, Robert James 2726 Washington av. Thacher, Arthur 4304 Washington boul. Thiele, Albert 2746 Park av. xii Trails. Acad. Set. of St. Louis. Thilly, Frank* 601 Hitt st., Columbia, Mo. Thorn, Charles 239 Hazel St., Ithaca, N. Y. Thomas, JohnR 420 N. 4th st. Thomson, Wm. H., Jr 3805 Lindell boul. Thurman, John S 416 Lincoln Trust bldg. Timmerman, Arthur H 2633 Park av. Tittmann, Harold H 3726 Washington boul. Trelease, William Mo. Botanical Garden. Tyler, ElzaEdward* State University, Columbia, Mo. Tyrrell, Warren Ayres 3620a Folsom av. Updegraff, Milton* 12 Goldsborough Row, Annapolis, Md. Valle, Jules F 3303 Washington av. VanOrnum, John Lane Washington University. Vickroy, Wilhelm Rees 2901 Rauschenbach av. von Schrader, George F Wainwright bldg. von Schrader, Otto U 3749 Westminster pi. Warren, William Homer ....1806 Locust st. Watts, Millard F 4362 Morgan st. Weller, Stuart* University of Chicago, Chicago, 111. Westgate, John Minton* 6023 Ellis av., Chicago, 111. Wheeler, H. A ....3124 Locust st. Whelpley, Henry Milton 2342 Albion pi. Whitaker, Edwards 300 N. 4th st. Whitten, John Charles* Colutubia, Mo. Widmann, Otto .. 5105 Morgan st. Wilson, Edward Allen 3745 W. Pine st. Winkelmeyer, Christopher 3540 Lawtca av. Winslow, Arthur* 104 W. 9th st., Kansas City, Mo. Wislizenus, Frederick A 3628 Cleveland av. Witt, Thomas D.* Rusliville, 111. Wood,ObadiahM 3016 Caroline st. Woodward, Calvin Milton Washington University. Zahorsky, John 1460 S. Grand av. THE ACADEMY OF SCIENCE OF ST. LOUIS. ORGANIZATION. The Academy of Science of St. Louis was organized on the 10th of March, 1856, in the hall of the Board of Public Schools. Dr. George Engelmann was the first President. CHARTER. On the 17th of January following, a charter incorporating the Academy was signed and approved, and this was accepted by vote of the Academy on the 9th of February, 1857. OBJECTS. The act of incorporation declares the object of the Academy to be the advancement of science and the establishment in St. Louis of a museum and library for the illustration and study of its various branches, and provides that the members shall acquire no individual property in the real estate, cabinets, library, or other of its effects, their interests being unsufruc- tuary merely. The constitution as adopted at the organization meeting and amended at various times subsequently, provides for hold- ins: meetings for the consideration and discussion of scientific subjects ; taking measures to procure original papers upon such subjects ; the publication of transactions ; the establishment and maintenance of a cabinet of objects illustrative of the sev- eral departments of science, and a library of works relating to the same ; and the establishment of relations with other scien- tific institutions. To encourage and promote special investi- gation in any branch of science, the formation of special sections under the charter is provided for. MEMBERSHIP. Members are classified as active members, corresponding members, honorary members and patrons. Active member- xiv Trans. Acad. Sci. of St. Louis. ship is limited to persons interested in science, though they need not of necessity be engaged in scientific work, and they alone conduct the affairs of the Academy, under its constitu- tion. Persons not living in the city or county of St. Louis who are disposed to further the objects of the Academy by original researches, contributions of specimens, or otherwise, are eligi- ble as corresponding members. Persons not living in the city or county of St. Louis are eligible as honorary members by virtue of their attainments in science. Any person conveying to the Academy the sum of one thousand dollars or its equiva- lent becomes eligible as a patron. Under the by-laws, resident active members pay an initiation fee of five dollars and annual dues of six dollars. Non-resi- dent active members pay the same initiation fee, but annual dues of three dollars only. Patrons, and honorary and corre- sponding members, are exempt from the payment of dues. Each patron and active member not in arrears is entitled to one copy of each publication of the Academy issued after his election. Since the organization of the Academy, 945 persons have been elected to active membership, of whom, at the present time, 293 are carried on the list. One patron, Mr. Edwin Harrison, has been elected. The list of corresponding mem- bers (Vol. X. p. xii) includes 205 names, among which are the names of 102 persons known to be deceased. OFFICERS AND MANAGEMENT. The officers, who are chosen from the active members, con- sist of a President, two Vice-Presidents, Recording and Cor- responding Secretaries, Treasurer, Librarian, three Curators, and two Directors. The general business management of the Academy is vested in a Council composed of the President, the two Vice-Presidents, the Recording Secretary, the Treas- urer, the Librarian and the two Directors. The office of President has been filled by the following well-known citizens of St. Louis, nearly all of whom have been eminent in some line of scientific work : George Engel- mann, Benjamin F. Shumard, Adolphus Wislizenus, Hiram A. Prout, John B. Johnson, James B. Eads, William T. Harris, Abstract of History. XV Charles V. Riley, Francis E. Nipher, Henry S. Pritchett, John Green, Melvin L. Gray, Edmuncl A. Engler, Robert Moore, and Henry W. Eliot. MEETINGS . The regular meetings of the Academy are held at its rooms, 1600 Locust Street, at 8 o'clock, on the first and third Mon- day evenings of each month, a recess being taken between the meetino; on the first Monday in June and the meeting on the third Monday in October. These meetings, to which interested persons are always welcome, are devoted in part to the reading of technical papers designed for publication in the Academy's Transactions, and in part to the presentation of more popular abstracts of recent investigation or progress. From time to time public lectures, calculated to interest a larger audience, are provided for in some suitable hall. The following dates for regular meetings for the year 1903 have been fixed by the Council: — Jan. Feb. Mar. April. May. June. Oct. Nov. Dec. 5 19 2 16 2 16 6 20 4 18 1 19 2 16 7 21 LIBRAEY. After its organization, the Academy met in Pope's Medical College, where a creditable beginning had been made toward the formation of a museum and library, until May, 1869, when the building and museum were destroyed by fire, the library being saved. The hbrary now contains 14,491 books and 11,017 pamphlets, and is open during certain hours of the day for consultation by members and persons engaged in scientific work. PUBLICATIONS AND EXCHANGES. Twelve thick octavo volumes of Transactions have been published since the organization of the Academy, and widely xvi Trans. Acad. Sci. of St. Louis. distributed. Two quarto publications have also been issued, one from the Archaeological section, being a contribution to the archaeology of Missouri, and the other a report of the observations made by the Washington University Eclipse Party of 1889. The Academy now stands in exchange rela- tions with 569 institutions or organizations of aims similar to its own. MUSEUM. Since the loss of its first museum, in 1869, the Academy has lacked adequate room for the arrangement of a public museum, and, although small museum accessions have been received and cared for, its main effort of necessity has been concentrated on the holding of meetings, the formation of a library, the publication of worthy scientific matter, and the maintenance of relations with other scientific bodies. December 31, 1902. RECORD, From January 1, 1902, to December 31, 1902. Meeting of January 6, 1902. Vice-President Smith in the chair; about forty persons present. The Council reported that the Academy had lost two mem- bers by the death of Judge George A. Madill and Mr. William McMillan, that the resignation of Messrs. C. T. Whittier, J. A. Conzelman and Ludwig Bremer had been accepted, and that the names of Messrs. A, I. Jacobs, E. W. Lazell, J. W. Lee and J. A. Seddon had been removed from the list of members. The nominating committee reported that one hundred and twenty-nine ballots had been counted, and the following officers for 1902 were declared duly elected : — President Henry W. Ehot. First Vice-President D. S. H. Smith. Second Vice-President William E. Guy. Recording Secretary William Trelease. Corresponding Secretary. . .Ernest P. Olshausen. Treasurer Enno Sander. Librarian G. Hambach. Curators G. Hambach, Julius Hurter, Hermann von Schrenk. Directors Amand Ravold, Adolf Alt. Mr. Eliot, the President-elect, on taking the chair, spoke happily of his interest in the work of the Academy and his hope to further it to the extent of his power. The Librarian submitted his annual report. The Treasurer submitted his annual report* showing in- * Transactions ll:xl. xviii Trans. Acad. Sci. of St. Louis. vested funds to the amount of $6,500.00, and a balance of $555.25 carried forward to the year 1902.* A letter from Mrs .William Bouton was read , offering on behalf of herself and other contributors to a purchase fund, to present to the Academy a collection of 633 butterflies mounted on Den- ton tablets, and the containing cases, on condition that the collection be held as an educational exhibit for the benefit of the public, and in all feasible ways kept open to public in- spection, and the following resolution was adopted: — Resolved, That Ttie A.caderay of Science of St. Louis gratefully accepts the gift as proposed by Mrs. Bouton, and agrees to hold the collection as an educational exhibit for the benefit of the public, and in all feasible ways to keep it open to public inspection. The following papers were presented by title : — K. K. Mackenzie and B. F. Bush, new species of plants from Missouri. B. F. Bush, Eevision of the North American species of Triodia. Professor A. S. Chessin exhibited a gyroscope and ex- plained how an accurately constructed and rapidly rotated gyroscope might be made to indicate the position of the meridian plane, the direction of the polar axis of the earth and the latitude of the place of observation, thus serving the purpose of the mariner's compass, but more accurately because of the fact that the compass indicates the magnetic and not the true pole. The following formulae pertaining to the subject were furnished : — ^ "" \ C con COS \ ' ^ .1 + (7. + ^, . rr _^ ^ IA+C\ + A, 0 (o n where T and Tj are the durations of a complete oscillation of the gyroscope when its axis is made to remain in the hori- zontal and the meridian planes respectively; (o and li the angular velocities of rotation of the earth and the gyroscope respectively; A, Ai, A2 and C, Ci, (72 the equatorial and the axial moments of inertia of the gyroscope and the Record. xix two rings on which it is mounted. From these formulae the latitude (\) of the place of observation is derived, , -^ 1 namely: cos X = jf2~* Professor F. E. Nipher made afurthur statement concern- ing his results in the attempt to produce ether waves by the explosion of dynamite. He had obtained some results which seemed to show that magnetic effects could thus be produced. " There is apparently no doubt that great solar outbursts like the one which Professor C. A. Young saw at Sherman in 1872,* produce enormous distortions of the ether. Why should it not be possible to reproduce this result? It goes without saying that large sun-spots may be slowly formed, without such ether disturbance, and certainly we can hardly expect to reproduce solar velocities. But terrestrial explo- sions do yield tremors and sound vibrations, and these lead to great experimental difficulties. The nickel-silver coherer can be operated by the sound waves from a tuning fork. The coherer can be either opened or closed by sound waves, when the coherer is properly placed in a magnetic field. The same result may be produced by changes in the magnetic field, due to the slow approach of a horse-shoe magnet. After the coherer circuit has been closed by a spark, the slow approach of a horse-shoe magnet will often open the circuit, precisely as it does when the coherer has been closed by the magnet held in a position of reversed polarity. When the magnet fails to open the coherer circuit, the cause is either a too rapid approach, which causes the coherer to close by a rever- sal of magnetic polarity, or by a wrong presentation of the magnet which confirms the condition produced by the spark discharge. The conditions under which experiments are made as yet, with the jarring due to the street traffic and the explosions, and the changing magnetic field due to the electric cars, have proven to be a source of some perplexity. It throws some doubt upon the results reached. There, how- ever, seems to be a residual effect which cannot thus be ac- counted for, and it may be due to an ether displacement." * The Sun, p. 156. XX Trans. Acad. Sci. of St. Louis. Meeting of January 20, 1902. President Eliot in the chair, nineteen persons present. Dr. George Richter addressed the Academy on the physi- cal and chemical properties of gelatin, which he described as a spongy substance differing materially from other solids. The manner of manufacture of gelatin and its chemical and physical characters were described in detail, and considerable attention was given to the rate of absorption and evaporation of water by gelatin and the phenomenon of its apparent solution in water. A new hygrometer was exhibited and described, tlie action of which was based upon the water absorption of gelatin. One person was proposed for active membership. Meeting of February 3, 1902. President EUot in the chair, nineteen persons present. Mr. Trelease presented, with the aid of lantern illustrations, some of the principal results of his recent studies of Yuccas and their allies. One person was proposed for active membership. Meeting of February 17, 1902. President Eliot in the chair, twenty -nine persons present. Dr. Gellert Alleman addressed the Academy on the chem- ical constitution and the manufacture of Portland cements. The growth of the cement industry was treated, the various steps of development being shown by lantern slides illustrating past and present types of machinery employed in its manu- facture. Several slides were shown giving tabulated results of a number of analyses of different commercial Portland cements. Mr. Charles Espenschied read a letter from Mr. Seymour Carter, of Hastings, Minnesota, in which was described a method of Professor Anderson of Columbia University, New Record. xxi York, by which it was claimed that cereals could be directly transformed to food-stuffs. The process consists of inclos- ing the cereal to be treated in a hermetically sealed vessel and subjecting it to a temperature of about 450° F. for a certain time, and immediately thereafter opening the vessel, when it is found that the grains expand to six or eight times their normal size. The inventor claims that the process does not alter the composition of the cereal. Samples of several cereals treated in this manner were shown. A written motion to amend Section 1 of Article V. of the Constitution by the addition of the words " and the Librarian " near the end of said article was submitted by Dr. Alt, seconded by Dr. Smith. Under the Constitution, action on this was deferred until the second following meeting of the Academy. Messrs. Wm. L. Boeckeler and John F. Meyer, of St. Louis, were elected to active membership. Two persons were proposed for active membership. Meeting of March 3, 1902. President Eliot in the chair, twenty-eight persons present. The Council reported that the resignation of Professor H. F. Roberts had been accepted. Mr. L. T. Genung gave a general discussion of the Lepi- doptera, their structural characteristics, habits, and adapta- tions. He exhibited some of the more striking specimens of the Denton collection of butterflies, recently presented to The Academy of Science, and discussed the meaning of the various colors. A paper by Mr. C. F. Baker, entitled A revision of the Elephantopeae, I., was presented by title. Mr. Willi Brown and Dr. F. C. Eieloff were elected to active membership. Two persons were proposed for active membership. Meeting of March 17, 1902. President Eliot in the chair, sixteen persons present. A letter from Mr. W. W. Robinet, of Eobinet, Tennessee, xxii Trans. Acad. Sci. of St. Louis. was read by the President, in which the writer presented to the Academy a small collection of fossils. Dr. E. R. Buckley addressed the Academy on the work being done by the State Bureau of Geology and Mines, giving a brief review of the work done by the Bureau in the past, since its creation in 1839, and an outline of the plans for the future . Meeting of April 7, 1902. President Eliot in the chair, twenty-eight persons present. Professor A. S. Langsdorf addressed the Academy on the subject of electric waves, illustrating his remarks by experi- ments, including some of the phenomena of self-induction, absorption, reflection, and resonance. Dr. H. von Schrenk exhibited a sample of the impregnated wooden paving blocks used on some of the streets of London and Paris. Mr. Frank Schwarz and Professor Frank Geeks were elected to active membership. Meeting of April 21, 1902. President Eliot in the chair, nine persons present. The Council reported the resignation of Dr. C. M. Jackson and Dr. E. W. Oelfcken. The Council reported that a ballot on the amendment of the Constitution had been canvassed, and that one hundred and one ballots had been cast; 97 for and 4 against the adoption of the amendment, so that the amendment had been carried. Article V, Section I, of the Constitution, as amended, now reading: — Section 1. The President, the two Vice-Presidents, the Rtconiiu.? Sec- re: ary, the Treasurer, the Librariau, and tha two Directors, shall constitute the Council of th" AcLidemy. Mr. Arthur Thacher delivered an interesting address on the present and the probable future of the Missouri mining indus- try, with particular reference to lead. One person was proposed for active membership. Abstract of History. xxiii Meeting of May 5, 1902. President Eliot in the chair. There being no quorum pres- ent, the Academy adjourned. Meeting of May 19, 1902. President Eliot in the chair, fifteen persons present. The Council reported that exchange relations had been established with the University of Montana, the University of Colorado and the State Historical Society of Columbia, Mo. Professor C. M. Woodward gave, in abstract, the results reached by him in a study of the stresses in a rotating disk. Mr. Egmont Pfeifer, of St. Louis, was elected to active membership. Four persons Avere proposed for active membership. Meeting of June 2, 1902. Dr. John Green in the chair, seventeen persons present. Professor A. S. Langsdorf described the factory tests that are made of electrical machinery, illustrating the subject by lan- tern diagrams, showing the circuits employed for the various tests, and by pictures of the machinery as set up for testing in the factory. Mr. H. A. Wheeler spoke of the occurrence, near Hematite, Mo., some forty miles below St. Louis, of a number of granite boulders, some of them showing the polishing action of ice; and accounted for their occurrence at this point, or some fifty miles beyond the southern limit of the termi- nal moraine, by the theory that they had been carried there on cakes of ice during the Loess period. Mr. Wheeler and Professor Nipher discussed a recent news- paper account of the alleged finding of a meteorite that was recently seen to fall in St. Louis, and agreed that the sup- posed meteorite, which both of them had examined, was merely a pyrite concretion from the coal measures, of the type xxiv Trans. Acad. Sci. of St. Louis. called " sulphur-balls" or" nigger-heads," which had probably been raked out from the grate-bars of the adjoining factory and passed off on its discoverer as a meteorite. Messrs. Tarleton H. Bean, Jos. A. Holmes, Geo. Richter, and Edward Allen Wilson of St. Louis, were elected to active membership. The following biographical sketch of the late Dr. A. Litton, one of the first members of the Academy, by Dr. G. C. Broadhead, was presented by Dr. Hambach : — ABRAM LITTON, M. D. Dr. Abram Litton, the son of Joseph and Kate "Warren Litton, was born In Dublin, Ireland, May 20, ISU, being next to the youngest of nine chil- n. He died in St. Louis on September 22, 1901, at 2:45 P. M. aged 87 years, 4 months and 2 days, and in the house he had built 53 years before and in which he had lived ever since. His health had been very feeble for two years. The father and mother of Abram Litton came to America about 1817- The family resided for awhile at Pittsburg, then came to Nashville, Tenn., where the older Litton and his wife resided during the remainder of their lives. Abram was educated in a private school in Nashville and for part of the time attended a school kept by a Mrs. Sterns. He then lived with his older sister, Mrs. Margaret Bostick at Franklin, Tenn., where he attended a school taught by Bishop Otey. In 1829 he entered the Junior Class of the University of Nashville, graduating in 1831, at the age of 17. He then studied another year with Dr. Lindsay. He then went to Paris, Tenn., and taught school. Then he taught two years at Jackson, Tenn. In 1835, four years after graduation, he was ofEered the professorship of Mathematics and Natural Philosophy in Nashville University. This he ac- cepted, remaining there three years. He then resigned his position in order to go to Europe and perfect himself in chemistry. He stayed a few weeks in London, then went to Paris, in July, 1840, and attended chemical lectures for about a year, but the laboratory not suiting, he decided to go to Germany. He walked through Switzerland to Heidelberg but stayed there only a short time. He then went down the Rhine to Bonn, and six months after leaving Paris he settled down at Giessen, to work with Liebig, with whom he stayed six months. From Giessen he went to Berlin to work with Rosa in his Laboratory, Liebig having given him letters of recommendation. After six months he took a vacation in Switzerland. He then studied about a year with Wohler in Gottingen. He returned to America and married Julia Alice Manning in Nashville. He soon after came to St. Louis and in 1842 took the position as Professor of Chemistry in St. Louis Medical College. Here he procured his honorary degree of M. D. The first year he taught in the school with no salary, the Record. xxv next year a small salary, then increased to 81,000. Here he continued to lecture for 49 years. One summer he lectured at Kemper College near St. Louis. He also gave a course of lectures at the Sacred Heart Convent. In 1849 he vFent to the State University at Columbia for a summer session, but being tendered a position as chemist to Belchers' Sugar Refinery, he re- turned to St. Louis. "When Washiugton University was formed Dr. Litton accepted the Chair of Chemistry, without salary for the first year, then a small salary for part of his time so that he could continue his other work in the St. Louis Medical College. During the first summer vacation he went East for the purpose of exam- ining eastern laboratories so as the better to direct the building and fitting up of the University laboratories. To do this he borrowed the money, pay- ing it back from his next year's salary. He continued at Washington University for 35 years, resigning in 1891. During all this time he lectured both at Washington University and at the Medical school. About 1850 he was for a while engaged in the Geological Survey of Wis- consin and Minnesota conducted by David Dale Owen. In this connection, I would say that David Dale Owen had charge of the Sur- vey and with him as principal assistant was Dr. Joseph G. Norwood. Other heads of sub-corps were J. Evans, B. F. Shumard, B. C. Macy, C. Whittlesey, A. Litton, aod Richard Owen: other assistants were G. Warren, H. Pratten, F. B. Meek and J. Beal. Dr. Abram Litton was the last one left of these pioneer geologists. In 1854 Dr. Litton, in the employ of the Missouri State Geological Survey, made an examination of the lead region of Southeast Missouri, which was published in the Geological Survey Report for 1855, occupying 94 pages of the volume. This was the first careful report made of that region, and was a very complete and carefully made report. In his early life Dr. Litton's desire was to become a doctor and not a pro- fessor. He studied medicine while teaching in Paris, Tenn., and afterwards took a Doctor's degree. He practiced for six months in Potosi and then concluded that it was not his vocation, and gave it up. In 1871 he went to Europe for instruments and self-improvement. Dr. Litton was always interested in microscopy and physics and his amusement was to work with the spectroscope, the barometer, electric battery, etc. He accumulated a large and fine chemical and scientific library which, in 1899, he gave to the Missouri State University. This library in- cluded from 1,000 to 2,000 volumes, some of the volumes being very rare and expensive. They were in the English, French and German languages. He gave a fine collection of rocks to the St. Louis High School, an insti- tution which he was very much interested in, and he served one year as Superintendent of St. Louis Public Schools. He had two sons, one a prominent lawyer, Joseph Norwood Litton, the other a good physician, Charles Manning Litton. Both died of consumption at the age of 33, and within three years of each other. He left one daughter, Alice M., his sole heir and executrix of his will and estate. Dr. Litton was twice married, his second wife being related to the first. His second wife was cousin to the first, and James Manning, the first hus- band of the second Mrs. Litton, was the brother of the first Mrs. Litton. xxvi Trans. Acad. Sci. of St. Louis. Dr. Litton left some valuable scientific apparatus, worth probably several thousand dollars. His daughter has since donated this to the Missouri State University, The Faculty of the University passed appropriate resolutions on the death of Dr. Litton, referring to his scientiflc ability and his value as a teacher, and extending sympathy to his damrhter in her bereavement. At a meeting of the Alumni of Washington University, the St. Louis Med- ical School and other institutions of St. Louis, held in Memorial Hall, St. Louis, at Nineteenth and Locust streets, April 19th, 1895, special reference was made to Dr. Litton by Dr. Henry H, Mudd, from which I extract the following appropriate passages. This was six years before the death of Dr. Litton. Dr. Mudd says: " Dr. Abram Litton is still with us — simple-minded as a child, but stern as ever in his unflinching demand for the truth. On May 15, 1843, he was appointed Professor of Chemistry and Pharmacy in the Medical Department of the Sc. Louis University. This was afterwards known as Pope's but now is the Medical Department of Washington Uni- versity. His salary was $300, later increased to $600 and finally to $1,000. Besides this and work on the Missouri Geological Survey, he was also chemist to the Belchers' Sugar Refinery. He attended to this for a while, but concluding that they were paying him too much he resigned it. He was so modest that his merits were not known so well at home as abroad, and when Judge Treat asked Professor Horsford of Harvard for a chemist for Washington University, he said, 'Why not Litton of St. Louis? ' In 1857 he was appointed to the Professorship in Washington University, which he held until 1892, for thirty-five years. Later, when hs traveled in the East in the interest of the University, he refunded the money which had been advanced to him to pay the expenses incurred. Where is there another who would show such unselfishness." Dr. Mudd further says: '• He in- fused into his teachings such a demand for accurate thinking and precise work as to call forth the best efforts of thoughtful students. A student of nature, he has sought nature's truths in the crucible, found the story of the sun in the spectroscope and wrung from the stars the mystery of the night. His whole life has been laboriously given to the accumulation of hard facts. Each one was stored away for future use, and became a part of the man. Fact upon fact until truth shines forth from every day in the mosaic of his life. There is not a black spot ia the whole pyramid of truth which was thus erected from the daily labor of a long and industrious life. He was loyal to his friends, loyal to his own ideals, loyal to his trusts, loyal to every purpose which he consented to serve." Such are the deserved tributes offered by Dr. Mudd to the noble character of Dr. A. Litton. Dr. Litton delivered many useful and instructive lectures, but the pub- lished list is small. The following I give: — 1. An Introductory Lecture to the course of Chemistry and Pharmacy in the St. Louis University — by A. Litton, Professor of Chemistry and Phar- macy, 1844. 2. Address to the graduates of the Medical Department of St. Louis Uni- versity, 18 pages, St. Louis, 1851. 3. Belcher and Bro. Artesian Well, 7 pages and plate. Transactions of St. Louis Academy of Science, 1857. Record. xxvii 4, Preliminary Report of some of the principal mines in Franklin, Jeffer- son, Washington, St. Fran90is and Madison Counties, Missouri, by A. Litton, chemist, 94 pages, included in Part II. of 2d Geological Report by G. C. Swallow, State Geologist, 1855. Meeting of October 20, 1902., President Eliot in the chair, seventeen persons present. On behalf of x'^. S. Horwitz, J.J. Singer and G. L. Kosen- berg, the President presented to the museum of the Academy a collection of fossil leaf prints from the Green River forma- tion at Florissant, Colo., for which the thanks of the Academy were ordered extended. A paper by Professor A. S. Chessin, On some relations between Bessel functions of the first and of the second kind, was presented by title and referred to the Council. Professor Trelease exhibited photographs showing the vari- ations in the ring or collar of Lepioia naucinoides and a series of lantern slides illustrating autumnal coloring of foliage. Five persons were proposed for active membership. Meeting of November 3, 1902. President Eliot in the chair, eighteen persons present. The Council reported that exchange relations had been es- tablished with the Institut Botanique, Bucarest, Musees Tcheque-Slavs, Caslav, and Botanisches Centralblatt, Leiden. Mr. G. G. Hedgcock gave an illustrated account of the sugar beet industry in the United States and some of the dif- ficulties attending it, tracing the development of the industry and reviewing some of the field and factory obstacles that it had been necessar}'' to overcome, and speaking particularly of the fungous diseases of the crop. Messrs. B. M. Duggar, of Columbia, Mo., August Eimbeck, of New Haven, Mo., and Charles H. Gundelach, A. A. Hen- ske and Frank Eyan, of St. Louis, were elected to active mem- bership. One person was proposed for active membership. xxviii Trans. Acad. Sci. of St. Louis. Meeting or November 17, 1902. President Eliot in the chair, eleven persons present. Dr. M. A. Goldstein delivered an address on the uses of the tuning fork as a means of medical diao;nosis. Dr. George J. Engelmann gave a brief but interesting account of the history of the Western Academy of Sciences, organized by Dr. George Engelmann and Dr. Wislizenus in 1836, and ten- dered to the Academy the record book showing the proceed- ings of that organization from its beginning until it ceased to exist. He also tendered for such uses as the Academy might elect, a skeleton specimen which was prepared by Dr. Wisli- zenus and which formerly was the property of the Western Academy of Sciences, Professor A. W. Greeley, of St. Louis, was elected to active membership. Meeting of December 1, 1902. President Eliot in the chair, twenty-five persons present. The Council reported the resignation of Messrs. B.C. Ad- kins, G. F. Durant and A. Q. Kennett. Dr. Adolf Alt delivered an address on the development of the eye, illustrated with colored drawings and stereopticon views made from microscopic sections prepared and photo- graphed by him . Two persons were proposed for active membership. In accordance with the by-laws of the Academy, a commit- tee— which consisted of Messrs. Evers, Hunicke and Langs- dorf — was elected to nominal'^ ofiicers for the year 1903. Meeting or December 15, 1902. President Eliot in the chair, twenty-three persons present. The nominating committee reported the following list of candidates for the year 1903 : — Record. xxix President Heury W. Eliot. First Vice-President D. S. H. Smith. Second Vice-President Wm. K. Bixhy. Recording Secretary William Trelease. Corresponding Secretary Ernest P. Olshausen. Treasurer Enno Sander. Librarian G. Hambacli. Curators G. Hambach, Julius Hurter, A. H. Timmerman. Directors F, E. Nipher, Adolf Alt. No nominations other than those by the committee were offered. A paper by C. F. Baker, entitled A revision of American Siphonaptera, together with a complete list and bibliog- raphy of the whole group, was presented by title and re- ferred to the Council. Dr. C. B. Curtis delivered an illustrated address on color photography, outlining the theory of color vision and the va- rious ways in which a given color sensation may be produced, and describing various processes by which the natural colors of objects can be reproduced by photographic means. Messrs. Robert H. Fernald and Frank A. Ruf , of St. Louis, were elected to active membership. Two persons were proposed for active membership. Reports of Officers for the Year 1902. Submitted January 5, 1903. The president, Mr. Henry W. Eliot, addressed the Academy as follows : — It is customary at this, the annual meeting of members of the St. Louis Academy of Science, for the retiring oflScers to give an account of their stewardship. In accordance with this custom, I have to report that, while the Academy has not made as material progress as I had hoped, we still XXX Trans. Acad. Sci. of St. Louis. have reason to congratulate ourselves upon the season's work. Notwith- standing losses by death and resignations, the list of active members shows a net gain of six for the year. The average attendance at meetings has been good, though somewhat less than in 1901. The number of publications has been above the average, and their char- acter has been equal to any in the past. The financial condition of the Academy is good. All the notes issued in payment of the Yandell collection have been met at maturity. There re- mains but one, to be paid in 1904. Collections have been prompt, and the number of uncollected dues has been decreased. The Library has been thoroughly sorted and catalogued. I regret to report the death of one member, Hon. Henry Hitchcock, for many years associated with this society, whose loss is a grievous one and much to be deplored. The records of the Academy tell us that its history has been similar to that of other scientific institutions. The same difficulties have been en- countered and overcome, and the same obstacles present themselves to bar active progress. The work of the Academy is not as thoroughly appreci- ated by our fellow-citizens as it should be. We have reached a period where it is necesf*ary to go forward, or we will inevitably go backward. The time is soon coming, if not already at hand, when we shall be obliged to seek new quarters. The pressing need of the Academy is a home of its own. The advantages of quarters under our own control are so evident as to make discussion unnecessary. We have no place for our valuable and growing library. Its uses are therefore much curtailed. We have the nucleus of an excellent museum, but it is packed in boxes and stored in various parts of the city. The beautiful collection of butterflies, presented by Mrs. Bouton a year ago, is scarcely known to our members. All of our property is exposed to the danger of loss by fire. We need a home of our own to give us a dignified standing in this com- munity; to compel our people to recognize fully the invaluable service rendered so freely and unselfishly to the scientific world. It should no longer be said that the St. Louis Academy of Science is better known abroad than in its own city. I therefore call upon every member of this society to take this need seriously to himself. In due season Volume XII of Trans- actions will be mailed to you, and will serve as excellent material for missionary work. The following table contains details of interest: — Academy membership at date — January 1, 1903 293 Elections for year 1902 19 Losses for the year 13 By death 1 Kesignations 12 Net gain for the year . . 6 The active members are classified as follows : — Patron 1 Resident 222 Non-resident 70 Record. xxxi Number of meetings held in 1902.. 15 Average attendance.. 21 '• " »' " '• 1901 16 " '« 28 Total attendance, 1902 314 «« " 1901 448 Number of papers published, 1902 10 By resident members 3 By non-resident members. 7 The average for the preceding four years is 9.75. The character of the publications has been as foUo'vs : — Average for four years 1902. (1898-1901.)* Mathematical 3 or 30% 3.50 or 36% Botanical 7 or 707o 3.25 " 33J% Zoological and Anatomical 0 1.75 " 18% Geological and Paleontological 0 1.52 " 12|% Number of authors 5 8.25 Resident 1 3.75 Non-resident 4 4,50 The treasurer reported as follows : — RECEIPTS. Balance from 1901 $555 25 Interest on invested money 496 60 Membership dues 1,466 00 Sales of publications 79 65 Contributions, for Yandell collection 105 00 $2,702 50 EXPENDITURE.^. Rent $500 00 Publication of Transactions 787 24 Mailing Transactions and library expense 643 57 Sundry expenses 133 60 Payment, account Yandell collection 280 00 Balance to 1903 358 09 $2,702 50 INVESTED FUND. Invested on security $6,500 00 The Librarian reported that during the year exchanges had been received to the number of 327 volumes and 667 pam- ♦ In which annua! volumes have been issued. xxxii Trans. Acad. Sci. of St. Louis. phlets, an increase of 68 numbers as compared with 1901. It was reported that during the year the Transactions of the Academy had been distributed to 569 societies or institutions, chiefly by way of exchange — an addition of 8 as compared with the preceding year ; and attention was called to the fact that the exchange list has now grown to such proportions that only 132 reserve copies remain after the regular distri- bution has been effected. \^^ Transactions of The Academy of Science of St. Louis. VOIj. XII. No. 1. ON THE TRUE POTENTIAL OF THE FORCE OF GRAVITY. ALEXANDER S. CHESSIN. 'Issued January 29^ 1902. - MR '02 ON THE TRUE POTENTIAL OF THE FORCE OF GRAVITY.* Alexander S. Chessin. 1. Assuming that the form of the earth is that of a solid spheroid covered by an ellipsoidal liquid mass of uniform density, that the density of the spheroid varies from center to surface but is constant in each one of the concentric layers, and that the liquid mass is in a state of equilibrium, Laplace arrives at the following expression for the potential of the force of attraction exercised by the earth on an external par- ticle of unit mass : t R' ("^-aJJ- -f where M denotes the total mass of the earth, JR the distance of the particle from the center of the earth, a^ the ratio of the centrifugal force to the force of attraction on the equator, ah the oblateness of the earth, a the mean value of its ra- dius, and, finally, fjL = cos 0, 6 being the angle of the radius vector of the particle with the axis of rotation of the earth. ♦'According to the most probable hypotheses," says La- 5 place, t ** the oblateness of the spheroid is less than ^ a<^,. . . . These assumptions are the more probable because they be- come necessary in the case when the spheroid had originally * Presented, and read by title, before The Academy of Science of St. Louis, December 2, 1901. t Laplace, Oeuvres completes, t. II. Livre III. p. 103. X Ibid. p. 101. (1) 2 Trans. Acad. Sci. of St. Louis. been fluid." In the case of a homogeneous ellipsoid of revolution, ah would be equal to ^ a(j> and the expression of the potential C/^ would become ^1+5|2«^(3-M^)^. M i ^ da B 1 3 , In general, ah — ^a<^ will differ but little from v ah. If, then, we put (1) N= — ^Ma^Ua—ah\ we shall have M jsr (2) ^=i^ + :R3(i-^^)- 2. Let us take a rectangular system of axes, as follows: Z along the axis of rotation of the earth in the northward direction, X and Y through the center (C) of the earth in the plane of the equator and invariably fixed in it. Then /* z will be equal to -p and (3) ^ ^-B-^B^- R' ' IB= y'x^-^y^-^zK 3. We will now transform our system of coordinate axes. The new origin ( O) will be taken at an external point on or near the surface of the earth in the meridian plane ZCX; the axes 0| and OK in this plane, namely, OK in the direc- tion of the mean * force of gravity at 0^, and O^ in the * that is, ou the assumption that the forces of attraction by the sun and the moon are neglected. Chessin — On the True Potential of the Force of Gravity. 3 southward direction perpendicular to 0^; finally, the axis Or] parallel to CY, eastward. Then, denoting by S the dis- tance of 0 from the center of the earth, X the latitude of the point O, and 6 the angle of the radius vector CO with the plane of the equator, the formulas of transformation will be: (4) X = 8 cos ^ + I sin X — ^ cos X, z =B sin 0 — ^ cos X — ^ sin X. 9U 9U 917 4. The expressions of the partial derivations ?p , 5 — , jp-, as obtained from (3), readily yield the derivatives of the same function with regard to ^, ?;, ^. Namely, (5). 9U W M 3iV \b Nz^ (h sin 6 + ^) + -^ 8 sin ^ cos X — -^5 ^ cos2 X — -^5 ^ s"i ^ cos X, M ^N IbNz' (5)= 9K M 3iV 15 iV^ i?3^ i25 Ri (S cos e — ^) »6 " Sin 6/ sin X — — ^ | sm X cos X — -^s ^ sin ^X, R'> R' where (6) e = X — (9, (7) i2 = i/S2 + |o2+2S(|sine — rcose), (8) p=^/|2 + ^2^^2. 4 Trans. Acad. Sci. of St. Louis. and z^i in fuaction of |, ?, 3, 6, \, is derived from the third one of the formulas ( 4 ) . 9U 9U 9U .„ , 5. The derivatives 7^v-, ^, ^ will now be expressed m function of iHf, iV, e, \, S, |, r), ^. All terms whose ratios to M ^ are small quantities of order higher than the first power of the oblateness of the earth will be neglected. It should be observed that e and ^ are small quantities of the order of the oblateness. In regard to e this fact is well known. To be convinced of it in regard to rt ^^^ ^^^Y needs to divide both sides of (1) by S*. Then M and since ^-- represents the approximate value of the accel- M eration of the force of gravity at 0, that is, -^ = 9"%78 and TIT" K^ differs little from unity, it is clear that -^ is a small o o* quantity of the order of — a^ — ah^ that is, of the oblate- ness of the earth. If, then, we put M (9), a = — -gysine + -g4~ [sin 2X — 3 ( 1 + sin 2 X) sin e + 9 sin X cos \ sin 'e] , (yjj 6 = _ -gj- sin e H — gg— sin 2X, €hessin — On the True Potential of the Force of Gravity. 5 {d)s c ^= Kj- cos e 3i\r 1 -f -gT [1— 3sm2\-|-4sin2\sine + ^(— Il + 23sm2\)sin2e], (9)5 2e = — -g3- ~-gg- +-g^sin2x, .n «^ 2il^ 12i\r 36iV^ . ^ (9)6 2/= -gg- + -g-^ _ ^gg- sm 2\, we shall have (10)i "^ = a+2d^ + H, 9U (10). ^=2e,7. (10)3 |^=c+2/r+6|, and, therefore, (11) U=a^ + b^K + c^ + cZP + ev-" ^- jV, It may be well to note that the coefficients d^ e, f satisfy the condition (12) cZ + e+/=0 in accordance with Laplace's equation A, C7^= 0. 6. A particle moving on the surface of the earth is subject not only to the attraction by the terrestrial mass, but also to the attractions by the sun and the moon. This latter influ- ence is exercised in part directly, in part indirectly through the medium of the tides, the liquid mass, which covers the 6 Trans. Acad. Sci. of St. Louis. solid spheroid of the earth and which we have heretofore assumed to be in a state of equilibrium, being really in motion. The direct influence here referred to gives rise to a force 4>j which is the resultant of 1 ) the forces of attraction of the particle by the sun and the moon and 2) the forces equal but opposite in direction to the forces of attraction by the sun and the moon of a mass equal to that of the given particle and placed in the center of the earth. The indirect influence of the sun and the moon through the medium of the tides gives rise to another, also very small, force ^^. Let $ be the resultant of these forces j and ^,. It will, of course, vary with the time, but for a comparatively small interval of time, as in the case of experiments and observa- tions on the surface of the earth we may assume the force , as well as its projections ^^, , c.on the coordinate axes, to be constant.* A rough computation will enable the reader to see that the forces fc,

fc^+ B^ + 6)2 8 cos 6> sin \ + 0)2 sin X (^ sin X — ^ cos X), PC/" 5?/ (13), 0=3;; +^^, + i? +0,2^, ( 13 )3 0 =^^ + 4)^^ + i?^ — ft)28 cos ^ cos X + (i)2 COS X (^ COS X — I sin X), lie., R , Ro. being the components of the reaction of the constraints to which the particle is subjected, and (o the angular velocity of rotation of the earth. At the point O, where |^'7=? = 0, the equations (13) Teduce to 0 ^ a + jRj, + >. = = ^^r;+^^^r-f-^p+^^2+/'^2+5^r. 9. In conclusion let us have a glance at the relative value of the several coefficients entering formula (16). As already remarked, the order of magnitude of ^c.„, ^ ^>- is that of " ^0' 770, ^0 the principal terms in the expressions of the coefficients D^ M E^ F^ that is, of the order of -^. The coefficient B and the secondary terms in the expressions of Z), E, F are of the M order of the product of "w by the oblateness of the earth.* Hence, if the components of the solar and lunar attraction are not taken into account when computing the forces of gravity at a point on the surface of the earth, it is needless to preserve any but the first term in the expression (16) of the potential, which, then, reduces to the familiar form * In the units here selected the approximate values of — , _, (o"^ are: M Kg = 0. 000 001 5 , N gg = 0. 000 000 001 5 , fo^ = 0. 000 000 005 3 . It may, also, be noted that, approximately, € = 0.0084 sin 2X and :^ sin e = 0. 000 000 006 sin 2X. S3 O'l'i^siii — On, the True Potential of the Force of Gravity. 9 (17) V'=g^. This discussion, also, shows that it is absurd to retain terms of the order of w^ in treating the motion of a body relatively to the Earth if the force of gravity is assumed to be constant in magnitude and direction, i. e. if formula (17) is taken to represent the potential of this force. Yet the delusion that by retaining terms of the order of (o^ they have reached more accurate results is still to be found among authors who dis- cuss the motion of a body relatively to the earth, taking into account the latter' s rotation about its axis. Issued January 29, 1902. PUBLICATIONS. The following publications of the Academy are offered for sale at the net prices indicated. Applications should be addressed to the Librarian, The Academy of Science of St. Louis, 1600 Locust St., St. Louis, Mo. TRANSACTIONS (in octavo). Vol. Number. Price per number. Price per vol. Price in set. 1* 2t 8,4 $7.60 (Nos. 2-4 only.) 1 $4.00 2.00 each. $7.00 (Nos. 2-4 only.) 2 1 to 3 2.00 each. 5.50 6.00 3 1 to 4 2.00 each. 7.50 7.00 4 1 to 4 2.00 each. 7.50 7.00 6 1-2,3-4 { 4.00 each, (double numbers) 7.60 7.00 ej 1, 2, 6, 8, 10, 11, 16, 17 4, 6, 7, 13, 14, 1.5, 18 3, 9 12 I 25 cts. each. > 60 cts. each. 75 cts. each. $1.00 7.60 7.00 n 2, 3, 4, 6, 7, 8, 13, 16, 16, 18, 19 5, 9 to 12, 14, 20 17 1 I 25 cts. each. ■ 60 cts. each. 75 cts. $1.00 7.50 7.00 8t 1, 3 to 6 8, 10, 12 2, 7, 9, 11 \ 25 cts. each. 50 cts. each. 3.76 3.50 OJ 1, 8, 4, 7, 9 2,6,8 6 25 cts. each. 50 cts. each. $1.25 3.75 3.50 lot 9 2, 4, 5, 10 1 3, 6, 7,8,11 10 cts. 25 cts. each. 40 cts. 60 cts. each. 3.75 3.60 lit 2,3 5-8, 10, 11 1 4 9 15 cts. each. 25 cts. each. 45 cts. 75 cts. 1.00 3.76 8.50 MEMOIRS (in quarto). Contributions to the archaeology of Missouri, by the Archaeological Section. Part I. Pottery. 1880. $2.00. The total eclipse of the sun, January 1, 1889. A report of the observations made by the Washington University Eclipse Party, at Norman, Califor- nia. 1891. $2.00. ' • Supply exhausted. «ai)Med° ^^ ^^'*^ ^^^^ *** purchasers of the entire volnme,— so far as this can be f Each number is a brochure containing one complete paper (or rarely two). MAY 23 1902 Transactions of The Academy of Science of St. Louis. VOL.. XII. No. 2. THE LESPEDEZAS OF MISSOURI. K. K. MACKENZIE and B. F. BUSH. 4 ^^ Ismed March 19, 1902, MAY S3 ?902 THE LESPEDEZAS OF MISSOURI.* K. K. Mackenzie and B. F. Bush. Various species of Lespedezas abound in the State of Mis- souri, especially in rocky woods in the Ozark Mountain region, in the southern and eastern portions. Observations in the field of the various forms which occur here have convinced the writers that there are several undescribed species in the State, and this has led to a more extended study of the speci- mens preserved in the herbarium of the Missouri Botanical Garden, and of those in the herbarium of Mr. K. K. Mac- kenzie. The result of this study is embodied in the following notes. We beg to acknowledge our indebtedness to Professor Wm. Trelease for the loan of the entire Missouri collection of this genus in his care, and for other courtesies extended. As an aid to the recognition of the species occurring in Missouri, the following key is offered : — Annual; calyx-lobes broad. 1. L. striata. Perennials; flowers yellow; calyx -lobes narrow. Peduncles exceeding the leaves. 2. L. hirta. Peduncles shorter than the leaves. Leaves glabrate above. Leaflets oblong. 3. L. capitata. Leaflets linear-oblong. 4. L. capitata longifolia. Leaves sericeous above. 5. L. capitata sericea. Perennials; flowers purplish; calyx-lobes narrow. Peduncles exceeding the leaves. Plants prostrate and widely spreading. Glabrate or nearly so. 6. L. repens. Strongly pubescent. 7. L. procumbens. Plants strongly bushy-branched, from erect to slightly procumbent. Flowers strongly paniculate, on pedicels often 6 mm. long; larger leaflets 18 mm. long, or longer. 8. L. violacea. Flowers scarcely paniculate, on pedicels about 1.5 mm. long; leaflets much smaller, rarely 18 mm. long. 9. L. violacea prairea. * Presented and read by title before The Academy of Science of St. Louis, December 16, 1901. (11) 12 Trans. Acad. Sci. of St. Louis. Plants strictly erect or ascending, the few branches ascending. Pods included or little exserted. . 10. L. Manniana. Pods much exserted. Pods obtusish, strongly pubescent. 11. L. NuUallii. Pods long acute, slightly pubescent. 12. L. acuticarpa. Peduncles shorter than the leaves. Pods much exserted. Leaflets linear or linear-oblong. Glabrate or appressed-pubescent. 13. L. Virginica. Strongly pubescent. 14. L. neglecta. Leaflets oblong, oval or wider, Glabrate or appressed-pubescent. 15. L . frutescens . Downy-pubescent. 10. L. Stuvei. Pods included or little exserted. 17. L. simulata. 1. Lespedeza striata (Thunb.) H. & A. Bot. Beech ey. 262. 1841. Abundantly introduced throughout the Ozark Mountain region in sterile fields and woods, and rarely extending as far north as Kansas City. Probably not of this genus, as the ovate calyx lobes and annual habit are clearly at variance with those characters in our other species. Specimens examined. — Bush, Bismarck, Sept. 10, 1893. — Bush, 225, Campbell, Aug. 3, 1895. — Bush, Dunlilin Co., Oct. 21, 1892. — Bush, 225, Sheffield, Sept. 5, 1895; 247, Aug. 5, 1896. —Bush, Shannon Co., Sept. 12, 1888; July 12, 1891; July 23, 1891. — Maclienzie, 210, Dodson, Sept. 18, 1895. — Trelease, 222, Iron Mountain, Aug. 17, 1897. — Trelease, 522, Pilot Knob, Aug. 18, 1897.— Russell, Pilot Knob, Sept., 1897.— Dewart, 33, Poplar Bluff, Aug. 7, 1892; Aug 14, 1892. 2. Lespedeza hirta (L.) Ell. Bot. S. C. & Ga. 2:207. 1824. Abundant in dry rocky woods throughout the Ozark Moun- tain region, but not seen from other portions of the State. Specimens EXAMINED. — Bush, Shannon Co., Oct. 21, 1893. — Bush, Bis- marck, Sept. 10, 1893. — Bush, 35, Eagle Rock, Sept. 28, 1896; 50, Sept. 28, 1896. —Mackenzie, Eagle Rock, Sept. 28, 1896; Sept. 28, 1896, a slender decumbent form. — Eggert, St. Louis Co., Sept. 4,1891. — Trelease, 227, Carter Co., Sept. 27, 1897. —Russell, Piedmont, Sept., 1897. — Blankinship, Oregon Co., Aug. 18, 1888. — Engelmann, Pilot Knob, Sept. 5, 1859. — Engel- manu, Meramec Hills, Nov., 1845. 3. Lespedeza capitata Michx. Fl. Bor, Am. 2 : 71. 1803. Apparently common throughout the State in dry open woods and on dry prairies. Mackenzie and Bush — Lespedezas of Missouri. 13 Specimens examined. — Bush, McDonald Co., July 24, 1893. — Bush, 230, Raytown, Sept. 19, 1897.— Bush, Shannon Co., Oct. 21, 1893.— Bush, Newton Co., Aug. 29, 1893. —Mackenzie, Swope Park, Jackson Co., Aug. 23, 1896. — Mackenzie, Jones' Creek, Jackson Co., Sept. 19, 1897. — Weller, Springfield, Aug. 6, 1887. — Bggert, St. Louis Co., Sept. 21, 1877. 4. Lespedeza capitata longifolia (DC.) T. & G. Fl. N. A. 1 : 368. 1840. A long narrow-leaved form of the last of very rare occur- rence in the State. Specimens examined. — Mackenzie, 123, Dodson, Aug. 26, 1895. 5. Lespedeza capitata sericea H. & A. Comp. Bot. Mag. 1: 23. 1835. A silvery-leaved, usually quite distinct form of quite fre- quent occurrence on dry prairies and in open rocky woods. Specimens EXAMINED. — Bush, Maiden, Sept. 12,1893. — Bush, Jackson Co., Sept. 22, 1893. — Trelease, 225, Pilot Knob, Sept. 18, 1897. — Trelease, 226, Clarksville, Oct. 10, 1897. — Mackenzie, 522, Lone Jack, Sept. 24, 1901. 6. Lespedeza repens (L.) Bart. Prod. Fl. Phil. 2: 77. 1818. This species is only occasionally found in the Ozark Moun- tain region in the State, in dry rocky woods. Specimens examined. — Bush, Maiden, Aug. 12, 1893, In part. — Bush, Shannon Co., July 16, 1891 ; July 21, 1891. 7. Lespedeza procumbens Michx. Fl. Bor. Am. 2 : 70. 1803. In similar situations to the last, but apparently much more common in the State. Probably intergrades with JL. repens, but is usually quite distinct. Specimens examined. — Bush, 40, Eagle Rock, Sept. 28, 1896. — Bush, Campbell, Sept. 16, 1893.— Bush, Greene Co , Sept. 4, 1893. —Bush, Mai- den, Aug. 12, 1893, in part. —Bush, McDonald Co., Sept. 1, 1893. —Bush, Shannon Co., June 28, 1888. — Mackenzie, Eagle Rock, Sept. 28, 1896.— Russell, Piedmont, Sept., 1897. — Russell, Pilot Knob, Sept. 20, 1898. 8. Lespedeza vioLACEA (L.) Pers. Syn. 2: 318. 1807. Probably not uncommon in rocky woods in the State, but not very often collected. 14 Trans. Acad. Sci. of St. Louis. Specimens examined. — Bush, Jackson Co., Aug. 31, 1891, in part. — Mackenzie, 448, Swope Park, Jackson Co., Sept. 13, 1901; 219, Aug. 7, 1895. — Mackenzie, 208, Westport, Oct. 5, 1895, an entirely apetalous form; Aug. 31, 1891, an entirely apetalous form. — Engelmann, St. Louis Co. 9. Lespedeza viol ace a prairea n. var. PI. i.f.1,2. An ascending or somewhat spreading, much branched perennial, glabrous below, short appressed-hairy above ; branches spreading, and much interwoven ; leaflets obovate to obcordate, 6-18 mm. long, 4-9 mm. wide, mucronate, and obtuse or retuse at the apex, rounded below, smooth above, appressed-pubescent beneath ; petiolules villous, 1 mm. long ; rachis (2-6 mm. long) and petiole (2-12 mm. long) ap- pressed-hairy; stipules linear-subulate, 4 mm. long; flowers subcapitate, not paniculate, 2-6 together, on peduncles less than 2 mm. long, but the inflorescence exceeding the leaves ; often two peduncles arise from the same leaf axis ; flowers on pedicels 1-2 mm. long, rarely a little longer ; calyx 3 mm. long, appressed-hairy, the teeth lanceolate-subulate or nar- rower, about the length of the tube and much shorter than the corolla; corolla purplish, 6-8 mm. long, the keel notice- ably longer than the wings and standard ; non-petaliferous flowers in short-pedunculate or subsessile clusters; pods sub- sessile or very short-stiped in the calyx, orbicular-oval, 3-4 mm. long, acute, strongly reticulate-veined, short appressed- hairy or subglabrous, much exceeding the calyx. Differs from the specific form in being smaller throughout, in its non-paniculate inflorescence, and in its much shorter pedicels. It is the common form in this State, and is inter- mediate between the species and L. repens. Its non-procum- bent character at once distinguishes it from both L. repens and L. procumbens. Further study will probably prove that it is entitled to specific rank. It is very common on dry prairies, where L. violacea is never found, whence the name given it. Type locality, Lee's Summit, Missouri; collected by Bush, No. 93, and Mackenzie, Sept. 2, 1895 ; type in herb. Mis- souri Botanical Garden, and in herb. K. K. Mackenzie. Mackenzie and Bush — Lespedezas of Missouri. 15 Specimens examined. — Type specimens as cited under type locality. — Bush, Dunklin Co., Oct. 26, 1892. — Bush, Bismarck, Sept. 10, 1892. — Busb, Jackson Co., Aug. 31, 1891, in part. — Mackenzie, Lee's Summit, Sept. 9, 1901. — Thompson, Pacific, Sept. 19, 1898. — Fritchey, Bridgeton, Sept. 29, 1859. — Russell, Piedmont, Sept., 1899. — Dewart, Spring Park, Aug. 8, 1892. Somewhat approaching the specific form are the following: Bush, Dunklin Co., Oct. 21, 1892. — Blankiuship, Greene Co., July 17, 1888.— Glatfelter, Pilot Knob, Aug. 20, 1895. A plant with strongly pubescent stems and foliage as in L. procumbens, but apparently ascending and bushy- branched as in L. violacea prairea, has been twice collected in the State, but the specimens are too few to enable us to definitely dispose of them. The specimens referred to are the following: Bush, McDonald Co., July 31, 1895.— Trelease, 223, Carter Co., Sept. 9, 1897. 10. Lespedeza Manniana n. sp. PI. II. f. 1. Perennial, 4-9 dm. tall, suberect, strongly pubescent above, glabrate below; branches erect-ascending; leaflets oblong, subcuneate, 1-4 cm. long, 4-12 ram. wide, obtuse and mucro- nate at the apex, cuneate or rounded at the base, somewhat ap- pressed-pubescent above, especially near the mid-vein, densely appressed-pubescent beneath ; petiolules densely hairy ; petioles (2-20 mm. long) and rachis less so; petaliferous flowers in short racemes, on peduncles 12-24 mm. long, ex- ceeding the leaves, the racemes often clustered near the summit of the stem, 6-12 flowered ; flowers short-pedicelled ; calyx strongly long-pubescent, the tube 2 mm. long, the long acuminate subulate teeth 4-6 mm. long, and often ex- ceeding the corolla; corolla purplish, 5-6 mm. long, the keel usually not exceeding the wings and standard ; non-petalif- erous flowers in nearly sessile clusters; pods oval, acute, somewhat pubescent, from shorter than and included in the calyx, to slightly exserted. Most closely related to L. N'lUtallii Darl., and to L. acu- ticarpa (infra), but easily distinguished by its long sepals and nearly included pod. Named in honor of Rev. Cameron Mann, now Bishop of North Dakota, an ardent lover of nature and a skilled botanist, with whom the writers have spent many pleasant days in the field. It is very common in open post oak land and in limestone barrens south of Kansas City. 16 Trans. Acad. Sci. of St. Louis. Type locality, Swope Park, Jackson County, Missouri; collected by K. K. Mackenzie, Aug. 23, 1896; type in herb. K. K. Mackenzie, duplicate in herb. Missouri Botanical Garden. Specimens examined. — Type specimens as cited under type locality. — Mackenzie, same locality, Sept. 13, 1896. — Mackenzie, Red Bridge, Sept. 18, 1901. — Bush, 555, Raytown, 1897. — Bush, Jones' Creek, Jackson Co., Aug. 31, 1891. 11. Lespedeza Nuttallii Darl. Fl. Cest. ed. 2, 420. 1837. Apparently a rare species in Missouri, at least it is not often collected. Spfximens examined. — Bush, "Wright Co., Sept. 18, 1885. — Engelmann, Pilot Knob, Sept. 8, 1859. — Trelease, 224, Aurora Spring, Sept. 17, 1897. 12. Lespedeza acuticakpa n. sp. Fl.IILf. 1,2. Erect or suberect perennial, 2.5-5 dm. tall, not bushy- branched, but growing in clumps: branches erect-ascending; stems in same plant varying from nearly glabrate to woolly- hairy ; leaflets 8-28 mm. long, 4-8 mm. wide, oblong-elliptic, glabrate above, appressed-pubescent beneath ; petiolules 1 mm. long, villous; leaf-rachis (2-6 mm. long) and petiole (2-20 mm. long) appressed-pubescent: stipules subulate; flowers in short few-flowered (6 or less) spikes, on peduncles 1-4 mm. long, the inflorescences much exceeding the leaves ; flower pedicels 2-4 mm. long ; flowers purplish, 6-8 mm. long, the keel somewhat exceeding the wings ; calyx 2 mm. long, its long subulate teeth 3 mm. long, short appressed-pubescent ; pod 6 mm. long, distinctly short-stiped, subglabrate or spar- ingly pubescent, ovate, twice the length of the sepals, strongly acute or almost acuminate, usually tipped by the long per- sistent style; non-petaliferous flowers sessile. Not very common in open post oak woods and limestone barrens. Distinguished from L. Nuttallii Darl. by its nar- rower leaves, fewer flowers, and large acuminate, less hairy pod. L. Manniana differs in its very long hairy sepals, and nearly included scarcely pointed pod. Mackenzie and Bush — Lespedezas of Missouri. 17 Type locality, Swope Park, Jackson County, Missouri; collected by K. K. Mackenzie, No. 449, Sept. 13, 1901; type specimens in herb. K. K. Mackenzie, duplicate in herb. Missouri Botanical Garden. Specimens examined. — Type specimens as cited under type locality. — Bush, 67, Eagle Rock, Sept. 28, 1896 Mackenzie, Eagle Rock, Sept. 28, 1896. 13. Lespedeza Virginica (L.) Britton, Trans. N. Y. Acad. Sci. 12: 64. 1893. In dry rocky woods. Apparently the most common species of Lespedeza in the State, judging from the collections. Specimens examined. — Bush, Jackson Co., Sept. 21, 1891; Sept. 29, 1891. — Bush, McDonald Co., Sept. 1, 1891. — Bush, Bismarck, Sept. 10, 1893; Bush, Jasper Co., Aug. 16, 1893. — Bush, Shannon Co., Sept. 12, 1893; July 24, 1891; Oct. 21, 1893. — Bush, Howell Co., Aug. 12, 1892.— Bush, Dunklin Co., Oct. 26, 1892. — Bush, Newton Co., Aug. 29, 1893.— Bush, 95, Independence, Sept. 1, 1895. — Bush, Greene Co., Sept. 21, 1893. — Blankinship, Greene Co., Aug. 23, 1888; Aug. 27, 1888. — Mackenzie, 441, Swope Park, Jackson Co., Sept. 13, 1901. — Mackenzie, Lee's Summit, Aug. 6, 1899. —Mackenzie, 948, Dodson, Aug. 26, 1895. — Thompson, Pacific, Sept. 19, 1898. — Glatfelter, Pilot Knob, Aug. 20, 1895. — Russell, Pilot Knob, Sept., 1897. — Dewart, Meramec Highlands, July 4, 1892. — Trelease, 229, Einstein Mine, Aug. 18, 1897. — Eggert, Forest Park, St. Louis, Oct., 1893. 14. Lespedeza NEGLECTA ( Britton ) . Lespedeza Stuvei neglecta Britton, Mem. Torr. Club, 5: 206. 1894. What appears to be this species occurs in the southeastern part of the State. To us it seems more closely related to L. Virginica than to L. Stuvei , and appears to bear the same relation to that species that L. Stuvei bears to L . frutescens . It is well worthy of specific rank. Specimens examined. — Engelmanu, Pilot Knob, Sept. 8, 1859. 15. Lespedeza frutescens (L.) Britton, Mem. Torr. Club, 5: 205. 1894. Found in rocky woods throughout the Ozark Mountain region in Missouri, but usually does not occur in such abun- dance as some of the other species. 18 Trans. Acad. Sci. of St. Louis. Specimens examined. — Bush, Shannon Co., Sept. 12, 1888. — Bush, McDonald Co., Sept. 1, 1893.— Bush, 53, Eagle Rock, Sept. 18, 1896.— Mackenzie, Eagle Rock, Sept. 18, 1896. — Dewart, Poplar Bluff, Aug. 14, 1892. — Letterman, Poplar Bluff, Aug. 15, 1895. — Russell, Pilot Knob, Sept., 1897. — Trelease, 228, Indian Hill, Dunklin Co., Sept. 28, 1897. 16. Lespedeza Stuvei Nutt. Gen. 2 : 107. 1818. A common species in dry rocky woods throughout the Ozark Mountain region in the State. Specimens examined. — Bush, McDonald Co., Sept. 1, 1893. — Bush, Campbell, Sept. 12, 1893. — Bush, Maiden, Sept. 12, 1893. — Bush, Shannon Co., Oct. 21, 1893. — Bush, Newton Co., Aug. 29, 1893. — Bush, Jasper Co., Aug. 16, 1893. — Bush, 42, Eagle Rock, Sept. 28, 1896. — Mackenzie, Eagle Rock, Sept. 28, 1896; Sept. 28, 1896, an entirely apetalous form. 17. Lespedeza simulata n. sp. Fl. IV.f.l, 2. An erect perennial, 6-9 dm. tall, glabrate to strongly rather short-pubescent, the rather few branches appressed- ascending; leaflets oblong-linear to oblong-elliptic, rounded at both ends, but strongly mucronate at the apex, 12-30 mm. long, 4-10 mm. wide, appressed silvery-pubescent on both sides, especially beneath ; petioles glabrate or pubescent, less than 12 mm. long, the leaf rachis about the same length, or a little shorter; petiolules villous, 1 mm. long; stipules sub- ulate, glabrate or hairy, 2-6 ram. long; petaliferous flowers in dense capitate spikes, the spikes sessile or on peduncles much shorter than the leaves; flowers on pedicels about 2 mm. long; flowers 6-8 mm. long, the purple carolla usually somewhat exceeding the long calyx-lobes, but sometimes almost included; calyx strongly hairy, 5-6 mm. long, the long acuminate sepals about twice the length of the tube; pod oval, acute or acutish, 4.5-5 mm. long, strongly pubes- cent, included or very slightly exserted ; non-petaliferous flowers in sessile axillary clusters. This species is most closely related to L. Manniana, but is at once distinguished by having the flowering peduncles shorter than the leaves, while in L. Manniana they are much longer. The included pod and long sepals distinguish it from all the other purplish-flowered species, but make faded dried Mackenzie and Bxish — Lespedezas of Missouri. 19 specimens greatly resemble some of the yellow-flowered species, whence the specific name. But here the presence of apeta- lous flowers at once furnishes a chie for its identification. The species is found in southwestern Missouri and adjacent Indian Territory in the Ozark Mountain region, in dry rocky open woods, and on high rocky mounds and prairies. Type locality, Newton County, Missouri ; collected by B. F. Bush, Aug. 25, 1893 ; type in herb. Missouri Botani- cal Garden, duplicate in herb. K. K. Mackenzie. Specimens examined. — Missouri : Type specimens as cited under type locality. — Bush, 61, Eagle Rock, Sept. 28, 1896. — Mackenzie, Eagle Rock, Sept. 28, 1896. Indian Territory: Bush, 1312, Sapulpa, Creek Nation, Sept. 29, 1895. EXPLANATION OF ILLUSTRATIONS. Plates I. -IV. Plate I. — Lespedeza violacea prairea. I, fruit, X 2. 2, flower, X 2. Plate II.— Lespedeza Manniana. 1, fruit, X '^• Plate III. — Lespedeza acuticarpa. 1, fruit, X 2- 2, flower, X 2. Plate IV. — Lespedeza simulata. 1, fruit, X 2. 2, calyx- lobes, X 2. Issued March 19, 1902. Trans. Acad. Sci. op St. Louis, Vol. Xll. Plate I. LESPEDEZA VIOLACEA PRAIREA. 1 ;;;!; l| ;■(: •i i 1 Tbans. Acad. Sci. of St. Louis, Vol. XII. Plate II. LESPEDEZA MANNIANA. Trans. Acad. Sci. of St. Louis, Vol. XII. Plate III. LESPEDEZA ACUTICARPA. Tkans. Acad. Sci. of St. Louis, vol. XII. Plate IV. LESPEDEZA SIMULATA. PUBLICATIONS. The following publications of the Academy are offered for sale at the net prices indicated. 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MAr 23 1902 Transactions of The Academy of Science of St. Louis. VOL.. XII. No. 3. ON THE MOTION OF GYROSCOPES. ALEXANDER S. CHESSIN. Issued May 13, 1902. MAY ON THE MOTION OF GYROSCOPES.* Alexander S. Chessin. The gyroscopes used to demonstrate the interesting phe- nomena connected with rapid rotary motion are, in many cases, «o constructed that the subsidiary parts of the apparatus are apt to greatly influence the character of the motion. Yet, these subsidiary parts are never taken into account in mathe- matical investigations because of the difficulties involved. I have in mind, especially, the gyroscope of Foucault and the polytrope of Sire. In the theory of these instruments, it has been customary to neglect the mass of the subsidiary parts of the apparatus. It is the purpose of this paper to show how the character of the motion of a gyroscope maybe determined without neglecting the mass of any part of the whole appar- ratus. Sire's polytrope was invented to demonstrate the influence of the earth's rotation on spinning tops. It is, in principle, a Foucault gyroscope mounted on a metallic circle which rep- resents a meridian of the earth and may be revolved about a diameter, thus producing an effect similar to that of the earth's rotation on the top. The polytrope of Sire, as dem- onstrating such effects, has a certain advantage over Fou- cault's instrument, because the metallic circle may be revolved with any velocity we please while, of course, experiments with a Foucault gyroscope are necessarily restricted by the actual angular velocity of the earth's rotation. This is not the place to describe either of the above men- tioned apparatus. A schematic figure will suffice to under- stand the derivation of our formulas. * Presented and read by title before The Academy of Science of St. Louis April 21, 1902, (21) 22 Trans. Acad. Sci. of St. Louis. Fig. 1. THE POLYTROPE OF SIRE. As already mentioned, the polytrope consists of two essential parts ; ( 1) a large metallic circle ( Cg) representing an earthly meridian and (2) a Foucault gyroscope mounted on this cir- cle in such a manner that it may be fixed at any point of it, thus demonstrating the influence of the earth's rotation on the gyroscope at any latitude, j^ The Foucault gy- roscope consists of the torus, or gyros- cope proper ( T) and two circular rings ((7j) and ((?,). The torus rotates freely about the diameter JVN' of the circle ( Cj, while the ring ( CJ itself revolves freely about the diameter PP ' of the circle (Cj, the axes i^iV' and PF' being per- pendicular to one another. The diameter ZZ' of the circle (C^) is perpendicular to PP' and may be fixed in any direction we please rel- atively to the meridian circle ( 6^). The origin of the axes XYZ is taken in the center of gravity (0) of the gy- roscope. This coordinate system is fixed with regard to the meridian circle ( C^ ) Fig. 2. p (^Gyroscope) which revolves about its ver- Chessin — On the Motion of Gyroscopes. 23 tical diameter D^ with a constant angular velocity (o. The direction Oil is that of the positive axis of rotation of ( Cg). The axis X is the projection of OH on a plane per- pendicular to ZZ' ; OB is a fixed line in the equatorial plane of the torus. The angles 0, (f>, yjr are Euler's angles defining the relative position of the body with regard to the moving coordinate system XYZ. The axis QQ' is per- pendicular to PP' and iVTV'. The angles which OP, OQ and ON form respectively with OO, will be denoted by 7, 7j ard y^; the principal central moments of inertia of the torus (including its physical axis) about OP, OQ and 0]SrhyA,A and C respectively ; A^, A^, C^, and A,,, A.,, C.^ will indicate the principal central moments of inertia of the ring ( C^) about OP', ON, OQ and of the ring ( C,) about OP', OZ, Oq. If, then, T denote the kinetic energy of absolute rotary motion of the gyroscope about the point ( O), we shall have (1) 2T=a (^' + ft)C0S7)2 + 6((/)' sin 6' + ft) C0S7J2 + C (1/^' + ' cos 6 -\- (o cos 72)^ + 0 ft)2 cos^ 7 + d (<^' + ft) sin fiy. where fi is the angle of OH with X, and (^^ {:: = A + Ai, b = A-\-C\ — A^, = A, — A,— C„ d = A^-{- A,. \ cos 7 = cos /i cos 4> ( 3 ) ^ cos 7j = sin /* sin 6 — cos /x cos 6 sin 4> ' I cos 72 = sin fi cos 0 + cos ft sin 0 sin ^. The differential equations of motion are given by the formula d(3T\ 9T ^ ^ , We obtain immediately two integrals, namely ( 5 ) i/r' -|- <^' cos 0 ■\- 0) cos 72 = ^1, 24 Trans. Acad. Sci. of St. Louis. (6) ae'^-\-{d + b^We)4>"^-\- C {^\r'-{- <^' cos (9)2 = 2h + (o^ [(<^ + c) cos^ 7 + 6 cos'7i + ^ ^05^72] the latter being the integral of kinetic energy. The relation between the angle /i and the latitude (X) of the point ( 0) is expressed by the formula ( 7 ) sin \ ■=■ cos a sin ^l + sin a cos /* cos yS . a being the angle of the axis Z with the line ( OK) passing through (0) and the center of the ring (C3), and yS the angle of the planes XZ and Z 0^. Suppose, now, that the axis ZZ' be made parallel to OH and the mounting of the gyroscope then fixed in this position. In this case /^ = -^ and, therefore, cos 7 = 0, cos 7j = sin dy cos 7^ = cos By (8) 2r = a6''2 + 6 (<^' + a))2sin2^ -^ d {' + ayf + C[^/r' + (<^' + a))cos(9]2. We can, now, obtain a new integral, namely, (9) ((^+6sin2 6')((/)'+a>) + C[A/r'+(<^'+a))cos6']cos6' = ?, while the integrals ( 5 ) and ( H ) take the form (10) i/r' + ((/)' + ft)) cos ^ = ?i (11) a^'2+ {d-\-b sin^ 6) <^'2+ G (^/r' + y Case I. — 1 < w < 1 . We will put m = cos t; and consider separately the cases of w >, = and < 1. A. 71 > 1. Equation (15) becomes ~ ^d + b sin2 e dd dt = ±\ll l/(cos 6 — cos?;) (n — cos^) and shows that the axis of the torus oscillates about ZZ\ the amplitude of these oscillations being 2r). If we put Chessin — On the Motion of Gyroscopes. 27 ^If l/d+ b sin^ 6 dO (17) '^ = \a L/ (cos ^ — cos v) (?i — cos d) 0 and remark that i yd-\-b^m^e dd y/(cos 6 — cos 7}) (n — cos 6) l/d + bsm^0 dd p I v/(cos ^ — cos v) {n — cos 6) we find that the oscillations of the axis of the torus are iso- chronic and that the period of a complete oscillation is 4t. B. n = 1. Equation (15) becomes dt it = ±^^2^~ l~a i/d + bsm'd dd e sin 2 t/cos 6 — cos rj and shows that the axis of the torus approaches assymptotically to the position OZ. In fact, after the moment of maximum ■deviation (t?) from ZZ\ where the sign of 6' changes, this sign remains unchanged throughout the motion, and if Tj de- note the time required for the passing of the axis of the torus from the position of maximum deviation (^) to the position OZ, we find that Vd^-b^xn^d dd I ad i_d dd_ 0 sm_ 2 4. e. T, = oo . 28 Trans. Acad. Sci. of St. Louis. C. n 1. It should be observed that if ^0' = ^ the case A) alone is possible. In fact, if ^0 = ^» since 7?j = — 1, we have d {I,— CI, cos e,y _ ^ d + b si"^2^i^ ~ ^'2 + Ch) ^ from which it is clear that l^ and Z^must have different signs» and, therefore, n < 1. Chessin — On the Motion of Gyroscopes. 29 A. If n < 1 The axis of the torus oscillates about ZZ'. These oscillations are isocJironic and their amplitude is 2rj^ where rj^ = cos"^ n. The period of a complete oscillation is ^r^ and /^2_ ]/( COS 0 , - , V d + b sin' e dd (20) t3 = x|?aI ^ 2 y' n — cos 6 B. If n ^ 1, the axis of the torus assymptotically approaches the position OZ' (where 6 = tt). Case III. m < — \ Let us put — m = 5, so that s > 1. Then l/d-\-hBm^e dd dt ' = ±VI 1/(5 + cos 6) {n — cos^) A. If n < 1, the axis of the torus performs isochronic oscil- lations about ZZ'. The amplitude of these oscillations is ^t]^ where rj^ = cos~^ n, and the period of a complete oscillation is 4X4, having put /V .21) I" I Vd + bsin'^ede |/ ( s + cos 6) (n — cos 6) B. If n > 1, the axis of the torus revolves about PP' with- out changing the direction of the revolution. The time re- quired for a complete revolution is 2r^ where TT M (22) r,= ^r-.' v/rf + isinM de \/{s + cos 6) (71 — COS 6) 30 Trans. Acad. Set. of St. Louis. It should, again, be observed that here, as in Case //, the condition 0'^ = O'ls compatible only with the condition n < 1. Remark. The motion of the axis iVTV' of the torus includes the motion of the ring ((7J. In the cases lA, IC, IIA, III A, this ring oscillates about PP' ; in the cases IB and IIB it assymptotically approaches the ring (C^); finally, in the case IIIB^ it revolves about PP ' without a change in the direction of this revolution. To complete the determination of the motion of the gyros- cope it is necessary to evaluate the angles ^ and y^r. The first angle defines the motion of the ring ( C^) about ZZ', the second determines the motion of the torus about its own axis NN '. These angles are given by the formulas S' l^ _ CI, cos d (23) * = *,-..+ I ';,^,^„., ^^ ^.-. , .17. i (lo — CZ, cos ^) cos ^ ,, In the following discussion the terms precession and nuta- tion will be used to indicate the rates of change of the angles (f) and 6 respectively. The problem which we set ourselves to solve is to determine when the motion of the gyroscope proceeds so that the nutation is = 0. The condition necessary and sufficient to obtain a motion without nutation is that sin 0,(1^— CI, cos e,) [(6 + d) CI, — bl, cos ^o] = 0 or, on account of the relations (16), ( 25 ) sin (9o ( 'o) ] = O. This equation may be satisfied in three ways. Chessin — On the Motion of Gyroscopes. 31 1. By putting sin 0^ = 0, i. e. at the start the axis of the torus is parallel to the axis ( O fi) of rotation of the meridian circle (C^). Equation (9)' shows that in this case ^/ic pre- cession has a constant value^ and equation (10), that the angular velocity of rotation of the torus about its axis NN' is constant. 2. By putting 0o = — ^- ^^ this case the precession has the constant value — (o and, besides, -»/r' = t^Tq'. This result is a priori obvious. In fact, the assumption of o' = — <"> together with 6^ = 0, is equivalent to assuming that at the start the axis of the gyroscope was fixed in absolute space {not relatively to the meridian circle). But we know that, in this case, the axis retains its fixed position in absolute space. 3. By putting 67^ = 6 (co -j- ^o') cos 6^, or, which means the same thing, Cylr^ + {C—b) (o+o>) cos6'o = 0. Again, we find that both the precession and the angular velocity of rotation of the torus about its axis, have constant values. We now pass to the gyroscope on the surface of the Earth. THE GYROSCOPE OF FOUCAULT. First of all, let it be remarked that we may neglect in our calculations all terms of the order of o)"^ and higher, oo being the angular velocity of rotation of the earth, if we assume that the force of gravity is constant in magnitude and direction for all positions of the gyroscope.* However, as we gain nothing by thus changing the appearance of our formulas, while we would be obliged, on the other hand, to retain the terms of the order of co^ if the point of observation were near one of the poles, it is advisable to leave the for- mulas as they are, with the explicit understanding, that the results are correct only to terms of the order ofoi. * See a paper by the author in the Transactions of this Society, Vol. XII., No. 1, On the true potential of the force of gravity. 32 Trans. Acad. Sci. of St. Louis. We may now immediately apply the formulas derived for the polytrope of Sire to the case of a gyroscope on the sur- face of the earth. The metallic ring ( C^) of the polytrope will, in the following discussion, be replaced by the meridian of the place of observation. We will assume that ZZ ' is parallel to the axis of the earth. Referring to the figures in the text it is clear that (o must be now replaced by — «, since the positive axis of rota- tion of the earth is directed southward. We will consider the motion only under Foucault's condi- tions, i. e. when 6\ = <^\ = 0 and -v/r'j, is very great. Then only one among the cases discussed for the polytrope pre- sents itself, namely the case /C, as can be readily seen. Therefore, ( 26 ) dt = ±\1 i/ d -\- h ^m^ d ae ;/(COS^ — C08?7)(COS7?^ — COS 6) If -v/r'j) > 0, i. e. the rotation of the torus appears from left to right to an observer standing along the axis ON^ with his feet at O, this axis forming an acute angle with the negative axis of the earth (i. e. its northward direction), then 17^ = 6q < 77. If, on the contrary, yjr'^ < 0, ^. e. the direction of rotation of the torus is opposite to the one just described, then 7? = ^5 > 77j. Hence, the axis of the torus oscillates between the positions 6 =^ 6q and 6 •= rj or ij^^ never passing through ZZ ' (which is parallel to the axis of the earth). The period of a complete oscillation is 2r^f where 4ij\ l/d + b sin2 e dO (27) '-- ' ■ ( cos 6 — cos r}) [ COS t]^ — COS 6) Of the three cases of motion when the nutation is == 0, only one is possible in Foucault's gyroscope, namely the one deter- Ckessin — On the Motion of Gyroscopes. 33 mined by the condition sin 6^ = 0, i. e. ^ = 0 or tt. Hence, the axis of the torus can he in equilibrium only if it is parallel to the axis of the earth. Indeed, this fact can be readily ascertained by the ordinary rules of mechanics. Moreover, it is clear, that one of the two positions 6^ — 0 or tt, in which the positive axis of the torus is parallel to the positive axis of the earth, is the position of stable equilibrium, while the other position is that of unstable equilib- rium; i. e. if y\r'Q > 0, then 6^ ■=■ tt \s the position of stable equilibrium and ^o = ^ ^^^ position of unstable equilibrium, while for ^Ir'^ < 0 the position ^^ = 0 is that of stable equilib- rium and Oq = IT one of unstable equilibrium. The motion is completely determined by the equation (26) and the following formulas giving the angles 0 and yjr. f- I _ CI, cos 9 -/■ 0 ^ = ir, + lj- I ' d + bsin^d (I— CI, COS 6) COS e It should be observed that 28 2ft) 26 2ft) I cos 77j — cos 77 = ^ = ^ J(tZ + 6sin'^)[A(6 + cZ) — 6^32] i. e. the difference cos rj, — cost) is a quantity of the order of -^ • The angular velocity of rotation of the earth (co) being very small and ■^'q by hypothesis, very great, the oscil- lations of the axis of the torus (and of the ring ( CJ with it) will be exceedingly small. The same is true with regard to 34 Trans. Acad. Sci. of St. Louis. the period (2X2) of these oscillations. It should also be ob- served that ^' is of the order of w, i. e. the precessional motion is extremely slow. Finally, as ^' differs from t/t'^ by a quantity of the order of w, the angular velocity of rotation of the tore about its axis will remain very nearly constant. Issued May 13, 1902. PUBLICATIONS. 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A report of the observations made by the A7ashington University Eclipse Party, at Norman, Califor- nia, isri. $2.00. ♦ Supply exhiiastcd. t Can be sold only to purchasers of the entire volume,— so far as this can be supplied. Bach number;.- a brochure containing one complete paper (or rarely two). Transactions of The Academy of Science of St. Louis. vol. XH. Xo. 4. I^IOTES ON SOME PLANTS OF THE SOUTHWESTERN UNITED STATES. 7. B. S. NORTON. ■ Umed May 14, 1902. MAY inn? KOTES ON SOME PLANTS OF THE SOUTHWESTERN UNITED STATES.* J. B. S. Norton. In connection with my work in the herbarium of the Missouri Botanical Garden during the past two years, a num- ber of things which seemed worthy of publication came to my notice concerning the plants of the Southwest. The preparation for publication of the notes collected has been somewhat delayed by my removal to Maryland in August, 1901, and some of the species have already been published by MAP OF THE UNITED STATES. Showing extent of botanical exploration. others. Mr. B. F. Bush and myself have worked up together the new species collected by him in Texas and southwestern Missouri. Some of these will be published by him in another paper. The accompanying map shows the comparative thorough- ness with which the United States has been worked for * Presented by title to The Academy of Science of St. Louis, April 21, 1902. (35) 36 Trans. Acad. Sci. of St. Louis. botanical collections ; the shading showing approximately where collections have been made, and the density of it in- dicating the number and extent of collections. The botanical centers of the country of course show up as spots of denser shading. The map is made up from lists of specimens found in our large herbaria of several large genera of wide distri- bution, species of which it would seem probable would be found in all parts of the United States. It will be seen that several regions of the west still need exploration. There is also a comparatively blank space along the eastern side of the Mississippi River. Portions of Arizona and Colorado have been well worked, and others are almost unknown. It may be that certain parts of the arid regions show blank on the map because of comparative dearth of species, northwestern Texas and part of Nevada for example. Most of the prairie region has been well explored, due to the energetic work in State botanical surveys. There is a region extending from South Central Missouri through Arkansas and Indian Territory to northern Texas which is not perfectly covered by any of our manuals, which has recently furnished many new species and others will, with more exploration, no doubt be found. These are not mere transition forms between the Eastern and Texan or Western floras, but distinct species peculiar to this limited area which is somewhat characterized by the Ozark Mountains which may have isolated and preserved these peculiar forms. The Middle Western States like Missouri and Arkansas would no doubt furnish a greater harvest for the " species makers" of recent years if they could be worked over as thoroughly as some of the Eastern States by persons of such tastes. It is desirable as an aid to the study of geographical dis- tribution, variation and the formation of species, that every . distinguishable form, especially when they may also be geo- graphically differentiated, should be published. However, in these studies, no effort has been made to discover new forms, although some have come to light simply in the determination . of the plants in certain Collections. A study of the slightly variant forms of some widely dis- Norton — Plants of the Southwestern United States. 37 tributed species in the desert regions of the Southwest seems to indicate that the isolation of mountain regions, affording favorable growth for certain species by intervening deserts where the same species cannot grow, offers a condition com- parable with the differentiation of forms in insular floras. This seems to me to be especially true with some mountain species of Euphorbia, which I have examined, in which the means of dissemination is limited, most of the isolated moun- tains of Arizona and New Mexico having their peculiar vari- ation not occurring elsewhere. Cyperus longispicatus n. sp. Perennial ; 1 to 2 m. high; leaves several dm. long, 1 to 2 cm. broad; peduncle naked, surmounted by an involucre of several leaves, the larges as much as 1 m. long, 1 cm. or more wide, prominently veined, rough margined ; umbel of 5 to 10 rays, some very short, others 15 cm. long, compound, with 2 to 5 spikes 1 to 3 cm. long ; spikelets slightly flattened, 2 to 4 cm. long, 20- to 40-flowered, spreading, falling away from the axis and breaking up; scales concave or slightly keeled toward the apex, imbricated, ovate, short pointed, light yellowish-brown with a prominent green stripe on the back and two distinct nerves between this and the broad membranous margin, persistent on the swollen joints of the rachis, the membranous margins of which almost inclose the obpyramidal, 3-angled, light brown, pointed achenes ; stamens 3 ; achenes 1 mm. long, the apex obtuse with a mucron which bears the 3-cleft style. — Plate V. Type collected by B. F. Bush at San Antonio, Texas, 1900, no. 1248. Common in water, conspicuous from its large size and the great length of the spikelets. DiTHTREA WiSLiZENi Engelm. The range of this interesting crucif er is extended eastward by specimens collected in western Oklahoma by Mark White, in 1899. 3 8 Trans. Acad. Sci. of St. Louis. Argemone pinnatifida n. sp. Low, 3 dm. high, scarcely branched ; leaves of the inflo- rescence small, thus giving a somewhat pedunculate appear- ance; spines few on stems and leaves, more abundant on the calyx; leaves deeply pinnatifid, the lobes deeply incised- dentate, the lobes and teeth spreading and not ascending as in related species; flowers rather small. I have seen two specimens of this species, both from Texas. They are: Heller, Corpus Christi, no. 1378, 1894; Jermy, Gillespie Co., no. 218. LiNUM Lewisii pratense n. var. Less than 3 dm. high, wide spreading, diffusely branched with many sinuous branches, the main stem short; leaves crowded, narrowly linear, somewhat fleshy, 5 to 15 mm. long, 1mm. wide; flowers small, whitish; capsule large, very obtuse. — Saline plains, Kansas to Texas. — Plate VI. Type collected in Kearney Co., Kansas, Aug. 27, 1897, no. 1078, A. S. Hitchcock, in herb. M. B. G. Other speci- mens seen are: Hitchcock, Medicine Lodge, Kan., 1892, Sherman Co., Kan., 1892, Cloud Co., Kan., 1892 ; Carleton, Cheyenne Co., Kan., no. 192; Mark White, Grant Coi, Okla., no. 196, 1899; P.J.White, Woods Co., Okla.. no. 46, 1900; Bush, Catoosa, I. T., no. 1155; Hall, Dallas, Texas, no. 69, 1872. Transition forms occur from Texas to Arizona, for example: Toumey, Flagstaff , 1894 ; Wright, no. 69, W. Tex., 1849; Wislizenus, Rock Creek, N. M., no. 487, 1846; Fendler, N. M., no. 92, 1847. The typical L. Leioisii Pursh, with tall, slightly branched stems, large blue flowers, larger, more lanceolate leaves and more pointed capsules, is found in the more mountainous parts of the Western States. Plantago rhodosperma Decaisne, DC. Prodromus 13:722. 1852. (?).P. Virginica longifoUa Gray, Synop. Flora 2^:392. 1878. The Texan plants referred to the above name were easily recognized by Mr. Bush as distinct from any recognized species of the United States, and they seem to be very easily Norton — Plants of the Southwestern United States. 39 placed with this Texan species of Decaisne. P. purpurascens Nutt. and P. occidenlalis, Dec. may be much more easily re- ferred to P. Virginica L. It is more likely that the plaijts referred to P. Virginica loiigifolia by Dr. Gray belong with P. rhodosperma than do the plants referred to it by him as synonyms. The following brief description is drawn from the plants mentioned below. The type is in DeCandolle's herbarium (see Prodromus 1. c). Leaves entire to dentate with large blunt salient teeth; spikes several, 5 to 7 mm. thick, 12 to 20 cm. long; peduncles 5 to 7 cm. long, much shorter than the leaves ; bracts as long as the calyx, rather rigid and projecting ; flowers crowded, erect, the petals rather rigid, closed together, forming a point over the ripened fruit, not much longer than the tube ; seeds flattish, with an indistinct border, red, 2 mm. long. — Plate VII. The species may be readily distinguished by the large dense spike, pointed corolla and large red seeds, they being twice the length of the yellowish-brown seeds of P. Virginica. Specimens have been examined as follows: Bush, Colum- bia, Texas, no. 107, 1900 ; Mearus, Ft. Clark, Texas, no. 1448, 1895; Ball, Alexandria, La., no. 552; Waugh, Oklahoma, no. 172; Palmer, Indian Territory, no. 213, 1868; Pringle, Tucson, Arizona, no. 15957 ; Bush, Columbia, Texas, no. 123. Verbena polystachya HBK. This species, reported in Gray's Synoptical Flora from California and Arizona as rare, is not at all uncommon from California to Florida. It has been confused with V. urticae- foliaLi. In the latter the sepals are but little longer than the ripened nutlets, giving the fruit a blunt appearance, while in V . polystachya they are enough longer than the fruit to make it appear pointed. This in addition to the thicker, smaller, less pointed, rougher leaves, and more dense spikes, easily distinguishes this tropical species. The following are repre- sentative specimens of V. polystachya: — Pollard, Scranton, Miss., no. 1191, 1896; Nash, Eustis, Fla., no. 1248, 1894; Curtiss, Jacksonville, Fla., no. 5111, 1894; Palmer, Biscayne Bay, Fla., no. 397, 1894; Hitchcock, Meyers, Fla., no. 40 Trans. Acad. Sci. of St. Louis. 269, 1900, with leaves more like F. urticaefolia ; Tracy^ South Pass, La., no. 22, 1900. Specimens are also common in West Indian collections. A specimen collected by Ball at Alexandria, La., no. 556, is a good example of V. urticae- folia from the Southern States. SiLPHIUM INTEQRIFOLIUM Michx. Two rather distinct forms have been placed under this name in the Middle West, besides the many variations from Texas found in herbaria, most of which could probably be placed more properly with some of the Texan species now recognized. One form is a large plant with glabrous and glaucous stem or with a few hairs on the upper part, and large glabrous or scabrous leaves. This is well represented by many collections from Central Kansas. It is possible that this is the variety laeve of Torrey and Gray, and if so should stand as a good variety under that name if not as a species. The other form is smaller with smaller leaves, and has the stem and leaves covered with a short, dense, staring pubes- cence, which appears quite different from the longer scat- tering appressed hairs found on other forms. This occurs eastward and is well represented by the following specimens : Hitchcock, Olathe, Kan., 1892 ; Fink, Fayette Co., Iowa, no. 535, 1894; Wolf, Center, 111., no. 28, 1881. Brauneria paradoxa n. sp. Stem glabrous or slightly scabrous or hispid, 3 to 8 dm. high ; lower leaves narrowly lanceolate, 12 to 25 mm. wide, about 2 to 3 dm. long including the petiole which is some- times 15 cm. long, glabrous or nearly so, entire; the 3 to 5 distinct nerves yellow, translucent; upper leaves smaller and wider in proportion, nearly sessile ; peduncle 2 to 3 dm. long, comparatively slender, striated, somewhat pubescent at the apex; heads 2.5 cm. wide, 3 cm. high, dark brown; rays bright yellow, drooping or spreading, 4 to 6 cm. long. Com- mon in prairie and barrens in Southwest Missouri. — Plate VIII. The type is from Swan, Mo., collected by B. F. Bush, June 10, 1898, no. 155. Also collected by Mr. Bush at Norton — Plants of the Sonthwestern United States. 41 Nichols Junction, Mo., 1898, no. 42, and Eagle Rock, Mo., 1897, no. 76, and in Texas by F. Lindheimer, Flora Texana exsiccata, 94, Fasc. 1, 1843. Haploesthes Gregg II Gray. The range of this species is extended into Oklahoma from New Mexico by specimens collected by Mark White in Grant County, in 1899. EXPLANATION OF ILLUSTRATIONS. Plates V-VIII. Flaite Y . — Cyperus longispicatus. Habit, one-half natural size. 2, Por- tion of spikelet showing scales, with a joint of the rachis at base inclosing an achene, X 6. Plate VI. — Limim Leioisii pratense. Habit, one-half natural size, Plate 'VII. — Plantago rhodospernia. 1, Habit, one-half natural size. 2, Flower and seed, X 6. 3, Flower and seed of P. Virginica, X 6. Plate VIII. — Brauneria paradoxa. Habit, one-half natural size. Issued May 14, 1902. TKAssi. Acad. Sci. of St. Louis, Vol. XII. CYPEKU.S LOXGISPICATUS. Trans. Acad. Sci. of. St. Louis, vol. XII, Plate VI. LINUM LEWISII PRATENSE. Trans. Acad. Sci. of St. Lotus. Vol. XII. Plate VII. PLANTAGO ERYTHKOSPEKMA. Trans. Acad. Sci. of St. Louis, Vol. XII. I'r.ATE VIII. BRAUXERI.V PARADOXA. PUBLICATIONS- The following publications of the Academy are offered for sale at the net prices indicated. Applications should be addressed to the Librarian, The Academy of Science of St. Louis, 1600 Locust St., St, Louis, Mo, TRANSACTIONS (in octavo). Vol. Number. Price per number. Price per vol. Price in set. 1* 2t 3-4 $7.60 (Nos. 2-4 only.) 1 $4.00 2.00 each. $7.00 (Nos. 2-4 only.) 2 1 to 3 2.00 each. 5.50 5.00 3 1 to 4 2.00 each. 7.50 7.00 4 1 to 4 2.00 each. 7.60 7.00 5 1-2,3-4 { 4.00 each, (double numbers) 7.60 7.00 6t 1, 2, 6, 8, 10, 11, 16, 17 4, 6, 7, 13, 14, 15, 18 3, 9 12 > 25 cts. each. 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JUN 19 1902 Transactions of The Academy of Science of St. Louis. VOL. XII. No. 5. A REVISION OF THE ELEPHANTOPEAE.— I. C. F. BAKER. .cUx Issued May 20, 1902. JUN 19 1902 A REVISION OF THE ELEPHANTOPEAE. — I.* C. F. Baker. Several years ago, while collecting in Alabama with Prof. Earle, the writer became convinced after numerous compari- sons and observations in the field, that the three names Carolinianus, tomeiitosus, and nudatus with the very brief descriptions accompanying them in the manuals, did not at all represent the true status of the genus Elephantopus in the South. While at St. Louis, through the kindness of Dr. Trelease, an examination was made of the literature and of all the material at the Shaw Garden. Later, through the kindness of Dr. Robinson and Dr. Rose, the material of the Gray Herbarium and of the National Herbarium was also studied. Unfortunately the studies were not finished at that time, departure for the field preventing, but Dr. Trelease, with his usual hearty desire to place facilities in the hands of students, kindly forwarded the Shaw Garden material to Stanford University where this paper was prepared in Prof. Dudley's laboratory and various favors from the latter are here acknowledged. These opportunities were wholly unexpected or arrange- ments would have been made for carrying out, in Alabama, a series of very important and necessary experiments, throwing lio-ht on many points which must remain obscure until such work is done. The range of variability in the flowers should be studied with a large quantity of fresh material at hand. No one thing of greater value could be done than the pro- duction and study of authentic hybrids between each two of the three species. Some most interesting surprises are likely to result from this. Seeds from a single parent plant (of which seeds the parentage is sure) should be raised under * Presented by title to The Academy of Science of St. Louis, Marcli 3, 1902. (43) 44 Trans. Acad. Sci. of St. Louis. widely varying ecological conditions and the progeny care- fully compared with each other and with the parent plants. It may be remarked here that such work in Experimental Ecology should have been gotten under way by our Gardens long ago. When this work shall have become cooperative it will yield results of wonderful import in systematic botany. A few years of it will give us more positive knowledge of plant forms than hundreds of years of herbarium study. Evidence drawn from the latter must remain circumstantial and opinionative. The experimental work would exercise a profound influence in the elucidation of such groups as Viola, Aster, Antennaria, Apocynum, Senecio, N'emophila, JEsch- schoUzia, Sisyrinchium, and the EleiJhantopeae . The study of the North American Elephantopae has led into an examination of those of our tropics and finally into a study of the whole group. The notes presented here are distinctly preliminary and tentative. If they shall call marked atten- tion to the group and the great necessity for the especial attention of field workers to it, the principal object of these first notes on the group (as a whole) to be published in English, will have been accomplished. The studies will be continued as more and better material accumulates. Those plants grouped under the Elephantopeae differ from the Vernonieae and Eupatorieae in having the few-flowered (two to four) anthodia small, sessile, and gathered into com- pact terminal or lateral glomerulae. In 1737 Linnaeus described the genus Elephantopus, of which scaber must be taken as the type. In 1792, Rohr fol- lowed with the genus Pseudelephantopus, using spicatus as its type. Later writers seem to have disregarded Pseud- elephantopus, for Cassini founded Distreptus, and La Llave, Maiamoria, on the same type. There seems to be no ques- tion as to the application of the un wieldly name Pseudelephan- topus to our well-known plant. Lessing, in 1829, described Elephantosis, basing it on quadrijlora, which afterwards he determined as synonymous with angustifolius. Spirochaeta Turczaninow, appeared in 1851 with Funckii as its type. This plant seems never to have been recognized except by its describer. The name Euelephantopus was first used as of sec- Baker — A Revision of the Elepliantopeae. — /. 45 tional value by Endlicher in 1836. It is the typical section of the old genus and synonymous with Elephantopus Linnaeus (sens, strict.). In 1847, Schultz Bipontinus separated the section Micropajjpus for the very interesting species of the same name. These generic and sectional names have met with varying treatment at the hands of botanical writers. In 1817 Cassini recognized Elephantopus and Distreptus. In 1829 Lessing re- duced Pseudelephantojnts to the later Distreptus and described Elephantosis . In 1836 De Candolle recognized Elephantopus^ Elephantosis and Distreptus. In the same year Endlicher used Euelephantopus, Elephantosis and Pseudelephantopus as sections of the old genus, reducing Distreptus and Matmnoi'ia to synonyms of Pseudelephantopus. In 1830, Sprengel men- tions Matamoria as a synonym of Elephantopus. In 1843 Walpers practically followed Endlicher. In 1847 Dietrich places all the species under Elephantopus, mentioning Ele- phantopsis and Distreptus as synonyms. In the same year Schultz Bipontinus rearranged the species, using the follow- ing names for sections of the old genus Elephantopus: Euelephantopus, Micropappus, Elephantosis, Elephantopsis, and Pseudelephantopus ( ^ Distreptus). In 1873 Bentham and Hooker discussed Matamoria as a synonym of Elephan- topus, Elephantosis as of sectional value, and Spirochaeta with Pseudelephantopus as equivalent to Distreptus, which is given sectional value. Finally, in the Index Kewensis, and in Engler and Prantl, all of these names are thrown together without remark under Elephantop)Us . The groups given generic value in this paper, with their types and type localities, are as follows : — 1. Elephantopus L. — scaber L. — East Indies. 2. Spirochaeta Turcz. — FrinckiiTuTcz. — Venezuela. 3. Elephantosis Less. — angustifolius Sw. — Jamaica. 4. Pseudelephantopus Eohr. — spicatus Sw. — Guiana. 5. ElephantQpsis Sch. Bip. — hiflora Less. — Brazil. 6. Micropappus (Sch. Bip.) — micropappus Less. — Brazil. 46 Trans. Acad. Sci. of St. Louis. The synonymic list is as follows ; — 1. Elephantopus L. 1737. =z Exielephantopus Eudl, 1836 (Sect.")- 2. Spirochaeta Turcz. 1851. 3. Elephantosis Less. 1829. 4. Pseudelephantopus Eohr. 1792. :^Distreptus Cslss. 1817. = Matamoria La Llave 1824. 5. Elephantopsis Sch. Bip. 1847. 6. Micropappus (Sch. Bip.) 1847. These names represent natural and well-marked groups in what would otherwise be a large, unwieldy, very heterogen- eous assemblage of species. Even if the names are discarded we will still divide the group along the same lines. No attempt has ever been made to divide the group in any other way, and these names have been repeatedly used to designate the sec- tions. These groups are as clearly differentiated as dozens of other so-called genera in the Compositae, as for in- stance Liatris and Trilisa, Gutierrezia and AmphiachyriSi Heterotheca and Chrysopsis, Brachychaeta and Solidago, Coreopsis and Bidens, etc. Viewed in the light of a com- parative study of the other genera, it is quite impossible, for instance, that the species tomentosus, spicatus, and a7i- gustifoUus should be congeneric. Botanists have apparently thrown these genera together more often through a lack of knowledge, than because of any additional evidence. This seems especially evident in the case of Spirochaeta. With the other genera separated, Elephantopus L. (sens, strict,) remains a compact, homogeneous group of species, closely related and evidently congeneric. In addition, and finally, the retention of these names would be a matter of great convenience in many respects. TABLE OF GENERA OF THE ELEPHANTOPEAE. A. Heads four-flowered. B. Pappus in one sei'ies, with distinct chaffy paleae. C. Stem not stolouiferous; glomeruli subtended by specialized leafy bracts; inflorescence terminal or subracemose; pappus of 5 to 10 straight setae, the paleae rarely united. Elephantopus. CC. Stem stolouiferous; glomeruli subtended by simple reduced leaves; inflorescence spicate; pappus of about 4 to 6 spirally twisted setae. Spirochaeta. Baker — A Eevision of the Elephcmtopeae. — I. 47 BB. Pappus iu two series, together of always more than 5 setae; inflorescence spicate; glomeruli subtended by simple reduced leaves. C. Pappus homogeneous, of numerous straight setae having en- tire, scarcely distinct paleae. D. Pappus several times length of achene. Elephantosis. DD. Pappus only about a third the length of achene. Micropappus. CC. Pappus heterogeneous; of comparatively few setae with strongly lacerate paleae; the two long sub opposite setae plicate near upper extremity. Pseudelephantopus . AA. Heads two-flowered; pappus in outer series short, in inner longer, twisted, and deciduous. Elephantopsis . Genus Elephantopds Linn. Gen. ed. 1. 249. 1737. In the study of the species of this genus the starting-point must be the exact determination of the type species — scaher. In Hort. Cliff., among the aggregate of forms there men- tioned, the locality Jamaica is given. But in the Linnaean description of 1753, its habitat is given simply as " in Indiis," while Willdenow particularizes in " India orientali." Speci- mens occur in the American herbaria from India, the Philip- pines and Formosa. The plant in its native regions is low and roughly haired with usually very long narrow oblanceolate, rather obtuse, radical leaves, merely rough scabrous above, sparingly rough hairy below. The glomeruli resemble those of our tomentosus, the heads being about as long, but the achenes are smaller, the pappus shorter, and the paleae with much longer thicker pubescence. It seem probable that scaber, like Pseudelephantopiis spicatus, has become widely dissemi- nated in the tropics. Some specimens from the Isthmus of Panama may prove to be this, though nothing like it has been seen from elsewhere. The species tomeniosus so far as the herbarium material examined goes, does not occur outside of the Eastern United States. In the earlier days there seems to have been no question of the distinctness of tomentosus . In 1829 Lessing considered it distinct, but De Candolle in 1836, and Dietrich in 1847 do not even mention it. In 1847 Schultz Bipontinus properly reserves scaher for the old world form, but combines all the 48 Trans. Acad. Sci. of St. Louis. American form8 uuder tomentosus. Grisebach in Fl. British West Indies, considered scaber as represented in America, with mollis and Carolinianus as distinct from it. Baker in Fl. Bras, places both mollis and tomentosus under scaber. Hemslev in Biol. Cent. Amer. Bot. unites tomentosus^ Martii, mollis and Carolinianus under scaber. This last must be considered as an extreme theoretical view. So far as the not inconsiderable material in American herbaria is concerned they are abundantly distinct with the possible exception of Martii. Gray paved the way to a more critical separation of the forms by the description of nudatus. But with nudatus must be accepted several other forms in the United States and numerous others in the West Indies, Mexico, Central and South America, Africa and the Far East. The relationships of some of our common forms are provisionally indicated herein, but anything approaching this will be, for most of the forms, absolutely impossible at present. It seems to the author wholly immaterial at this juncture as to whether the names represent good " species " or not. They represent wonderfully distinct plant forms which must in any event be recognized, no matter to what grade of relationship they may eventually be assigned. It seems as if we would arrive at some clear and comprehensive view of the genus much sooner by means of clearly defined segregates than by shuffling ofi" all responsibility in Hemsley's roomy aggregate. More and more attention is being given our tropical flora, so that many of the doubtful points will soon be cleared up. SPECIES OF THE UNITED STATES. These species, all of which occur east of the Rocky Moun- tains, may be listed as follows : — 1. Garoliniaims Willd. C= flexuosus Raf.). Var. violaceus (Sch. Bip.). 2. tomentosus, L. (= Carolinianus var. simplex Nutt.) Var. nudicanlis (Poir.). (= nudicaulis Ell.). 3. elatus Bertol. 4. ntidatits Grav. Baker — A Revision of the Elephantopeae. — /. 49 They may be separated as follows : — A. Stems leafy, lower cauline leaves like radical; paleae of pappus long triangular, gradually narrowed into the setae; vestiture of compara- tively few loosely spreading hairs. Carolinianus. AA. Stems scapiform, with a rosette of leaves at the base; cauline leaves differing widely from radical. B. Paleae of pappus long triangular, narrowing gradually into setae; plant distinctly pubescent. C. Pappus much longer than achene; glomeruli pubescent, but not densely canesceut villose; heads long (10-12 mm.) with inner bracts of involucre acuminate; stems usually little branched above. tomentosus . CC. Pappus usually about as long or shorter than achene; glomeruli densely canescent villose in typical forms ; heads shorter (6-8 mm.) with inner bracts of involucre obtuse submucronate ; stem usually much branched above. elatus. BB. Paleae of pappus short and broad, suddenly narrowed into the setae; plant nearly nailed. nudatus. 1. Elephantopus Carolinianus Willd. Sp. PI. 3 : 2390. 1804. This is the commonest and most easily recognized species in North America. The variety violaceus (Sch. Bip.) with purple pappus is not uncommon from Missouri to Louisiana and Alabama. 2. Elephantopus tomentosus Linn. Sp. PI. 814. 1753. As the type of this species, is taken that form having short ovate or elliptical radical leaves. Canby's No. 62 (1898) from Alabama and Pollard's No. 1048 (1896) from Missis- sippi may be taken as very typical examples, though it is common from New Jersey to Texas. There is, however, a very great amount of variation in the vestiture and in the form of the floral and radical leaves. In some the radical leaves are very much narrowed proximally and it seems prob- able that the name nudicaulis Poir. applies to such varieties. Kearney's No. 738 (1897) from Tennessee and Heller's No. 77 (1890) from Pennsylvania well illustrate this form. The name nudicaulis Ell. apparently applies to the same thing. It was at first supposed these were the same as elatus Bertol., but for nudicaulis the involucral bracts are spoken of as 50 Trans. Acad. Sci. of St. Louis. longer than in Carolinianus while in elatus they are dis- tinctly shorter. 3. Elephantopus elatus Bertol. Misc. Bot. 11:21. 1851. This very striking form from the Southern States has occasioned no little trouble. Dr. Robinson kindly furnished a transcription of the original description and a tracing of the plate. Here is referred the tall, heavily clothed, much branched form with radical leaves narrowed at base, and with short heads and pappus, as is beautifully illustrated by speci- mens of Chapman's, and by Rolf's No. 657, both from Florida. It apparently occurs throughout the Southern States east of the Mississippi and is somewhat variable. In the short heads it resembles nudatus. In its leaf forms it resembles var. nudicaulis of tomentosus. In its vestiture and length of pappus it is distinct from either. Some of the forms under consideration may be hybrids, though only actual experimentation can give us any direct evidence. There seems to be no reason why the name elatus is not avail- able here. 4. Elephantopus nudatus Gray. Proc. Am. Acad. 15 : 47. 1880. Dr. Gray separated this species on the very short and broad paleae of the pappus, and the character of the vestiture. It occurs from Delaware to Florida and Louisiana. It is most typical in the Northeast, while towards the Southwest some very puzzling forms occur, though whether these are due to extreme variability within the species or to hybridiza- tion is impossible to say. With Prof. Earle, the author distributed some of these very peculiar forms from the Her- barium of the Ala. Biol. Survey. The above species may be compared as to length of achene and pappus by the following table prepared by averaging in millimetei-s a number of measurements taken from fairly typical specimens. Baker — A Revision of the Elephantopeae. — I. 51 Elephantopus. Length of ACHENE. Length of Pappus. Carolinianus Tomentosus. Elatus Nudatus .... 6. 6,8 3.75 5. The last three of these species seem usually to possess a hibernating winter rosette which the first does not have, though this calls for more extended observation. SPECIES OF MEXICO. In the literature at hand five species are credited to Mexico: glaher Sesse & M09., litoralis Sesse & Moc., cuneifolius Fourn., Colimensis Sesse & M05. and mollis HBK. The glaher of Sesse and Mogino seems to belong among some of the spicate forms. Neither litoralis, Coli- mensis or cuneifolius have been recog-nized amonsf material at hand. The descriptions do not mention several most im- portant characters. Forms of mollis apparently occur in this region, as illustrated by specimens of Dr. Palmer's col- lecting. More material and from type localities will readily clear up the whole matter. It may be here mentioned that a complete specimen suitable for study must include both flowers and fruit. Specimens in our herbaria usually lack good material of the former and too often of the latter. It seems likely that our C aroliiiianus extends to Mexico and may have been redescribed there, and similarly tomentosus, also. SPECIES OF THE WEST INDIES. Mollis has been reported from Porto Rico, Jamaica and other islands. Forms similar to our Carolinianus occur in Cuba and Jamaica, but the material examined is scarcely sufficient for definite determination. In Cuba occurs the very interesting and very distinct pratensis of Wright. It is a small plant as represented in our herbaria, low, the leaves cauline and lanceolate, the stems slender and usually numerous 52 Tram. Acad. Sci. of St. Louis. from a woody base, and the floral leaves glandular punctate and greatly produced at tips. This last character separates it from all other species of the tribe. The sericeus of Graham is described from *' West Indies," though not noticed since its description. SPECIES OF CENTRAL AND SOUTH AMERICA. In the study of these species attention must first be centered on the exact determination of mollis. Dr. Gray followed Grisebach, who knew it well, in considering it a distinct and well-marked species, and our herbarium material amply sup- ports this view. It seems to be entirely distinct from either scabe7^ or tomentosus, which have the stem scapiform and the pappus paleae long and acuminate, gradually narrowed into the setae, while in mollis the stem is leafy without a rosette of leaves at base, and the pappus paleae are of the nudatus type — short and broad and suddenly narrowed into the setae. One of the most characteristic things about mollis is its vestiture. In general the plant is rather thickly clothed with rough hairs, but the lower surface of the leaves is soft tomentose or almost villose, its feeling to the touch being very characteristic. Bang's No. 497 of the PlantaeBolivianae seems to be a typical example, though it was diijtributed as scaber, which it is totally unlike. Rusby's No. 1105 from Bolivia is near mollis but apparently not that — certainly not scaher for which it was distributed. Morong's No. 258 from Paraguay is likewise neither mollis nor scaber, but apparently an inter- esting new thing. It seems likely that Martii represents a variety of mollis, as it is closer to it in many respects. One of the most distinct of all the South American forms is hirtifiorus, which has a scapiform stem and most remark- able pappus, the limbs being flattened, not only at base but throughout their length, making it distinct in this regard from all other Elephantopeae . The whole plant is villose throughout — even to the corollas. The heads are of un- usual length and the floral leaves are unmodified, which is unusual for species of this habitus. Likewise the coalesced and consequently coroniform paleae of vaginalis separates that species distinctly from all others. Baker — A Revision of the Elephantopeae. — /. 53 The species, most of which are little known, or as to our herbaria, entirely unknown, may be listed as follows: — 1. elongatus Hook. — Brazil, 2. hirtifiorus DC. — Brazil. 3. Martii Grali. — Brazil. 4. mollis HBK. — Widely distributed. 5. palustris Gardn. — Brazil. Q, panicidatii^s Maxt. — Brazil. 7. racemosus Gardn. — Brazil. 8. Biedelii Sch. Bip. — Brazil. 9. riparius Gardn. — Brazil. 10. scaber L. — Isthmus of Panama? 11. vaginatus Gardn. — Brazil. • 12. virgaUis Desv. — Guiana. On the Isthmus of Panama also occur forms which are ap- parently uu described, as for instance, Fendler's No. 163, as well as many others from other regions. SPECIES OF AFRICA. Only two species appear to be reported from Africa ; scaber L. and senegalensis (Klatt. ) O. & H., both representing dis- tinct and well-marked forms. Herbarium material, however, indicates the existence of several other species in Africa. SPECIES OF THE FAR EAST. Here we find the original home of scaber. Besides India, it apparently occurs in Ceylon, Formosa, and many of the Malasian and Australasian islands. In the Flora Filip., Blanco describes serratus and dubius. We are likely to know more of these soon. Two species have also been described from Java — sinuatus ZolL & Mor. and dliatus Zoll. & Mor. Genus Spirochaeta Turczaninow, Bull. Soc. Nat. Mosc. 24^: 166. 1851. This clearly separable genus, well described and founded on remarkably good characters, unique in the tribe, has either been wholly neglected or thrown in with Elephanto'pus, appa- rently because the single species did not have in the original description a separate characterization. But this cannot be held as a vital deficiency, when incorporated with the generic definition is a perfectly clear diagnosis of the species. This 54 Trans. Acad. Sci. of St. Louis. same thing has been done many times in other instances in both botany and zoology, and has been held as filling the requirements. The species was described from Colombia. This plant has been collected a number of times since its description, and always labeled in our herbaria, " Elephant- opus spicatus " with which it has scarcely anything in com- mon excepting the spicate arrangement of the glomeruli. Indeed in the Bernhardi herbarium is a single sheet bearing a slip of Spirochaeta and another of Pseudelephantopus side by side under the same label. These specimens probably came from somewhere along the northeast coast of South America. Rusby's No. 1109 and Bang's No. 357, both from Bolivia, belong to this genus and apparently to this species, 8. Funckii, though both were distributed as E. spicatus^ without question or remark. The freely rooting runners at base of stem are quite pecu- liar to this form, while the pappus clearly distinguishes it. This latter is in one series with the paleae minute and lacer- ate and the setae spirally twisted toward their tips. These setae are very brittle and easily broken off, so that an at- tempt to remove them entire should be made with care. Genus Elephantosis Lessing, Linnaea. 4 : 322. .1829. This genus, distinct by its pappus of numerous straight setae in two series, contains the common and variable West Indian E. angustif olius (WiWd.) Less., and also several other species, but one of which, quadrijiora Less., has ever been described. The latter was originally described from Brazil. Neither Bang's No. 344 from Bolivia nor Morong's No. 313, from Paraguay, appears to be angustif olius, though both were distributed as such. Far more material will be necessary to any satisfactory arrangement of the species. Lessing regarded the nudiflorus of Willdenow from Jamaica and San Domingo as distinct from angustif olius. Genus Pseudelephantopus Rohr, Skrift. Nat. Selsk. Kobenh. 2:214. 1792. All of the forms of this genus examined, present the same peculiar structure of pappus which marks them as widely dis- Baker — A Revision of the Elephantopeae. — I. 55 tinct from any other portion of the group. Two of the setae are longer and stouter than the rest and plicate in the upper third. The chaffy paleae are very lacerate, the lacerations long, frequently becoming short setae. From the descrip- tions, crispus Cass., and spiralis Less., apparently do not belong in this genus. As a well recognized species, we have the very common tropical spicatus, first described from Ja- maica, enormously variable and now introduced into the Far East. The miscellaneous series of specimens that have been picked up here and there, show this species to be composed of a number of very distinct and interesting forms. In no case in the Elephantopeae is there such need for the collection of large suites of specimens at every possible point. Kuntze in the Revis. Gen. Plant. 1 : 335, recognizes two varieties, but this does not begin to enumerate the forms which exist, and hence which we must recognize. Perhaps the glaber of Sesse and Mogino is one of the many forms. Some speci- mens have the achene thickly haired, others thinly; in some the achene is about 6 mm. long, in others 7.5; in some the smaller setae of the pappus are but 5 or 6 in number, in others they are numerous ; in some the floral leaves are shorter than the glomeruli, in others they are longer ; and these characters occur in most confusing combination. Wide variations in vestiture and foliage commonly occur. Whether any of these be of specific value can only be ascertained by the examination of far more material. Genus Elephantopsis Sch. Bip. Linnaea. 20 : 515. 1847. This genus is represented only by the single species bijiora Sch. Bip. from Brazil. Genus Micropappus Sch. Bip. Linnaea. 20: 515. 1847. Represented only by the unique M. micropappus Sch. Bip. from Brazil. 56 Trans. Acad. Sci. of St. Louis. EXPLANATION OF ILLUSTRATIONS. Plate IX. Fig. A. — Elephantopus Carolinianus. — B. Spirdchaeta Funckii. — C. Elephantopus scaler. — D. Elephantosis angustifolius. — E. Elephantopua hirtiflorus. — F. Elephantopus mollis. — G. Pseudelephantopus spicatus. — All drawn to same scale ; see measurements of ^. Carolinianus. Issued May 20, 1902. Trans. Acad. Sci. of St. Louis, Vol. XII. PLATE IX. xiCHENES OF ELKPHANTOPEAE. PUBLICATIONS. The following publications of the Academy are offered for sale at the net prices indicated. Applications should be addressed to the Librarian, The Academy of Science of St. Louis, 1600 Locust St., St. Louis, Mo. TRANSACTIONS (in octavo). Vol. Number. Price per number. Price per vol. Price in set. 1* 2t 3,4 $7.50 (Nos. 2-4 only.) 1 $4.00 2.00 each. $7.00 (Nos. 2-4 only.) 2 1 to 3 2.00 each. 5.60 5.00 3 1 to 4 2.00 each. 7.50 7.00 4 1' to 4 2.00 each. 7.50 7.00 5 1-2,3-4 { 4.00 each, (donble numbers) 7.60 7.00 6J 1, 2, 6, 8, 10, 11, 16, 17 4, 5, 7, 13, 14, 15, 18 8, 9 12 1 25 cts. each. I 50 cts. each. 75 cts. each. $1.00 7.50 7.00 n 2, 3, 4, 6, 7, 8, 18, 15, 16, 18, 19 5, 9 to 12, 14,20 17 1 I 25 cts. each. I 50 cts. each. 75 cts. 11.00 7.60 7.00 8t 1, 3 to 6 8, 10, 12 2, 7, 9, 11 I 25 cts. each. 50 cts. each. 3.75 3.50 9t 1, 3, 4, 7, 9 2,5,8 6 25 cts. each. 60 cts, each. $1.25 3.75 3.50 lot 9 2, 4, 5, 10 1 3,6,7,8,11 10 cts. 25 cts. each. 40 cts. 50 cts. each. 3.76 3.50 lit 2, 3 5-8, 10, 11 1 4 9 15 cts. each. 25 cts. each. 45 cts. 75 cts. 1.00 3.76 8.50 MEMOIRS (in quarto). Contributions to the archaeology of Missouri, by the Archaeological Section, Parti. Pottery. 1880. $2.00. The total eclipse of the sun, January 1, 1889. A report of the observations made by the Y/ashington University Eclipse Party, at Norman, Califor- nia. 1801. $2.00. • Supply exhausted, t Can be sold only to purchasers of the -entire volume,— so far as this can be •upplicd Bach number i-; a brochure containing one complete paper (or rarely two). '.!^ Transactions of The Academy of Science of St. Louis. VOL. XII. No. G. THE NOETH AMERICAN SPECIES OF CHAEEOPHYLLUM. THE NOETH AMEEICAN SPECIES OF TEIODIA. B. F. BUSH. iaixA\0,i^ •^ ^ Issued June 9, 1902. JUN 19 1902 THE NORTH AMERICAN SPECIES OF CHAERO- PHYLLUM.* B. F. Bush. Any one looking over a large collection of specimens of this genus, will at once be struck by the remarkable confu- sion of the species, such very different species as O. Tex- anum, C. Tainturieri, C. procumhens, and G. dasycarpum, being labeled C procumhens or G . Tainturieri indiscrimi- nately. All of this tends to show that the species of this genus have never been clearly understood, and it is my inten- tion in the present paper to show that the species are readily distinguishable by good permanent characters. My attention was first drawn to this genus by some plants collected on my journeys to Texas in 1899 and 1900, which were so noticeably different from the supposedly same species of Missouri, that I began an investigation, which resulted in the conclusion that there was an unnamed species in Eastern Texas. Early in last year I had the pleasure of receiving Dr. Rose's splendid monograph of the North American Umbelliferae, in which I found he had described G haerophyllum Texanum, the unnamed species that I had under consideration. Having already done some work on the genus, I still con- tinued to observe the species in the field during last year, and also studied the plants in the herbarium, and now present the results in this paper. The conclusions I have come to are somewhat at variance with the disposition of the species by Dr. Rose in the mono- graph of the North American Umbelliferae, but Dr. Rose himself in this work differs very much from Dr. Gray, Dr. Chapman and Prof. Britton in the acceptation of species in this genus, giving specific rank to G. Tainturieri and estab- lishing one more new variety, G. Tainturieri Floridanum, ♦ Presented by title to The Academy of Science of St. Louis, April 21, 1902. (57) 58 Trans. Acad. Sci. of St. Louis. besides recognizing C. procumbens 8hortii and C. Taintu- rieri dasycarpum. Dr. Gray at first recognized only C. procumbens and C. procumbens Shortii. Dr. Chapman rec- ognized C. procumbens and C. Tainturieri, the first being C. Tainturieri and the last being smooth Tainturieri and Dr. Rose's 0. Tainturieri Floridanum. Dr. Britton in the Illus- trated Flora recognized two species and one variety, C. pro- cumbens, C procumbens Shortii, and C. Tainturieri, the last largely made up of C. Texanum. To my mind it is much better to consider these varieties as good species, especially as each exhibits individual characters that are very stable. After several years of field observation and herbarium work, it is with no little confidence that I present the fol- lowing : ANALYSIS OF SPECIES. Leaves coarsely divided. Nortliern species. Fruit beaked, smooth, ribs narrow. 1- C procumbens. Fruit beakless, pubescent, ribs narrow. 2. C. Shortii. Leaves finely divided. Southern species. Fruit beakless, smooth, ribs broad. 3. C. Texanum. Fruit beaked, pubescent, ribs broad. 4. C. dasycarpum. Fruit beaked, smooth. Ribs thicker than the intervals. 5- C. Tainturieri. Ribs narrower than the intervals. Base of fruit broad, obtuse. 6. C. Floridanum. Base of fruit narrow, acute. 7. C reflezim. 1. Chaerophyllum procumbens (L.) Crantz, Class. Umb. 77. 1767. Seandix procumbens L. Sp. PI. 1 : 257. 1753. From glabrous to very pubescent; stems weak, spreading or procumbent, or rarely erect, 2-5 dm. high ; umbels sessile or peduncled, few-rayed; rays 1-5 cm. long; fruiting umbels open, of 2 to 4 fruits on weak and usually spreading pedicels 4-9 mm. long; fruit narrowly oblong, about 8 mm. long, glabrous, narrowed and commonly beaked at the apex ; ribs filiform, much narrower than the broad intervals; styles very short; seed face deeply sulcate. Rich, shaded ground along streams, April and May. Type locality: "Virginia;" collected by Gronovius, No. 147. Bush — North American Species of Chaerophyllum. 59 Carolinian and Louisianian areas. Alabama, Arkansas, District of Columbia, Delaware, Illinois, Indian Territory, Iowa, Kansas, Michigan, Mississippi, Missouri, New Jersey, New York, North Carolina, Ohio, Ontario, Pennsylvania, South Carolina, Tennessee and Virginia. This species is very variable as to pubescence, some plants being nearly or quite smooth, and others pubescent to a marked degree. Fully 30 per cent, of all the specimens ex- amined were very pubescent, the remainder being smooth or smoothish. This variability of pubescence has been the cause of much confusion, as very pubescent plants of this species have been placed with C. Tainturieri, and smooth or smoothish plants of C. Tainturieri, under this species. The species has a more northerly range than any other of the genus, reaching its southerly limit in Northern Alabama and Missis- sippi, the specimens upon which Dr. Chapman based his C procutnbens being clearly referable to C. Tainturieri. Specimens examined. — Illinois: Proviso, Agnes Chase, May 17, 1900; American Bottom, Engelmann, 734, 1842; same locality, Ge>ier. — Indian Terkitory: Limestone Gap, 5?t«Zer, 1875. — Iowa: Moscow La.ke, Beppert, 599, May 8, 1894; Decatur County, Fitzpatrick, May 8, 1897; Marshalltown, Pammel, 323, May 8, 1897. — Kansas: Leavenwortli County, Hitchcock, 699, 1896; Turner, iJfacA;e?isJe, April 26, 1896. — Missouri: Greene County, Blankinship, May 5, 1888; same locality, Weller, April 20, 1889; same locality, Shepard, April 18, 1879; Independence, Bush, 149, May 23, 1894; .Courtney, Bush, 78, April 19, 1896; Jackson County, Bush, April 30, 1888; Jefferson City, Krause, May 9, 1869; St. Louis, Liiders; same locality, Engelmann, 1833, — New Jersey: Camden, Parker, 1866.— New York: Ithaca, collector not given. May 8, 1880. —Ohio: Cincinnati, Lloyd, April 26, 1890; same locality, B. Frank, April, 1835; Norwalk, Stair, May 3, 1894. — Pennsylvania: Philadelphia, M. C Lea, 1843; same locality, Bedfield, 2540, May 24, 1872; same locality, Beyrich, in Bernhardi Herba- rium. -Tennessee: No locality, Buckley. 2. Chaerophyllum Shortii (T. & G.) B. F. Bush. Chaerophyllum procumbens Shortii T. & G. Fl. 1 : 637. 1840. Stems 2-5 dm. tall, erect or decumbent, branched, pubes- cent or nearly smooth ; fruit broadly oblong to ovate, about 6 mm. long, obtuse and blunt at the apex, not at all beaked> pubescent; ribs narrow, much narrower than the intervals. Moist rich ground in woods, April and May. Type locality: •« Kentucky;" collected by Br. Short. 60 Trans. Acad. Sci. of St. Louis. Carolinian and Louisianiau areas. Arkansas, Kentucky, Louisiana, Maryland, Ohio, Pennsylvania and Virginia. Specimens examined. — Ohio : Cincinnati, Lloyd, 1888. 3. Chaerophyllum Texanum C. & R. Mon. N. A. Umb. 59. 1900. An erect tall plant, 2-6 dm. high, usually quite smooth above the first fork, even the petioles smooth, or sometimes the lowest ones ciliolate; fruiting umbels more dense, of 8 to 15 fruits; fruit oblong, smaller and not beaked, tapering to a blunt point, 4-5 mm. long, glabrous; ribs very promi- nent, much wider than the intervals, nearly twice as wide and almost obliterating them ; fruit with base about as wide as middle; involucres spreading. Dry, rocky barrens and prairies. May. Type locality : nears Houston, Texas; collected by Z>?'. J. .N. Rose, No. 4173, May 6, 1899; type in U. S. Nat. herbarium. X/Ower Sonoran area. Kansas, Missouri and Texas. "Specimens examined, — Kansas: Ctierokee County, Hitchcock, 1085, May 7, 1?97. — Missouri: Glen Allen, i??tsseH, May 20, 1898; Lee's Summit, Mackenzie, 57, May 22, 1898; same locality, Mackenzie, May 28, 1899. Shef- field, Mackei^zie, May 16, 1897. — Texas: Columbia, Bush, 184, 1899. 4. Chaerophyllum dasycarpum Nutt. in T. & G. Fl. 1:638. 1840. Chaerophyllum procumbens dasycarpum (Nutt.) C &R. Bot. Gaz. 12: 160. 1887. Chaerophyllum Tainturieri dasycarpum (Nutt.) Watsou, Bibl. Index. 416. 1878. Stems 2-6 dm. high, erect, much branched, very pubescent; fruit very pubescent, with a beak about one-fourth as long as the body; ribs broad, from one-third to a little over one-half as wide as the intervals. Low rich ground in fields and woods. Abundant in some places. March to September. Type locality not given; collected by Nuttall; type in Gray Herbarium. Lower Sonoran and Louisianian areas. Mississippi and Texas. Bush — North American Species of Chaerophyllum. 61 Specimens examined. — Mississippi: Biloxi, Tracy, 4469,1898. — America BoREALi: Bernhardi Herbarium. — Texas: Columbia, BwsA, 6, 1899; same locality, Bush, 112, 328, 463, 1900; Hempstead, Hall, 260, 1872, in part. This has two specimens, the smaller whole plant is C. dasycarpum, the other is a branch of a nearly smooth larger plant of C. Tainturieri ; Dallas, Bever- chon, 2618, 1901; New Braunfels, Lindheimer, 616, 1848; Brazos Bottom, Lmdheimer, 1 832 ; Crab Apple, Jermy; Enchanted Eock, Jertny; Neuces Bay, Heller, 1521, 1894; no locality given, Lindheimer, 1847. 5. Chaerophyllum Tainturieri Hook. Comp. Bot. Mag. 1:47. 1835. Chaerophyllum procumbens Tainturieri C. & R. Bot. Gaz. 12:160. 1887. An erect tall plant, commonly pubescent, sometimes smooth or smooth] sh but with the foliage always more or les& pubescent or puberulous, fruiting umbels more compact, of (> to 8 fruits, either sessile or the outer on short stout erect or somewhat spreading pedicels sometimes reaching 6 mm. in length ; fruit linear-oblong, 6-7 mm. long, with a distinct beak, glabrous, the beak about one-third the length of the bo(iy, the base obtuse and as wide as the widest part of the fruit; ribs very prominent, about as wide as the intervals or broader, but not obliterating them ; styles longer than in 0. procumbens ; seed face less deeply sulcate ; involucres spreading. Sandy soil at mostly low elevations. March to June. Type locality: *' N. Orl. " (New Orleans); collected by M. Tainturier. Carolinian, Louisianian and Lower Sonoran areas. Ala- bama, Arkansas, Florida, Indian Territory, Louisiana, Mis- sissippi, Missouri, Tennessee, Texas and Virginia. Specimens examined. — Alabama: Auburn, Lee and Baker, May Iff^ 1897. — Arkansas: Little Mamelle Bottom, Engelmann, 1^31 . — Florida: Jacksonville, Curtiss, 1039, in part, April. This sheet contains- two plants, the smaller pubescent plant is C Tainturieri and the larger smooth plant is C. Floridanum. A sheet of the same No. 1039, in the Redfleld Herbarium, has two small pubescent plants- of C. Tainturieri and one large nearly smooth plant of C. Flori- danum; Apalachicola, Chapman, three plants on one sheet, two evi- dently of same collection, and one of another later collection, in Chapmaa Herbarium; no locality, but presumably Apalachicola, Chapman, in Buck- ley Herbarium; no locality, but presumably Apalachicola, Chapman, in Parker Herbarium. — Indian Territory: Sapulpa, Bush, 1020, May 29, 1895; same locality, Bush, 1083, May 13, 1895. — Louisiana: Lake Ponchartrain, Lindheimer, 1839; Baton Rouge, Dodson, 1896; New Orleans, Joor, April 1887, in Joor Herbarium. — Mississippi: Starkville, Tracy, 1350, April 9, 1892. — 62 Trans. Acad. Sci. of St. Louis. Missouri: Dunklin County, E-fi^grerf, May 6, 1893. — Tennessee: Nashville, Hubbard, 1039,1880; Dandridge, Buckley, April, 1842, in part. This sheet contains two plants, the larger is C. Tainturieri, the smaller is Carum Carui. — Texas: Dallas County, Beverchon, 2619, 1901; Mill Creek, Lindheimer, March, 1844, in Buckley Herbarium; no locality given, Lindheimer, 1844; Columbia, Bush, 80, 1900 ; Hempstead, Hall, 260, June 12, 1872, in part. This sheet contains two plants, the large smoothish plant is C. Tainturieri, the smaller one is C. dasycarp^m; same locality, Hall, 261, June 8, 1872, in the Redfield Herbarium. 6. Chaerophyllum Floridanum (C. & R.) B. F. Bush. Chaerophijllum Tainturieri FloridanumC & R. Mon. N. A. Umb. 60. 1900. An erect nearly smooth or somewhat pubescent plant 2-6 dm. tall ; fruit with a beak one-fourth or one-fifth the length of the body ; ribs about one-half as wide as the intervals ; fruit glabrous, oblong, the base about as broad as the middle ; involucres spreading. Low, sandy ground. March and April. Type locality: shell banks, Sister Islands, St. John's River, Florida; collected by A. H. Curtiss, No. 1040, March, 1880; type in the U. S. Nat. Herbarium, duplicate in the Missouri Botanical Garden Herbarium. Louisianian area. Florida and South Carolina. Specimens examined:— Florida: Shell banks. Sister Islands. St. John's River, Curtiss, 1040, March, 1880, in part. This sheet has a small pubescent plant, and a branch of a larger nearly smooth plant; the branch is C. Floridanum, and the whole plant is C. Tainturieri. A sheet of this same No. 1040 in the Redfield Herbarium has two small pubescent plants of C Tainturieri, and one branch of a larger nearly smooth plant of C. Florida- num; Jacksonville, Curtiss, 1039, April, in part. This sheet also contains two plants, the larger smoother plant is C. Floridanum, and the smaller pubescent plant is C. Tainturieri. A sheet of this same No. 1039 in the Redfield Herbarium has one large nearly smooth plant of C. Floridanum, and two smaller pubescent plants of C. Tainturieri; Jacksonville, Curtiss, April. 1893, in part. This sheet also bears two different species, there being one large and one very small nearly glabrous plant of C. Floridanum, and one small pubescent plant of C. Tainturieri. 7. Chaerophyllam reflexum n. sp. An erect slender plant, 2-4 dm. high, commonly quite smooth above the first fork, the lower petioles sometimes ciliolate ; fruit 6-8 mm. long, with a beak about one-third the length of the body, tapering to an acute base, broadest in the middle ; ribs about one-half as wide as the intervals ; Bush — North American Species of Chaerophyllum. 63 involucres strongly reflexed in fruit. Open rocky woods ; uncommon. May and June. Type locality : Eagle Rock, Barry County, Missouri ; col- lected by B. F. Bush, No. 62, June 18, 1897 ; type in the Missouri Botanical Garden Herbarium, duplicates in U. S. Nat. Herbarium, and in Herbarium K. K. Mackenzie. Lower Sonoran area. Missouri. Specimens examined. — The type specimeus are the only ones seen. Issued June 9, 1902. THE NORTH AMERICAN SPECIES OF TRIODIA.* B. F. Bush. While studying some specimens of Triodia collected in Texas, I was led to examine more closely the species of this genus, and through the kindness of Prof. Wm. Trelease was enabled to study the specimens preserved in the Herbarium of the Missouri Botanical Garden. I now present the results of my observations, which are somewhat at variance with the commonly accepted interpre- tation of the species. The species have been described under no less than five generic names, four of which must be considered as syn- onyms, one of which must stand for the genus, and these five generic names are: Sieglingia Bernh., Triodia R. Br., Tricuspis Beauv., Uralepis Nutt., and Windsoria Nutt., given in the order of their publication. The first name was originally applied to some Old World forms, which are now generally conceded to be distinct from the North American species under consideration ; the second name, Triodia, was given to the genus by Robert Brown in 1810, and appears to me to be the only tenable name for the genus, as the third name Tricuspis^ given to the genus by P. Beauvois in 1812, is doubly barred by being a later name, and by being a homonym of the Tricuspis of Persoon, 1807, a genus in the Tiliaceae. Both of Nuttall's names are of a later date, and are therefore not tenable. The following arrangement shows the result of my con- clusions : — Triodia R. Br. Prodr. Fl. Nov. Hall. 1 : 182. 1810. Sieglingia O. Kuntze, Rev. Gen. PI, 2 : 789. 1891, and authors, not Bernh. Syst. Verg. Pfl. Erf. 40. 1800. * Presented by title to The Academy of Science of St. Louis, January 6, 1902. (64) Bush — North American Species of Triodia. 65 Tricuspis Beauv. Agrost. 77, 1812, not Tricuspis Pers. 1807, a genus in Tiliaceae. Uralepis Nutt. Gen. 1 : 61. 1818. Wmdsoria Nutt. Gen. 1 : 70. 1818. — Trans. Am. Phil. Soc. II. 5 : U7. 1837. KEY TO THE SPECIES. Spikelets subcompressed, oblong, in a rather dense spikelike panicle. Panicle elongated, spikelets about 5 mm. long. Lower scales much longer than the lower flowers. 1. T. Hrieta. Lower scales about as long as the lower flowers. 2. T. albescens. Panicle short, oblong, spikelets about 10 mm. long. 3. T. congesta. Spikelets compressed, crowded in short subcapitate panicles on the simple nearly naked culms, bleaching white at maturity. Flowering scale entire or merely mucronate. 4. T.pilosa. Flowering scale deeply cleft at apex; awns from sinus exceeding the lobes. Flowering scale lance-ovate; lobes subacute. 5. T. grandiflora. Flowering scale linear-oblong; lobes obtuse. 6. T. Nealleyi. Spikelets compressed, panicle verticillate, short, leafy. Flowering scales 4-6 mm. long. 7. T. pulchella. Flowering scales 2-3 mm. long. 8. T. pulchella parviflora. Spikelets compressed, panicle open, branches spreading. Flowering scales entire or emarginate, sometimes mucronate. Spikelets 6-12 mm. long; lower scales about one-half as long as the adjacent flowering scales. 9. T. Tezana. Spikelets 5-7 mm. long; lower scales nearly equaling or slightly exceeding the adjacent flowering scales. Plant mostly smooth. 10. T. eragrostoides. Plant scabrous throughout. 11. T. eragrostoides scabra. Flowering scales somewhat 3-toothed, the nerves all slightly excurrent. Panicle narrow, pedicels stout. 12. T. Langloisii. Panicle open, pedicels slender. Sheaths pilose. 13. T. Drummondii. Sheaths smooth. Spikelets broad. 14. T. Elliottii. Spikelets narrow. Plant pale, panicle branches spreading with tufts of white hairs in axils of the panicle. 15. T. Chapmani. Plant purplish, panicle branches upright. 16. T. seslerioides . Spikelets terete, panicle narrowly linear. Lower scales both l-nerved. 17. T. mutica. Second lower scale 3-5 nerved. 18. T. elongata. 1. Triodia stricta (Nutt.) Benth. ex Vasey, Gr. U. S. 35. 1883. Windsoria stricta Nutt. Gen. 70. 1818. Tricuspis stricta (Nutt.) Munro, A. Gray, Proc. Phila. Acad. Nat. Sci. 1862 : 335. 1863. Tricuspis stricta Nutt. fide Heller, Cat. PI. N. A. 28. 1900. 66 Trans. Acad. Sci. of St. Louis. Tricuspis stricta CNutt.) Thurb. Ms. name. Sieglingia stricta (Nutt.) O. Kuntze, Rev. Gen. PI. 2: 789. 1891. Culms 4.5-12 dm. tall, erect, a little compressed. Leaves 1.5-3 dm. long or more, flat, long-acuminate, smooth beneath, scabrous above; spike-like panicle 1.25-3 dm. in length, the branches appressed, the lower 2.5-5 dm. long; spike- lets 4-10-flowered, 4-6 mm. long; lower scales usually about two-thirds as long as the spikelets, rarely extending beyond the flowering scales, acute, glabrous ; flowering scale ovate, the nerves pilose for more than half their length, the middle and often the lateral excurrent as short tips. Low prairies and marshes; common. July to October. Perennial. Carolinian and Louisianian areas. Alabama and Mississippi to Louisiana, Arkansas, Kansas, Indian Territory, Oklahoma, Texas and Arizona. Type locality not ascertained. Specimens examined. — Alabama : Wilcox County, S. B. Buckley, 1878. — Mississippi: Starkville, Kearney, 81, 1896. — Louisiana: Lake Charles, Tracy, 3964, 1897; same locality, K. K. Mackenzie, 448, 1898; Feliciana, Car- penter.— Arkansas: Fayetteville, Harvey, 73. — Indian Territory: Tulsa, Creek Nation, Bush, 795, 1894; Sapulpa, Creek Nation, Bush, 14 j4, 1895. — Kansas: Crawford County, Hitchcock, 917, 1896. — Texas: Texarkana, Heller, 4248, 1898; Dallas County, Beverchon, 12365; Columbia, Brazoria County, Bush, 1668, 1900; Houston, Lindheimer, 1840. — Oklahoma: Still- water, Waugh, 60, 1893. 2. Triodia albescens (Munro) Benth. ex Vasey, Gr. U. S. 35. 1883. Tricuspis albescens Munro, A. Gray, Proc. Phila. Acad. Nat. Sci. 1862 : 335, name only. 1863. Sieglingia albescens (Munro) O. Kuntze, Rev. Gen. PI. 2 : 789. 1891. Bhombolytrum albescens (Munro) Nash in Britton, Man. Nor. States & Can. 129. 1901. Culms 3-5 dm. tall, tufted, the sterile shoots one-half as long as the culm or more. Leaves smooth beneath, roughish above, acuminate, 6.25-27.5 cm. long, 2-4 mm. wide, panicle dense and contracted, white, 6.25-12.5 cm. long, 6-18 mm. broad, its branches erect or ascending, 2.5 cm. or less long ; spikelets 7-11-flowered, 4-5 mm. long, the lower scales white, 1-nerved, about equal; flowering scales about 3 mm. long, 3-nerved, the lateral nerves vanishing below the apex, the Bush — North American Species of Triodia. 67 midnerve excurrent in a short scabrous point. Dry prairies and barrens; not common. September and October. Per- ennial. Louisianian and Lower Sonoran areas. Kansas to Texas, New Mexico and Arizona. Type locality not ascertained. Specimens examined. — Kansas: Kiowa County, Hitchcock, 916, 1896. — Texas: San Antonio, B^xslt County, Nealley,Gi, 1892; Crab Apple, Gillespie County, Jenny, 17; Fort Worth, Tarrant County, Glatfelter, 1898; San Antonio, Bexar County, Bush, 1250, 1900; Marion, Guadalupe County, Hall, 1872; Dallas County, Bush, 1171, 1900; no locality given, Lind/ieimer, 737, 1847. 3. Triodia congesta (Dewey) B. F. Bush. Sieglingia congesta Dewey, Contr. U. S. Nat. Herb. 2 : 538. 1894. Tricuspis congesta (Dewey) Heller, Cat. PI. N. A. 28. 1900. Culms 4-8 dm. tall, from a perennial rootstock. Nodes and throats of striate sheaths usually purple ; leaves 5-15 cm. long ; panicle 5-8 cm. long ; rays single, 1-3 cm. long, crowded with sessile spikelets; spikelets 10-15-flowered, 8-12 mm. long, turgid ; lower scales slightly shorter than the adjacent flowers, 1 -nerved; flowering scales 4-5 mm. long, ovate- oblong, obtuse, mucronate, the lateral nerves slightly or not at all excurrent, pubescent on the nerves near the base ; palet one-fourth shorter than the flowering scale, the keels promi- nently arcuate near the base. Plains and rocky barrens; not common. September to October. Perennial. — Plate X. Lower Sonoran area. Texas. Type locality: "Corpus Christi, Texas;" collected by Nealley. Specimens examined. — Corsicana, Navarro County, Beverchon, 2558; Dallas County, Beverchon, 121, 1879; Corpus Christi, Nealley, 2i, 1891, 1893; Guadalupe, Wright; Comanche Peak, Hood Conntj, Beverchon, 3456, September. July. 4. Triodia pilosa (Buckley) B. F. Bush. Uralepis pilosa Buckley, Proc. Phila. Acad. Nat. Sci. 1862 : 94. 1863. Tricuspis acuminata Munro, A. Gray, Proc. Phila. Acad. Nat. Sci. 1862: 335, name only. 1863. Triodia acuminata (Munro) Benth. ex Vasey, Gr. U. S. 35. 1883. Sieglingia acuminata (Munro) O. Kuntze, Rev. Gen. PL 2: 789. 1891. 68 Trans. Acad. Sci. of 8t. Louis. Sieglingia pilosa (Buckley) Nash, Britt. & Brown, 111. Fl. 3, append. 504. 1898. Tricuspis pilosa (Buckley) Heller, Cat. N. A. PL 28. 1900- Culms 6.25-30 cm. tall, tufted, the sterile shoots 1dm. tall or less. Sheaths smooth, a tuft of hairs on each side of the apex, much shorter than the internodes; leaves strict or curved, thick, linear, obtuse, 1-nerved, the margins white, serrulate, 3.75 cm. long or less, less than 2 mm. wide, folded, at least when dry, pubescent with long hairs, especially be- neath ; panicle almost raceme-like, long-exserted, 1.25-3.75 cm. long; spikelets 3-10, crowded, 8-12-flowered; lower scales acuminate, 1-nerved ; flowering scales 6.-6.5 mm. long, acuminate, 3-nerved, the midnerve generally excurrent as a short tip, all the nerves pilose, the lateral at the top and bottom, the midnerve below the middle. Dry prairies and barrens ; common southwestward. April to October. Peren- nial. Upper and Lower Sonoran areas. Kansas and Colorado to Indian Territory, Oklahoma, Texas, New Mexico, Arizona and Mexico. Type locality not ascertained. Specimens examinbd. — Kansas: Gove County, Hitchcock, 914, 1896; Gray County, Hitchcock, 1897. — Colorado: Canon City, Shear, 982, 1896. — Oklahoma: Gloss Mountains, Mark White, 165, 1899. — Texas: Dallas County, Beverchon, 1112, 1900; same locality, Bush, 631, 1900; Kerrville, Kerr County, Miller, 1637; Gillespie County, Jermy, 55; Santa Anna, Cole- man County, and Chenate Mountains, Presidio County, Nealley, 817; San Antonio, Bush, 331, 1901. — New Mexico: Lincoln County, Josephine Skehan, 34, 1898; no locality given, Fendler, 738, 915, 1847. — Mexico: Monterey, Trelease, 1900; Diaz, Pringle,8306, 1900. 5. Triodia grandiflora Vasey, Contr. U. S. Nat. Herb. 1:59. 1890. Sieglingia avenacea grandiflora (Vasey) Dewey, Contr. U. S. Nat. Herb. 2: 538. 1894. Sieglingia grandiflora (Vasey) Beal, Gr. N. A. 2 : 471. 1886. Tricuspis grandiflora (Vasey) Heller, Cat. PI. N. A. 28, 1900. Culms 2-3 dm. tall ; leaves narrow, rigid, plane or condupli- cate, 5-10 cm. long, lower with the sheaths softly pubescent; panicle oblong, dense, 3-5 em. long, branches appressed; spikelets 6-8 flowered, 8-10 mm. long; lower scales unequal, Bush — North American Species of Triodia. 69 lanceolate, the upper one 8 mm. long, 1-nerved, the lower one rather shorter, 3-nerved ; flowering scales 7-8 mm. long , acute, apex 2-lobed, lobes acute, the fissure less than 2 mm. long, the awn about 2 mm. long, the lateral nerves densely ciliate the entire length, and the midrib below; palet narrow, a third as long as its scale, pubescent on the nerves, abruptly acute. Rare in high plains. August to October. Perennial. Lower Sonoran area. Texas to Arizona, New Mexico and Mexico. Type locality: " Cheuate Mountains, Presidio County, Texas; " collected by NeaUey. Specimens examined. — Mexico: Chihuahua, Pringle, 406, 1885. — Ca- denas, Pringle, 3930, 1891. — Texas: Chenate Mountains, Presidio County, Nealley, 823; Cibolo Canon, Nealley, 154, 1892; Western Texas, Wright, 751. 6. Triodia Nealleyi Vasey, Bull. Torr. Club. 15 : 45. If Sieglingia Nealleyi (Vasey) Dewey, Contr. U. S. Nat. Herb. 2: 538. 1894. Tricuspis Nealleyi (Vasey) Heller, Cat. PI. N. A. 28. 1900. Culms 3-5 dm. tall, slender. Leaves short, blunt pointed, strongly keeled ; panicle lance-oblong, 3-5 cm. long; spikelets 5-8 flowered, 6-8 mm. long ; first empty scale nearly equal- ing and second slightly exceeding the lower flowers ; flowering scales linear-oblong, deeply cleft, the lobes obtuse, promi- nently pubescent ; palet about one-half as long as the flower- ing scale. Rare in mountain canons. August to October. Perennial. — Plate XL Lower Sonoran area. Texas. Specimens examined. —Texas : Chenate Mountains, Presidio County, Nealley, 825; Sierra Blanca, Presidio County, NeaUey, 2305. 1893. 7. Triodia pulchella H. B. K. Nov. Gen. & Sp. 1: 155. t. 47. 1815. Tricuspis pulchella (H. B. K.) Torr. Pac. R. Kept. 156. 1857. Uralepis pulchella (H. B. K.) Kunth, Rev. Gram. 1 : 108. 1829. Sieglingia pulchella (H. B. K.) O. Kuntze, Rev. Gen. PI. 2 : 789. 1891. Culms 1 dm. tall, fasciculately branched from a stolonifer- ous base. Leaves 1-3 cm. long, fasciculate, involute ; pan- icles short, leafy, verticillate; spikelets 5-10 flowered, 5-8 mm. long, white; flowering scales 4-6 mm. long, prominently 70 Trans. Acad. Sci. of St. Louis. pubescent, oblong, cleft to the middle. Dry sandy mesas; common south westward. July to October. Perennial. Lower Sonoran area. Texas to New Mexico, Utah, Ne- vada, Arizona, California, Mexico and Colorado. Type locality : "In subfrigidis, siccis, apricis regni Mexi- cana inter Guanaxuato, Mina de Belgrado et Cubilente, alt. lOSOhexap." Specimbxs examined. — Texas : Chenate Mountains, Presidio County, Nealley, 826; Sierra Blanca, Nealley, 1893.— Colorado: San Juan, Br andegee, 1203, 1875 —New Mexico: Las Cruces, TFooton, 457, 1897; no locality given, Wright, -2059, Parry, 1867.— Utah: No locality given, Parry, 260, 1874.— Arizona: Cienega, Bothrock, 575, 1874; Tucson, Tourney, 89, 1894; no locality given, Pringle, 540, 1882. — California: Los Angeles, Palmer, 500, 652 and 1359. — Mexico: No locality given, Schaffner; Durango, Palmer, 740, 1896. 8. Triodia pulchella parviflora Vasey, Gr. U. S. Q6. 1885. Sieglingia pulchella parviflora (Vasey). Dewey, Contr. U. S. Nat. Herb. 2:538. 1894. Culms I dm. tall, slender, fasciculately branched from a stoloniferous base. Leaves .5-1.5 cm. long, fasciculate, in- volute; panicles very slender, leafy, verticillate ; spikelets 3_4.tlowered, 3-6 mm. long, white; flowering scales 2-3 mm. long, pubescent, oblong, cleft to the middle. Dry sandy mesas. August to October. Perennial. Lower Sonoran area. Texas and Arizona to California. Type locality not ascertained. Specimens examined. — California: San Diego County, Orcutt, 1487, U 9. Triodia Texana (Thurb.) Benth. ex Wats. Proc. Am. Acad. 18 : 180. 1883. Tricuspis Texana Thurb. S. Wats. Proc. Am. Acad. 18 : 180. 1883. Sieglingia Texana (Thurb.) O. Kuntze, Rev. Gen. PI. 2 : 789. 1891. Culms 3-5 dm. tall, slender, leafy. Leaves 2-3 dm. long, often exceeding the panicle; spikelets 6-10-flowered, 6-12 mm. long; lower scales unequal, about one-half as long as the adjacent flowers; flowering scales broadly ovate or ro- tund ; palet broadly ovate or almost hastate lobed at the base. Bush — NortJi American Species of Triodia. 71 one-third shorter than the flowering scale. Mountains and hills; common. August to October. Perennial. Lower Sonoran area. Louisiana and Texas to Arizona, New Mexico and Mexico. Type locality not ascertained. Specimens examined — Texas: San DiegO; Nealley, 65,1892; Point Ysa- bel, Cameron County, Nealley, 829; Laredo, Mackenzie, 103, 1900; San An- tonio, Bush, 810, 811, 1901. — Mexico: Monterey, Pring^Ze, 1970, 1888; Monclova, Palmer, 1371, 1880. — New Mexico: No locality given, Wright, 776, 777 and 2055. 10. Triodia eragrostoides V. & S. Contr. U. S. Nat. Herb. 1: 58. 1890. Sieglingia eragrostoides (Y. & S.) Dewey, Contr. U. S. Nat. Herb. 2 : 539. 1894. Tricuspis eragrostoides (V. & S.) Heller, Cat. PI. N. A. 29. 1900. Culms 6-9 dm. tall, leafy ; sheaths longer than the inter- nodes, roughish ; ligule short, ciliate toothed ; leaves 2-3 dm. long, flat, scabrous, acuminate; panicle large and spread- ing, 3 dm. long, the branches slender, rather distant, single or in twos, the lower ones 12.5-15 cm. long, lax-flowered; spikelets 5-9-flowered, 5 mm. long, short-pediceled, alternate, and mostly single; lower scales nearly equal, lanceolate- acuminate, 1-nerved; flowering scales 2-2.5 mm. long, 3- nerved, oblongs obtuse, emarginate, short-cuspidate, the lateral nerves and midrib pubescent below ; palet one-fourth shorter than the flowering scale, obtuse and denticulate. Sandy soil; common. August to October. Perennial. Louisianian area. Florida and Texas to New Mexico and Mexico. Type locality : " Florida, Blodgett, Texas, Buckley, Nealley, Reverchon.'^ Specimens examined.— Mexico : Monterey, Pringle, 1972, 1888.— Texas : No locality given, Nealley, 822, Beverchon.— New Mexico : No locality given, Wright, 426, 478 and 2054. 11. Triodia eragrostoides scabra (Vasey) B. F. Bush. Sieglingia eragrostoides scabra Vasey, Beal, Gr. N. A. 2 : 65. 1896. Plant scabrous throughout; lower blades broader. Louisianian area. Texas. Type locality : " San Diego, Duval County, Texas." 72 Trans. Acad. Sci. of St. Louis. Specimens examined.— Texas: Saa Diego, Duval County, iVeaZiej/, 96. 1892. 12. Triodia Lanqloisii (Nash) B. F. Bush. Tricuspis Langloisii Nash, N. Y. Bot. Gard. Bull. 1 : 293. 1899. Culms 5-15 dm. tall, erect, tufted, round ; basal leaves crowded, equitant and shining: culm leaves two or three; sheaths coarsely striate, much shorter than the intervals, often pilose at the apex; ligule a ring of copious silvery hairs about 1 mm. long; blades erect or ascending, flat, sometimes folded when dry, glaucous and minutely pubescent on the upper surface, long acuminate, the basal 2-4 dm. long and 2-5.5 mm. wide, the lower culm leaves 7-15 cm. long, and 2-3.5 mm. broad, the upper blade much smaller, 2 cm. or less long; panicle narrow, 1-2 dm. long, about 2 cm. broad, its triangular branches arranged singly, rarely in pairs, erect or nearly so, the larger 6-10 cm. long and usually sub- divided ; spikelets 6-7 mm. long, oval when mature, appressed to the branches, on stout pedicels about 1 mm. long; scales six to eight, the outer empty two acute, 1-nerved, or the second rarely 3-nerved, the lower half with ascending hairs about 5 mm. long, the callus pilose, the lower scales about 4 mm. long, and 2.25 mm. wide when spread out ; palet as long as or a little shorter than the scale, 2-nerved, the nerves ciliate and about equally curved at the base and the apex, hence the internerve is elliptic or nearly so, about 1.6 mm. wide. Pine- woods and clearings. Perennial. Louisianian area. Florida, Mississippi and Louisiana. Type locality : " Slidell, Louisiana, in pine-woods clear- ings; collected by A. B. Langlois; type in Herbarium of Geo. V.Nash." Specimens examined. — Florida: No locality given, Chapman, several collections. — Mississippi: Biloxi, Tracy, 1891; same locality^ Tracy, 1897; same locality, Zear/iey, 208, 1896 ; Waynesboro, Kearney, 114, 1896; Bayou Porto, Tracy, 3869, 1897. — Louisiana : Slidell, Langlois, 1891. 13. Triodia Drummondii (S. & K.) B. F. Bush. Tricuspis Drummondii S. & K. Bull. U. S. Agrost. 4 :37. 1897. Culms 12-16 dm. tall, slender, erect, from strong, scaly rootstocks. Radical leaves 24-48 cm. long; nodes 2-4, dark Bush — North American /Species of Triodia. 73 purple ; sheaths of the basal leaves crowded, somewhat com- pressed, closely imbricated, sparsely to densely pilose with long white hairs ; upper leaf sheath shorter than the inter- nodes, glabrous or pilose at the throat ; ligule a dense fringe of very short white hairs ; blades of the radical leaves about 5 mm. wide, alternate, acuminate, and involute toward the apex, shortly pilose below near the apex ; uppermost cauline leaf 4 cm. long or less; panicle 18-24 cm. long, contracted, somewhat drooping, simple, the appressed rays solitary, the lowermost 2.5-5 cm. long, slightly glandular, but not villose, in the axils; spikelets commonly 3-tiowered, 8-10 mm. long; lower scales ovate-acute, 1-nerved, whitish or purplish, except the prominent nerve, 4-5 mm. long, subequal; first flowering scale 5-6 mm. long, ovate-lanceolate, trifid, 3-nerved, the nerves extending into short, awn-like teeth, the central one equaling or a little exceeding the narrow obtuse lobes of the scale, nerves ciliate in the lower half with rather long, erect white hairs; palet slightly shorter or a little longer than the scale, oblanceolate, obtuse, minutely ciliate along the keels to- wards the apex. Dry soil in low pine barrens. July to October. Perennial. Louisianian area. South Carolina and Georgia to Florida and Mississippi. Type locality: "Jacksonville, Fla., Drummond; Aiken, S. Carolina, Ravenel; Biloxi, Miss., Kearney ^ 324. 1896. There is also a specimen in the National Herbarium from Georgia without locality." Specimbns EXAMINED. — Mississippi: Manuel, Tracy, 4560, 1898.— South Carolina : Aiken, Bavenel. 14. Triodia Elliottii B. F. Bush. Poa ambigua Ell. Sk. 1 : 165, 1817, not Triodia ambigua, R. Br. 1810. Tricuspis ambigua (Ell.) Chapm. S. Fl. 559. 1860, not Triodia ambigua R. Br. 1810. Triodia ambigua (Ell.) Benth. ex Vaaey, Gr. U. S. 35. 1883, not Triodia ambigua R. Br. 1810. Sieglingia ambigua (Ell.) O. Kuntze, Rev. Gen. PI. 2 : 789. 1891, not Triodia ambigua R. Br. 1810. Culms 4-8 dm. tall, simple. Leaves attenuate, 1-3 dm. long; panicle 1-2 dm. long, open, branches spreading; 74 Trans. Acad. Sci. of St. Louis. spikelets o-8-flowered, 4-6 mm. long, short-oblong, broadly oval when mature, usually purple; lower scales slightly shorter than the lower flowers; flowering scales broadly oblong, pubescent below the middle; palet equaling the flowering scales, ciliolate on the nerves which are more curved at the base than at the rounded and apiculate apex. Low swampy pine barrens. July to October. Perennial. Louisianian area. South Carolina and Georgia to Alabama, Florida, Texas and Arizona. Type locality: " Found in the mountains of Carolina, by Dr. McBride, and in the lower country of Georgia, by Dr. Baldwin.'^ Specimens EXAMINED. — Florida: Apalachicola and Quincy, Chapman; Duval County, Curtiss, 10736; Jacksonville, Curtiss, 3455, 1877.— Texas: Point Ysabel, Nealley, 819.— Louisiana: De Quincy, Bush, 973, 1901. 15. Triodia Chapmani (Small) B. F. Bush. Sieglingia Chapmani Small, Bull. Torr. Club. 22 : 365. 1895. Tricnspis Chapmani (Small) Heller, Cat. PI. N. A. 28. 1900. Culms 9-15 dm. tall, mostly purple about the nodes, erect, wiry, glabrous, bright green. Lower leaves rather numer- ous, nearly erect, 4-6 dm. long, the upper few, divaricate, somewhat shorter, all firm, flat when young, soon involute and almost filiform, 7-11-ribbed, smooth and glabrous ; lower sheaths about 1 dm. long, the upper ones often 2 dm. long, all 1/3 to 1/2 shorter than the internodes; ligule a short f rinse of rigid villous hairs, above which on the surface of the leaf, is a tuft of longer villous hairs; panicle averaging about 2 dm. high, viscid above, broadly ovoid, its branches rigid, filiform, divaricate, the nodes tufted with bunches of silvery-villous more or less viscid hairs ; spikelets very slender, pedicelled, rather few, 7-8mm. long, tinged with purple, almost linear, about 5-flowered ; empty scales lanceolate, 1-nerved, the lower one 3/4 longer than the upper ; flowering scales oblong-elliptic, 5-nerved, 3-pointed by the excurrent nerves which are villous for one-half their length ; palet 2-nerved, scabrous on the two nerves, slightly curved. Dry sandy pine barrens. August to October. Perennial. Louisianian area. Georgia and Florida to Alabama and Texas. B ush — North American Species of Triodia. 75 Type locality: Slopes of Currahee Mountain, near Toccoa, Georgia, and along Yellow River in Gwinnett County, in the same State; collected by J. E. Small 1894; type in Herba- rium of the New York Botanical Garden. Specimens examined. — Florida: No locality given, Chapman, various collections; Duval County, Curtiss, 3454 — Texas : Paris, Lamar County, Heller, 4222; Texarkana, Letterman, 16, 1894; Columbia, Brazoria County, Bush, 952, 1901; no locality given, Reverchon; Camp 4, Bigelow. 16. Triodia seslerioides (Michx.) Benth. ex Yasey, Gr. U. S. 35. 1883. Poa seslerioides Michx. Fl. Bor.-Am. 1 : 68. 1803. Triodia cuprea Jacq. Eclog. Gram. 2i2l.pl. 26. 1814. Tricuspis seslerioides (Michx.) Torr. Fl. N. & Mid. U. S. 1 : 118. 1824. Sieglingia sesUrioides (Michx.) Scribn. Mem. Torr. Bot. Club, 5 : 48. 1«94. Sieglingia cuprea (Jacq.) Millsp. Fl. W. Va. 471. Culms 6-15 dm. tall, erect, somewhat flattened, often viscid above. Sheaths sometimes villous at the summit, the lower short, overlapping and crowded, the upper longer, equaling or shorter than the internodes ; leaves 1-3 dm. long or more, 6-12 mm. wide, flat, attenuate into a long tip, smooth beneath, scabrous above; panicle 1.5-4.5 dm. long, the branches finally ascending or spreading, the lower 1-2.5 dm. long, usually dividing above the middle; spikelets 4-8- flowered, 6-8 mm. long, purple; empty scales glabrous, obtuse, generally slightly 2-toothed; flowering scales oval, the nerves pilose, excurrent as short tips. Dry borders of woods and fields. July to October. Perennial. Carolinian and Louisianian areas. Maine and New York to Minnesota, Iowa, Kansas, Missouri, Arkansas, Indian Ter- ritory, Illinois, Alabama, Florida, Tennessee, Texas, Louis- iana, Oklahoma, Ohio, New Jersey, Mississippi and North Carolina. Type locality: ♦' Hab. in region Illinoensi et in montosis Carolinae." Specimens examined. — Texas: Dallas County, Beverchon, 1111, 1899; Marshall, Bush, 1015, 1901.— Missouri: Eagle Rock, Barry County, 5wsA, 1896; Clay County, Mackenzie, 646, 1901.— Kansas; Wyandotte County, Mackenzie, 1896; Manhattan, A'e^erman, 1888.— Arkansas: Fulton, Hemp- stead County, Bush, 1044, 1901.— Indian Territory: Sapulpa, Creek 76 Trans. Acad. Set. of St. Louis. Nation, Bush, 1445, 1895.— Ohio: Cincinnati, Lloyd, 585, 1890.— New Jersey: Camden, Parker, ^Wi, 1863.— Oklahoma: Stillwater, Waugh, &i, 1893.— North Carolina: Cherokee, Swain County, Beardslee Issued November 24 ^ 1902. ^r ON SOME RELATIONS BETWEEN BESSEL FUNC- TIONS OF THE FIRST AND OF THE SECOND KIND.* Alexander S. Chess in. The general solution of Bessel's equation n) ^ A_l ^_L_(i_^\^ =0 dx^ X dx \ x^j ^ is of the form (2) y = AJA'-^)-\' BK^ix), or of the form (2)' y = AJ^{x^^BJ_,{x), according as n is, or is not, an integral number, A and B being arbitrary constants, while ^i?- + (l 45^K»= = 0. or, we may say that u ^yVx is the general solution of the differential equation (o \ Ct %C ^> -d^2-^uf(x)=0, * Presented by title to The Academy of Science of St. Louis, October 20; 1902. (99) 100 • Trans. Acad. Sci. of St. Louis. where / (ic) = 1 — — ^71 — ' ^^^^ if ^^ given by the formulas (2) or (2)' according as n is, or is not, an integral number. Now, let V be a solution of the diiferential equation (3), and w a solution of the diiferential equation (•^^ ^^, i-y/c^(x)=0, /(x) and ^{x) beinoj arbitrary functions of x. Then dhfj -^ + w(f)(x) = 0, and, therefore, dhv (Pv But, on the other hand, ^'^^^ + Constant. We will proceed to make some applications of the last two formulas. If we put ( 5)j y = V xJJ^ax)., w = V xJ,^(^x) , Chessin — On Some Relations Between Bessel Functions. 101 )i being an integral number, then the function v will satisfy 4,n^ — 1 the equation (3) when/ (a?) =a2 — — j—^ — , while the function 10 will be a solution of the differential equation (3)' when (x) = ^_i^^^. Therefore, by (4), Likewise, n still being an integral number and the func- tions/(x) and <^(x) being selected as above, if we take, in succession, (5), V = l/^J'„(ax), w = VxK^{l3x) ; (5)3 v=.VxK^{ax), to=VxK^{^x)i we obtain the formulas = (a'' — ^^)xIi„{ax)KJJx). When n is not an integral number we take successively (7)i V = VxJ^^(ax), w = VxJn{/3x) ; (7), v = VxJ„{ax), iv = VxJ_,,{^x); (7)3 V = V'xj_,^(ax), 10 = VxJ_^(^x); and arrive at the identities = {a'^—^-^)xJ,,{ax)J,{^x), 102 Trans. Acad. ScL of St. Louis. = (a2_/32)xJ,(ax>/_„(/3x), = (a2 — /32>J_„(aa3)J_„(/3x), of which the first one is identical with (6)^ in form. Now, we know that, whatever be n, (9) -d^ - x'^n{^'^)—^Jn+,(^^)^ dJJax) ^ r / X I T / \ (10) 2; = — ^^«(««^) +«^»-i("^)' dKJax) _n (11) ^ =x^^'^^''''^~''^"+>^''^^' and that similar relations exist when a is replaced by /3. Substituting into the identities (6) and (8) the above ex- pressions for the derivatives of Bessel functions we readily obtain the formulas : (12), ^{x[aJ„(/3x)J-„+,(ax)-/3,/„(ax)^„+i(^x)]j (12), ^|x[a/i'„(/3x)./„+i(ax)-/9./„(ax)/r,+i(/3a^)] j = (a2— /32)xJ-„(ax)/r„(^aj) (12)3 -^|x[aA'-„(^x)/iVi(«^)— ^^'n(«a^)/C+i(/3a^) ] } = (a2 — /32)x/i;,(ax)/r„(^x) when n is an integral number, and d (13), ^|x[aJ'„(/3x)J",+i(ax) — /3J„(ax)J„+,(^x) ] = (^a'' — ^'i)xJ^{ax)Jn{^x), Chessin — On Some Relations Between Bessel Functions. 103 (13)3 ^1 ft;[ae7_,,(/3x)J_„+i(ax)— /3J_„(ax)J.„^.i(^x)] = (a2_/32)xJ_,(ax)J_„(^cc), whenn is not an integral number. When a = /8 the formulas just derived assume the form 0=0. This is obvious in the case of (12)j, (12)3, (13)^, and (13)3. It is, however, quite as evident in the other cases if we take into consideration the relations 1 (14) J^^^{x')K,,{x) — J^{x)K,,^^{o:) =-, when n is an integral number, and 2 sin nTT (15) Jn(^y-n+l(^) + J-ni^yn-li^) = ^^ , when 71 is not an integral number.* To derive the relations corresponding to (12) and (13) when a = ^8 we, therefore, differentiate both sides of the identities (12) and (13) with respect to a and put /3 = a in the results. We then arrive at the formulas : (16)i a^W\yl(''^0 —J^_^{ax)J^^-,(ax)'j\ = 2xJl(ax), (16)2 -^ I x'^[j^(ax)K^(ax) —J,^_^(ax)Ii^_^^(ax)'^ I = 2xJ^(ax)K„(ax), d ( 16)3 ^ I x2[/lf (ax) — K,,_^{ax) Ii,,+i{ax)'^ when n is an integral number, and ^2 = 2xlL^(ax), * See the treatise on Bessel functions by Gray and Mathews, p. 16. 104 Trans. Acad. Sci. of St. Louis. (17), ^lx^[^jl(ax) — J,_r{ax)J,+,(ax)']'j = 2xJl{ax), = 2xJn{ax)J_Jax) (17)3 ^|x2[j!„(ax) — J_„+i(ax)J_„_i(ax)] j = 2xJLn{ax), when n is not an integral number. If, instead of applying formula (4), we liad made use of formula (4)'; or, which amounts to the same thing, if we integrate both sides of the relations (12), (13), (16) and (17), we arrive at the formulas: (18), a;jaJ„(^x)J"„+i(ax) — /3J'„(ax)J„+j(/3x) = (a'-J— /32) I xJn{ax)Jn(l3x)dx + Const. (18), x\ aKn(0x)Jr,+,{ax)—^Jn(^x)Kri+i{^x) = (a2_^2>) 1 xJn(ax)lLn{i3x)dx + CoUSt., (18)3 xl aKn(^x)K^+,(ax) — ^Kn{<^x)J^n+i(^^) = (a2_ ^^) 1 xKn {o,x)Kn (/3a5) dx + Const. , when a ^ /3, and (19), x2|j^(ax)— J„_,(ax)J„+,(ax)| = 2 I xJ^(ax)cZx + Const., Chessin — On Some Relations Between Bessel Functions. 105 (19), x^ \^Jn{ax)K„(ax)—J,_^{ax)K,^,(ax) | = 2 I xJn [ax)lLn {ax)dx + Const., (19)3 x2 I Kl{ax) — K,,_^{ax)K^^^{ax) l r 2 = 21 xKn{Q'X)dx + Const., when /3=a. Both sets of formulas (18) and (19) refer to the case of an integral n. When n is not an inteo^ral number these formulas should be replaced by the following ones: (20), x^aJ^{^x)J,,^,{ax)—^J^{ax)J^^,{^x) | = (a2 — /32) I xJn(ax)Jn(^x) dx -\- Const., (20), X I aJ_^(^x)Jr^,(ax) + ^J„ (ax)J^+, (^x) | = (^2_a2) I xJ'„(aa;)J_„(/8x)c^x+ Const., (20)3 X I aJ_„(^x)J_„+,{ax) — ^J_„(aa;)J_„+XA^) } = (a2_ ^2) I xJ_^(ax)J^(^x)dx + Const., provided a ^ ^. If /3 = a, the last relations assume the form (21), x"^ I Jl(ax) — J„_,(a:7;)J'„+,(a.'«) | '' (ax)c?x + Const. = 2 aJe/n 106 Trans. Acad. Sci. of St. Louis. (21), x^ij^(ax)J_n(<^x) +J_„+,(a.'»)'/„+i(aa;) I = 2 I xJn {ax)J_n{cix)dx + Const., (21)3 X^ijLn{ax) — J^n-,i'^Xy-n+,(^^) | f 2 = 21 xJ_n{ctx)dx-^ Const. With the exception of formulas (18)3, (19)3, (20)^, (20)3, (21)i, and (21)3, the integration may be assumed between the limits 0 and 1, the only restriction on the number n being that specified above. Thus, with ^^a and n being an integ- ral number, positive or negative (zero, of course, included), (22) aj-„(^)e4+,(a) — /3e7„(a)J-„^^(^) = (a2_/32)l xJn(ax)Jn(^x)dx, (23) aR\{l3)J^+^{a) — ^J,{a)lL,^^(/3) = (a2 — jS^^ I xJn{ax)Kn(^x)dx, (24) Jn{a) —Jn-MJn+M = 2 1 xjl{ax)dx, (25) J„(a)/r„(a) — J-„_,(0, is only possible if | n \ <1. Hence, formulas (28) and (29) are still valid if — li