use of seaweeds in the manufacture of iodine and soda-ash. Dr. Rusby exhibited specimens of Fucus vesiculosus and an unnamed form, which are used medicinally.

Dr. Howe spoke of dulse as an article of food and of its occurrence in the markets of New York.

After further discussion, adjournment followed.

L. H. LIGHTHIPE, Secretary pro tem.

THE AMERICAN MATHEMATICAL SOCIETY.

A REGULAR meeting of the society was held at Columbia University on Saturday, April 29. On the preceding Saturday the Chicago section met at the University of Chicago. The two sessions of the New York meeting were attended by thirty-eight members. President W. F. Osgood occupied the chair, being relieved by Vice-President E. W. Brown and the secretary. The following new members were admitted: J. H. Grace, Peterhouse, Cambridge, Eng.; H. B. Leonard, University of Chicago; R. B. McClenon, Yale University; W. S. Monroe, Columbia, Mo.; J. C. Morehead, Yale University; Henri Poincaré, University of Paris; R. G. D. Richardson, Yale University; Miss S. F. Richardson, Vassar College; F. R. Sharpe, Cornell University; Miss M. S. Walker, University of Missouri. Six applications for membership were received. The total membership of the society is now 490, including 34 life members.

An appropriation of $100 was made toward binding the rapidly accumulating library material. The catalogue of the library now includes nearly 2,000 volumes, accessions amounting to some 500 volumes per annum. The greater part of the expense of binding is borne by the Columbia University Library, in which the collection is deposited.

The society has recently issued, through The Macmillan Company, an octavo volume of 175 pages containing the lectures on mathematics delivered at the Boston colloquium, September, 1903, by Professors E. B. Van Vleck, H. S. White and F. S. Woods.

The following papers were read at the April meeting:

ARTHUR SCHULTZE: Graphic solution of quadratics, cubics and biquadratics.'

MAX MASON: On the derivation of the differential equation of the calculus of variations.' D. R. CURTISS: Theorems converse to Riemann's on linear differential equations.'

VIRGINIA RAGSDALE: On the arrangement of the real branches of plane algebraic curves.' J. C. MOREHEAD: Numbers of the form 2q+1 and Fermat's numbers.'

E. B. VAN VLECK: Supplementary note on theorems of pointwise discontinuous functions.' JAMES PIERPONT: 'Inversion of double infinite integrals.'

JAMES PIERPONT: Multiple integrals (second paper.'

R. B. MCCLENON: On simple integrals with variable limits.'

E. O. LOVETT: 'On a problem including that of several bodies and admitting of an additional integral.'

M. B. PORTER: Concerning Green's theorem and the Cauchy-Riemann differential equations.' M. B. PORTER: 'Concerning series of analytic functions.'

J. E. WRIGHT: 'Differential invariants of space.' EDWARD KASNER: On the trajectories produced by central forces.'

E. B. WILSON: 'Sur le groupe qui laisse invariant l'aire gauche.'

E. J. WILCZYNSKI: 'Projective differential geometry.'

I. M. SCHOTTENFELS: On the simple groups of order 8!/2' (preliminary communication). I. M. SCHOTTENFELS: 'Certain trigonometric formulas for the quantity +ey, where =0,' EDWARD KASNER: A theorem concerning par tial derivatives of the second order, with applications.'

J. E. WRIGHT: 'On differential invariants.' L. P. EISENHART: 'Surfaces of constant curvature and their transformations.'

L. E. DICKSON: On the class of the substitutions of various linear groups.'

JOSIAH ROYCE: The fundamental relations of logical and geometrical theory.'

The summer meeting of the society will be held at Williams College, Williamstown, Mass., on Thursday and Friday, September 7-8. The San Francisco section will also meet in September. F. N. COLE, Secretary.

DISCUSSION AND CORRESPONDENCE. MARINE ZOOLOGY IN THE HAWAIIAN ISLANDS.

TO THE EDITOR OF SCIENCE: At a time when zoologists are making their plans for summer vacation work it seems opportune to direct attention to the advantages offered even in such a distant territory as the Hawaiian Islands. During a visit to the islands last year, under the auspices of the Carnegie Institution, for the purpose of studying the living corals, I was afforded the privileges of the public aquarium recently established near Honolulu, and the directors of the institution desire it to be known that they will be prepared to accord a similar courtesy to other zoologists visiting the islands for purposes of research.

The aquarium is a modest structure, erected a little over a year ago, and is under the control of the Rapid Transit Company, though the funds were largely provided by the generosity of different gentlemen interested in the welfare of the islands. It is most advantageously situated at Waikiki Beach, a suburb of Honolulu, and the adjacent coral flats constitute most favorable collecting ground. Though no special appliances beyond exhibition and experimental tanks are available, yet the advantages of these and a constant supply of sea-water appeal to any student desirous of carrying out investigations on living forms. Moreover, with a generosity which is very praiseworthy, the directors are prepared to make whatever reasonable adaptations may be required.

Our knowledge of the marine fauna of the Hawaiian Islands is becoming rapidly extended, mainly through the reports on the collections made by the U. S. Fishery Bureau, under the direction of President D. S. Jordan, during the two successive seasons, 1901 and 1902. The large addition to the number of species of fishes alone shows how very desirable was such faunistic work, and other groups are yielding a corresponding number of new forms. The physical conditions of the coral reefs have been studied in part by Professor A. Agassiz. Though the luxuriance of the life on the reefs does not equal that in

the more distant Tahiti, Samoa, or the Philippine Islands, yet there is sufficient, particularly in such places as Kaneohe Bay, to satisfy the most ardent investigator.

For the student of terrestrial forms the islands are particularly interesting on account of the influence of introduced animals and plants upon an indigenous fauna and flora. Representatives from the east and from the west, from temperate and from tropical regions, here flourish, and against the pests a strong corps of entomologists is engaged in further introduction of possible remedial forms. The fact that the land shells of the islands served to supply the Rev. J. T. Gulick with material for the theory of isolation adds an interest to the evolutionary biologist. ethnology and various departments of natural history are well cared for by Professor T. H. Brigham, of the Bishop Museum, and his staff of assistants.

The

As a last word of attraction regarding the situation of the aquarium one may quote from the 'Report on Collections of Fishes made in the Hawaiian Islands' by Professor O. P. Jenkins:

Of all situations about the island of Oahu, the submerged reef which extends from the entrance of the harbor of Honolulu to some distance past Waikiki furnishes the most prolific supply of fishes, both as to number of species and amount of the catch. This reef at low water is from a few inches to a few feet under water and extends from one mile to two or three miles from the shore, where the water abruptly reaches great depths. Over the surface and along the bluff of this reef may be found representatives of most of the shore fauna of the Hawaiian Islands. This reef, so favorably situated, so accessible, and so rich in material, can not fail to be of increasing interest to naturalists who may have the good fortune to devote themselves to the study of its wonderful life. J. E. DUERDEN.

RHODES UNIVERSITY COLLEGE,
GRAHAMSTOWN, CAPE COLONY.

THE GREENE EXPLORING EXPEDITION.

TO THE EDITOR OF SCIENCE: The W. C. Greene Exploring Expedition consisting of Robert T. Hill, John Seward, Frank H.

Fayant and E. O. Hovey has finished its first exploration of the northern part of.the Western Sierra Madre Mountains of Mexico. A summary account of the first half of the trip, from El Paso to Guaynopita, has been given to the readers of SCIENCE. The second half of the journey was no less interesting than the first and was fully as productive of scientific observations.

Leaving Guaynopita by pack train on March 11, the first stage of the journey was the climb of 3,500 feet out of the Yaqui (Aros) cañon in which Guaynopita is located on to the great mesa out of which the mountains of the region have for the greater part been carved. The contrast in vegetation between different parts of this section may be illustrated by the statement that fan-leaf palms flourish in the gorges near the river, while on the high mesa one finds the great long-leaf sugar pine predominant.

Our course lay southward for sixty or seventy miles along the broad plains and narrow divides forming the mesa, or connecting different parts of it, and we had abundant opportunity of studying the topography of the great Tutuaca Cañon, which is tributary to the Yaqui (Aros), and of observing the contest for the drainage of the plateau between the streams flowing to the west and those flowing to the east. The dissection of the plateau is more pronounced toward the west, and our cross-section of the cañon of the Tutuaca River from its eastern boundary at the edge of the Mesa Venado disclosed acid and basic lavas, tuffs, agglomerates and conglomerates through six thousand feet of beds. The western rim of the Tutuaca Cañon is near the important Dolores mineral district. Some of the extensive igneous action has been accompanied and followed by strong mineralization of veins. At Dolores a fifteen-stamp mill of the most up-to-date construction is just being completed under the supervision of Manager J. Gordon Hardy for the treatment of the rich gold and silver ores of the Alma Maria vein by the direct cyanide process.

Near Dolores we turned southward again and pursued our course along a series of high

mesas, divides, arroyos and river channels until we reached the little Indian town of Yepachic. In this part of our route we passed through three or four fertile ranches and at Yepachic found the people (Tarahumares and Pimas) living for the most part from the tillage of a small alluvial plain surrounded by low mountains. Here we turned westward again and within a few miles reached the Cerro Boludo (Bald Mountain) district, which, like several others on our route, is characterized by a mineralized quartz vein twenty to eighty feet wide which can be seen traversing hill and vale for miles.

Six or eight miles south of Cerro Boludo lics the little Mexican camp of San Francisco, where a diminutive two-stamp mill feeds a primitive arrastra as a preliminary to pan amalgamation of the gold. Thence the Ocampo trail leads over a divide and across the deep cañon of the Rio de Mayo, down into and out of the Rosario arroyo before the great arroyo is reached in the bottom of which, at the junction of two branch arroyos, is crowded the mining camp of Ocampo-a place better known by its old name of Jesus Maria. This is the site of many rich gold and silver mines, the most famous of which is the Santa Juliana.

From Ocampo to Miñaca, 100 miles, the trail crosses the high mesa, which has a gentle slope eastward and is partly dissected by comparatively shallow cañons of varying depths. Miñaca, the present terminus of the Chihuahua and Pacific Railway, is in a beautiful broad basin about 7,000 feet above tide, which is traversed by the headwaters of the Rio Verde, a tributary of the Yaqui (Aros) River.

At Miñaca our party took train for Chihuahua and thence went by rail to El Paso, completing our noteworthy circuit in the western Sierra Madre Mountains of northwestern Mexico. The circuit was not very long, compared with the mileage of some expeditions, but the results along lines of physiographic, dynamic and economic geology are of importance and will be published as soon as they can be put into proper shape, while the photographs taken illustrate as completely as prac

THE undersigned is compiling a 'Biographical Directory of American Men of Science.' It was begun as a manuscript reference list for the Carnegie Institution of Washington, but arrangements have now been made for its publication. The book should be ready in the autumn, nearly 4,000 biographical sketches being in type. The proofs have been corrected by those concerned, but in order to secure as great accuracy as possible a revised proof will be sent in the early autumn.

This letter is written with a view to securing biographical sketches from those living in North America who have carried on research work in the natural or exact sciences but who have not received proof of a sketch for correction. Some of those who were asked to send the information required did not reply even in answer to a second and third request, and there are, of course, many who should be included in the work but who for one reason or another did not receive the request for information.

It is intended that each biographical sketch shall contain information, as follows:

1. The full name with title and mail address, the part of the name ordinarily omitted in correspondence being in parentheses.

2. The department of investigation given in italics.

3. The place and date of birth.

4. Education and degrees with dates. 5. Positions with dates, the present position being given in italics.

6. Temporary and minor positions.

7. Honorary degrees and other scientific honors. 8. Membership in scientific and learned societies.

9. Chief subjects of research, those accomplished being separated by a dash from those in progress.

The undersigned will be under great obligations to those men of science who will send him biographical sketches of themselves or who will secure sketches from those who should be included in the work-those who live in the United States, Canada, Newfoundland, Mexico or Cuba, and who have contributed to the advancement of one of the following sciences: mathematics, astronomy, physics, chemistry, geology, botany, zoology, pathology, physiology, anatomy, anthropology, psychology.

The compiler of the book hopes that any assistance given him to make it as complete and accurate as possible will be at the same time a contribution to the organization of science in America.

J. MCKEEN CATTELL. GARRISON-ON-HUDSON, N. Y.

SPECIAL ARTICLES.

THE NOMENCLATURE OF TYPES IN NATURAL HISTORY.

PRACTICAL Work in the arrangement and cataloguing of 'types' and other museum material has shown us that the present nomenclature is not yet sufficient for critically distinguishing all the different classes of such specimens. Further, some of the terms which have been proposed for the purpose are already employed in other ways: for instance, homotype is in use in biology; monotype is the name of a printing machine; autotype is the term for a printing process. We wish, therefore, to submit the following system of nomenclature; and we hope that, in making it more complete, we have provided a scheme which will render efficient service in the labeling and registration of types and typical material.

The terms printed in broad-faced letters are the additions or modifications for which we are at present responsible. A fuller explanation of all the terms will be found in the 'Catalogue of the Type and Figured Specimens of Invertebrate Fossils in the U. S. National Museum,' a work which has been prepared by Charles Schuchert and is now passing through the press; and the present article gives a synopsis of the terms which it has been found necessary to use in connection with that and similar work.

After

We now make another suggestion. the different terms we have placed, in brackets, the contractions which we propose should be used in the actual marking of small specimens to which it is impossible or inadvisable to affix the full label. Our plan for such contractions is this: For types of the first class, two capital letters; for those of the second class, one capital and one small letter; for typical specimens, two small letters.

In the definitions which follow, the term 'description' indicates either a description by words, or by a picture, or by both combined. For the sake of accuracy we suggest that the original description by words (type-description) be called the protolog, the original description by a picture (type-figure), the protograph. It is obviously more easy to identify actual types from the latter than from the former.

Primary types Proterotypes. Material upon which original descriptions of species are based.

Holotype [H. T.]. The only specimen possessed by the nomenclator at the time; the one specimen definitely selected or indicated by the nomenclator as the type; the one specimen which is the basis for a given or cited protograph.

Cotype (more properly Syntype) [S. T.]. A specimen of the original series, when there is no holotype.

Paratype [P. T.]. A specimen of the original series, when there is a holotype.

Lectotype [L. T.]. A cotype chosen, subsequently to the original description, to take the place which in other cases a holotype occupies (ezrós, chosen, picked).

Supplementary types (Apotypes vice Hypotype in use). Material upon which supplementary descriptions of species are based.

Heautotype (vice Autotype in use) [H. t.]. Any specimen identified with an already described and named species, selected by the nomenclator himself in illustration of his species, such specimen not being identifiable as one of the proterotypes.

Plesiotype [P. t.] Any specimen identified with an already described and named species, but not selected by the nomenclator himself.

Neotype [N. t.]. A specimen identified with an already described and named species, selected to be the standard of reference in cases when the proterotypes are lost, destroyed or too imperfect for determination, such specimen being from the same locality and horizon as the holotype or lectotype of the original species.

Typical specimens (Icotypes) (¿czós, what is like).* Material which has not been used in literature, but serves a purpose in identification.

Topotype [t. t.]. A specimen of a named species from the locality of the holotype or lectotype, in paleontology from the same locality and horizon.

Metatype [m. t.]. A topotype identified by the nomenclator himself.

Idiotype [i. t.]. A specimen identified by the nomenclator himself, but not a topotype. Homoeotype (vice Homotype, preoccu pied) [h. t.]. A specimen identified by a specialist after comparison with the holotype or lectotype gots, resembling).

Chirotype [x. t.]. A specimen upon which a chironym is based (chironym, a Ms. name, Coues, 1884).

In addition to the above, we have the use of the word 'type' in connection with genera-a given species is the type of the genus. The classification of such types is as follows:

TYPES OF GENERA (Genotypes). Genoholotype. The one species on which a genus is founded; or a series of species on * εikós, gen. Éɩkótoç, eiko for ɛlkoto, to make. Ico type for euphony.