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United States, but especially common in the action. The effect of this change has been to west and southwest, in the more arid parts of produce a shell with a wide, flaring aperture the country, where water st ds for but a and a larger foot area, a direct response to be small part of the year and where the lymnæas, environment which demands a larger foot area and other mollusks must be able to withstand for resisting the waves. The lymnæas are the period of drouth by hibernating in cracks not, as generally supposed, mollusks chiefly of in the bottom of the pond or stream. Such ponds and ditches, as might be thought from species as Galba caperata (Say), G. cubensis reading the paper in SCIENCE, but also of the (Pfr.), and G. bulimoides and its varieties are larger inland lakes, in fact a greater variety typical of these habitats. Galba palustris and is found in the lakes than in any other kind some other species normally living in marshes of habitat. may at times be compelled to adopt this hiber- The fossil lymnæas, as well as other freshnating type of habitat during unusual periods water fossil groups, are in need of careful reof drought.
vision in the light of modern work on the exThe writer has not found lymnæas as a rule isting species. As the shell in a measure inhabiting moss, although the little amphib- reflects the internal structure, this revision ious species (parva, dalli, etc.) may do so in ought not to be difficult with ample matesome places and have, indeed, been collected rial of fairly well-preserved specimens. The from such a habitat. All lymnæas as well as twenty-five or more species described appear other fresh water mollusks, whether in lako to represent the larger groups recognized or marsh habitats, prefer a location where among the recent forms. Several of these there is a quantity of vegetation and where species, as mentioned by Hannibal, are probthere is an abundance of filamentous alge lematic and may belong to other groups, but (Cladophora, Edogonium, etc.) upon which more perfect material is needed for this purthey largely feed, in some cases to such an ex- pose. Some confusion of species has occurred tent as to give a green color to the shell. in figuring and describing a few of these The relation of algæ to molluscan and other lymnæas, attention to which has already been life has recently been rather fully stated by directed by the writer." the writer.?
FRANK COLLINS BAKER It is interesting to note that fresh-water UNIVERSITY OF ILLINOIS mollusks, the lymnæas in particular, respond quickly to changes in environment, a species
SPECIAL ARTICLES characteristic of a marsh adapting itself to a
SOUND AND FLASH RANGING rough lake shore habitat if compelled to make The location, by means of sound, of active the change. Thus typical stagnalis is char
enemy batteries and the direction of the fire of acteristic of quiet, pond-like bodies of water, the friendly artillery on these and other enemy while the variety lilliance lives on a shore ex- objectives is new; has been successfully pracposed to the full force of the waves. The tised by the Allies and has been clumsily pracchange in habitat has resulted in a larger tised by the Germans. The location and rangaperture and foot in lilliance the better to ing by visual observation (flash ranging) is an resist the moving power of the waves. In
outgrowth of standard artillery methods and Oneida Lake, a large colony of Galba palustris differs from these chiefly in the extent of front was forced by a change in the environment,
covered by a single group of observers and by caused by the barge canal construction, to
the adoption of certain electrical devices and change from a shallow swampy habitat to that 8 Baker, Tech. Pub. No. 9, N. Y. State College of an open rocky shore exposed to violent wave
of Forestry, p. 180.
O" Mon. Lymn. N. Am.,'' pp. 89, 95, 96. 7 Tech. Pub., No. 9, N. Y. State College of For- 1 Abstract of paper presented before the Ameriestry, Syracuse University, 1918.
can Philosophical Society, April 26, 1919.
methods of observation designed to avoid con- arrival of the sound of the enemy guns at a fusion in operation on a very active front. The series of instruments at surveyed positions Germans had an extremely efficient flash rang- near the front line and covering a length of ing service, many of the good features of about five miles; this instrument delivered auwhich were copied by the Allies as they became tomatically developed and fixed photographic known through captured documents. The records in less than a minute after the sound flash ranging reported not only the positions of the enemy gun reached the front line and and activity of hostile batteries, but also the this record could be interpreted by the use of exact locations of other enemy objectives such quick graphical methods so that the position of as traffic on roads, troop movements, position of the enemy gun could be telephoned to the observation balloons, etc. Being provided with friendly artillery in about a minute more. The high-power telescopes, and since observation probable accuracy of the location could be was obtained from stations on a wide base given and also the caliber and target of the (from five to eight miles) the flash ranging sec- piece which had just fired. The service was tions were particularly well suited for obser- not interfered with by rain or fog or darkness, vation and ranging in the enemy back areas, though it was rendered less accurate by strong and these sections rendered invaluable services winds. Calculations were rendered difficult by both to the artillery and to the army intelli- great artillery activity though not impossible gence.
except under actual “barrage" conditions. A battalion of five companies (74th Engi- In ranging the friendly artillery on enemy neers) furnished the ranging troops for an objectives it was possible to range all the guns American army.
A sound ranging section of the battery simultaneously, thus effecting was in the field with the first American division considerable time saving over other methods of to enter the line (March, 1918) and on the ranging. If the ranging was being done on an signing of the armistice the entire front of the enemy battery which had just fired the accusecond American army was covered with both racy attained was very great (less than twentyflash and sound ranging sections and a portion five yards), because of the fact that in this of that of the first American army was covered case no wind or temperature corrections need by flash ranging, although the ranging battal- be applied in the calculations. ion allotted to this army had not yet arrived After the American advances of September in France.
The ranging service was thus a and November a careful survey was made of “going concern from the very first and was most of the enemy positions which had been not one of the many which could have delivered located by either the sound or the flash ranging results had the war but lasted a little longer. sections on a part of the American front; the
A flash ranging section consisted of about result of this survey was that of the locations one hundred men commanded by a lieutenant of the flash ranging about one third were accuwho was assisted by three other officers and by rate to within fifty yards, another third to an exceptionally high grade of non-commis- within one hundred yards and the other third sioned officers and men, all of whom had been with errors of more than one hundred yards. given a month's intensive training in France.
In the first third were many extremely accuThe instruments and methods employed were rate locations of guns the positions of which those suited for accurate survey and present no were visible from two or more observation special features of interest.
posts; in the last third were mostly locations of A sound ranging section was similar in or- concealed heavy caliber distant guns generally ganization to the flash section except that there more easily located by sound ranging, whose were fewer enlisted men (60–70) due to the positions could only be inferred from smoke fact that instruments took the place of living puffs by day or flares in the sky by night. observers to a great extent. The central” in- The survey showed that the estimates of strument recorded photographically the time of accuracy made by the sound rangers in-reporting a location had been very conservative; a flash sections are very useful and important location reported not accurate to within fifty sources of information. During rapid advance yards was often accurate to within twenty-five the sound ranging does not get into action as yards. In general, the average of a half dozen often or as soon as the flash. In this period locations of the same gun taken on different the greater part of the information comes from days under differing weather conditions was of the air observation. a very high order of accuracy; often a matter Both sound and flash ranging have proved of but five or ten yards.
their value in the American Expeditionary In general a location either by sound or by Forces and are to be retained in the peaceflash which had been rated “fair” when re- time army; the sound because it is the one ported to the artillery was found on survey to source of information when all others fail in have been within the unavoidable errors in foggy weather and because thus far no camouartillery fire.
flage has been devised to prevent its working; An idea may be gained of the amount of the flash because of its relatively great mobilartillery information supplied by the ranging ity and consequent importance in open warsections from the following figures taken from fare. the reports of the artillery information officer
AUGUSTUS TROWBRIDGE of one of the American corps. This officer had
PRINCETON UNIVERSITY at the time the following sources of information: three American sound ranging sections, THE AMERICAN MATHEMATICAL two American and three French flash ranging
SOCIETY sections, aviation and observation balloons. THE two hundred and third regular meeting of During a period of three weeks of rapid ad- the society was held at Columbia University on vance when the sound sections were out of Saturday, April 26, extending through the usual operation while moving for a considerable por- morning and afternoon sessions. This being the tion of the time 425 separate locations of
first eastern meeting since October, the attendance enemy batteries were made. Of these the two
was large, including sixty-seven members, indi. American flash sections reported 64 per cent.
cating, as it may be hoped, a revival of the con
ditions preceding the war. the three French flash sections reported 16 per
President Morley occupied the chair, being recent. and the three American sound sections
lieved by Professor Kasner. The election of the reported 21 per cent. In a period of two
following persons to membership in the society weeks when the advance had been checked by was announced: Mr. N. W. Akimoff, Philadelphia, the Germans the total number of locations Pa.; Dr. Tobias Dantzig, Columbia University; were 392, and the percentages were: From the Mr. A. C. Maddox, Guthrie, Okla., High School; three American flash sections 38 per cent. ; Mr. Montford Morrison, Chicago, Ill.; Professor from the two French flash sections 8 per cent.,
Ganesh Prasad, Central Hindu College, Benares, and from the three American sound sections
India; Mr. F. M. Weida, State University of Iowa;
Mr. C. L. E. Wolfe, University of California. Two 56 per cent. The following figures taken from another
applications for membership were received.
It was decided to hold the coming summer meetand very active sector are also instructive.
ing of the society at the University of Michigan For a period of three days preparation for an in the first week in September. Professors Beman, advance the following locations were made: Bliss, Karpinski, Osgood and the secretary were Sound, 22; flash, 22; balloons, 0; aviation, 0. appointed a committee on arrangements for this For a period of sixteen days of rapid advance:
meeting. A committee was also provided to preSound, 4; flash, 46; balloons, 30; aviation 77.
pare nominations for officers to be elected at the
annual meeting in December. For a period of four days of stabilization:
Professor E. W. Brown, L. E. Dickson and H. S. Sound, 6; flash, 34; balloons, 13; aviation, 15.
White were appointed as representatives of the These figures are characteristic. During prep- society in the division of physical sciences of the arations for an advance, both the sound and national research council; and President R. S.
Woodward, and Professors Birkhoff and MacMillan as representatives of the society in the American section of the International Astronomical Union,
The committee on the publication of a mathematical year book presented a preliminary report and was continued and asked to make a further report at a future meeting.
A special feature of the meeting was the reports by Captain Jackson, Dr. Gronwall and Major Veblen on the work in ballistics at Aberdeen and Washington, which occupied the first part of the afternoon session. The titles of these reports are included in the list of papers below.
About fifty members and friends gathered at the midday luncheon; thirty-two attended the dinner at the Faculty Club in the evening. Much satisfaction was expressed at the revival of these pleasant occasions.
The Chicago Section held its regular spring meeting on March 28–29. The San Francisco Section met at the University of California on April 5.
The following papers were read at the New York meeting:
C. J. Keyser: “Concerning groups of dyadic relations in an arbitrary field.”
J. K. Whittemore: “Certain functional equations connected with minimal surfaces.'
W. B. Fite: "Linear functional differential equa
Oswald Veblen: “Progress in design of artillery projectiles."
G. D. Birkhoff: "Boundary value and expansion problem for differential systems of the first order."
G. D. Birkhoff: “Note on the closed curves described by a particle moving on a surface in a gravitational field.”
G. D. Birkhoff: “Note on the problem of three bodies.''
Edward Kasner: “A characteristic property of central forces."
J. F. Ritt: “On weighting factor curves for low elevations.'
A. C. Lunn: “Some functional equations in the theory of relativity."
J. R. Kline: “Concerning sense on closed curves in non-metrical plane analysis situs."
R. L. Moore: “On the most general class L of Fréchet in which the Heine-Borel-Lebesgue theorem holds true.''
H. S. Vandiver: "On the class number of the . field Nezininn) and the second case of Fermat's last theorem."
F. W. Beal: “On certain points of congruences of circles."
L. L. Silverman: “Regular transformations of divergent series and integrals.'
T. C. Fry: “The application of the modern theories of integration to the solution of differential equations."
C. A. Fischer: “Completely continuous transformations and Stieltjes integral equations."
Arnold Emch: “On closed curves described by a spherical pendulum."
H. S. White: “An explicit formula for two old problems."
L. P. Eisenhart: "Triply conjugate systems with equal point invariants.'
F. N. COLE,
L. B. Robinson: “Note on a theorem due to Wilczynski."
L. B. Robinson: “A curious system of polynomials, continued.”
0. E. Glenn: “Covariants of binary modular groups.'
0. E. Glenn: “Modular covariant theory of the binary quartic. Tables" (preliminary report).
0. E. Glenn: “Invariants of velocity and acceleration."
F. H. Safford: “Reduction of the elliptic element to the Weierstrass form."
Philip Franklin: “Computation of the complex roots of the function P(2).”
A. R. Schweitzer: “On the history of functional equations" (preliminary report).
E. D. Roe, Jr.: “The irreducible factors of 1+ 3 + + 2n-1. Second paper.'
E. D. Roe, Jr.: “The irreducible factors of a cir. culant."
Dunham Jackson: “Small arc computations and related questions."
T. H. Gronwall: “Qualitative properties of the ballistic trajectory."
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