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lels the different coal beds of northern France tian or Mississippian) but one order is known; with those of Belgium and England.

early in the Westphalian three orders are The greater part of the volume is taken up “scarcely outlined”; and at the end of the with the insects (pp. 93–321), and the author Westphalian “almost all the Paleozoic phyla confirms Handlirsch's conclusion that during are fully established.” Westphalian time hexapods were large, in fact, The evolution of insects was especially rapid at that as a rule they were “ giants.” Pruvost the base of the Westphalian (Flines member), thinks that the Westphalian insects were not again at the base of the upper part of the same all carnivorous, 'but that some may have fed series (Ernestine), and at the top of the Weston the pollen, etc., of plants like the cordaites phalian in the Edouard member. And this threeand cycadophytes; in other words, that the rise fold acceleration in insect evolution is in harmony of the insect world was largely conditioned by

with the floral enrichment. the development of inflorescence among plants. We must add here that the supposed insects

Insect impressions, to be preserved in the found in the Horton formation (early Missisrocks, must be entombed in the very finest of sippian) of New Brunswick, Canada, and

, sediments. The author states that they are mentioned in the table opposite page 293, have found only in shales, in association with deli- been shown to Professor H. F. Wickham and cate plant remains, and with those of animals Dr. David White, with the result that both as well. The very best ones, of rare occurrence, paleontologist and paleobotanist agree that have, however, suffered no appreciable trans- they are not insects but the carbonized fragport or maceration, but were buried quickly ments of woody plants. along with the most fragile plants in the soft- To the young author, a favorite student of est of muds; while the majority of the speci- Professor Barrois under whose direction are mens found commonly in the “insect beds” being carried out a series of studies designed have undergone more or less long periods of to apply the “paleontologic method” to the floating, and consequent maceration and disso- problems of the coal basin of northern France, ciation. The floated specimens occur at times are extended our congratulations on his great with stronger plant fragments and the remains

achievement. of animals, all in varying degrees of decompo

CHARLES SCHUCHERT sition. Pruvost breaks up Handlirsch's order Prot

SPECIAL ARTICLES orthoptera, and puts the majority of his fam

THE RELATIVITY SHIFT OF SPECTRUM LINES ilies in a new suborder, the Archiblattids (3 species described), which are present as early THREE experimental tests of Einstein's as the base of the Westphalian. These are Relativity Theory of Gravitation have been " the simplest and oldest of Protoblattoidea ” proposed. Two seem to have been verified and they may have had their origin in the experimentally. The

experimentally. The third, the predicted Paleodictyoptera, the original source-stock of shift of solar spectrum lines, is still very all insects. Two other suborders of Proto

much in dispute. Evershed and Royds, and blattids are erected, Mimoblattids (for Ameri- Schwarzschild? obtained very discordant rocan forms) and Archimantids (1 described). sults. St. John, with very fine apparatus, The author remarks on “ the homogeneity and

also obtained very discordant results with antiquity of the blattid phylum,” describing however a zero effect, on the average. Grebe 43 forms, and on its early separation from the

and Bachem+ at first obtained discordant rerest of the orthopterids. Of Paleodictyopter- sults, but a more careful analysis of their ids he describes but 3 forms. He believes that

1 Bulletin 39, Kodaikanal Observatory. the greatest evolution of Paleozoic insects took

2 Sitzungsberichte, Berlin Akad., p. 1201, 1914. place during the Westphalian, and states that 3 Astro. Jour., 46, 249, 1917. at the top of the Lower Carboniferous (Dinan- 4 Verh. d. D. Phys. Ges., 21, 454, 1919.

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data5, 6, 7 yielded more consistent results and have different spacing and so are continually results in agreement with theory. Using the crossing, resulting very frequently in an aplines near the head of the N 3883 band, the parent broad, unsymmetrical line, even with shift of solar wave-lengths, compared to ter- the best resolving power at our disposal. But restrial, should be 0.0082 Å to the red, equiv- this complex is really only the superposition, alent to the Doppler effect of a descending or partial superposition of two current on the sun of 0.634 km./sec.

sharp, symmetrical lines. It is self-evident It appears to the author that a spectral line that the apparent center of gravity of such a must rigidly fulfill three conditions, in order complex depends on the length of exposure, to be suitable for use in this work. (1) It etc., while the position of the “peak” of a must show no pressure shift, pole-effect, or micro-photometric curve depends on the relaother variation of frequency with physical tive intensity and position of the component condition of the source (excluding gravita- members of the complex. It is known that tional effects), (2) it must be a single, sharp, the relative intensity of certain series in the symmetrical line, (3) it must, in the solar 3883 band changes with physical conditions, spectrum, be quite free from other “foreign" and there is evidence that their relative lines.

intensity in the sun is different from that in Band lines are used because they seem to the ordinary carbon arc. Hence any apparent fulfill condition (1). In the early work “line” which is really a complex is entirely proper attention was not paid to condition unsuitable for the detection and measurement (3). Grebe and Bachem, by obtaining micro- of so small a shift as that predicted by Einphotometric curves, have attempted to rigidly stein. This is especially true as the solar satisfy condition (3), and in doing so have lines are in absorption, while the arc lines had to discard all but eleven of the 36 lines are in emission. formerly measured by them. But no investi- The author, in his analysis, has identified gators have made an attempt to rigorously many series lines, not previously identified, satisfy condition (2). Now the author, in and by obtaining accurate formulæ for the arriving at a new formula for band series, stronger series, has been able to compute obtained very fine spectrograms of the 3883 “ theoretical” positions for all lines of these band, and made an extended investigation of series, including those entering into comits structure, supplementing the work of plexes. In all cases tested, the actual appearUhler and Patterson. There are a number

ance of the complex was in agreement with of different series in this band (twenty in the theoretical structure thus built up. Also, all, commonly classified as ten series of

many complexes have been recognized which doublets), but without exception the indi

may not previously have been suspected as vidual members of the various twenty series such, and the presence of several extraneous are sharp, symmetrical lines. This is a note

lines in the normal arc spectrum (carbon worthy characteristic of most band series,

lines, but not band lines) has been detected. differentiating them from line series, the

Thus material is at hand for a rigid investimembers of which are all complex, according

gation of the eleven lines finally used by to the Bohr-Sommerfeld theory. Moreover

Grebe and Bachem. The details of this work these latter are quite susceptible to changing

will be published elsewhere. Only the results electrical conditions.

are given here. But the ten doublet series of the 3853 band

Of the eleven lines only two ( 3873.504 5 Zeit. f. Phys., 1, 51, 1920.

and , 3858.822, on the Rowland system) fully 6 Zeit. f. Phys., 2, 415, 1920.

satisfy condition (2). Even this is not 7 Phys. Zeit., 21, 662, 1920. 8 Astro, Jour., 46, 85, 1917; Phys. Rev., 11, 136,

strictly correct, for the two lines are unre1918; 13, 360, 1919.

solved doublets, the 31st and 49th member, 9 Astro. Jour., 42, 434, 1915.

respectively, of the A, series. But the two

components of the doublet (in the case of the and , 3851.427 being accidentally omitted), hundred or so members which can be re- the agreement among different observers is solved) are of exactly equal intensity, and worse than indicated, due to Grebe and therefore it seems safe to assume that the un- Bachem's consistent misquoting of St. John's resolved doublets are at least symmetrical, results, as well as other errors. The correct and to use them. · For 3873.504, Grebe and averages are: G. and B. 0.57, Schwarzschild Bachem obtained a shift of 0.58 km. (average 0.63, St. John 0.17 (or 0.26 using methods of five consistent determinations from differ- a and b only), Evershed and Royds 0.67. ent plates), and Schwarzschild 0.45 km. General weighted average 0.50, or 0.52, using (average of four consistent plates). No other 0.26 for St. John. investigators have used this line. For 3858.- If all eleven lines are used, the averages 822, Grebe and Bachem obtained 0.42 km. become: G. and B. 0.52 (eleven lines), (average of six consistent determinations), Schwarzschild 0.57 (nine lines), St. John St. John 0.40 (average of four different 0.22 (eight lines, or 0.30, two good methods methods, of which only the first two are only), Evershed and Royds 0.67 (two lines). wholly independent and so entitled to the Average (weighted according to the number most weight, these two, a and b, yielding of lines), 0.46, or 0.48, using 0.30 for St. 0.46 km.), Schwarzschild 0.39 km. (average of John. To all these values should be added four readings-three consistent).

0.12 km. to obtain the true rim-arc value. Using the 0.46 km. value of St. John, these It should also be added that, in the author's five determinations for the two lines average opinion, St. John's method (c), and Grebe 0.46 km./sec. In all cases this is the shift and Bachem's recent calculation? of 100 ON between lines radiated by the center of the lines add comparatively little weight to the sun, and by the arc. But St. John (loc. cit.) argument, as they involve the use of Rowand Adams have both obtained reliable evi- land's standards. Since Rowland used both dence that at the center of the sun there is terrestrial and solar wave-lengths, in obtaina rising current of about 0.12 km./sec., com- ing his table of standard lines, the Einstein pared to the rim.10 This tends to mask shift (if real) is hopelessly involved in the the Einstein effect. The true value of this measurements and can not be definitely exeffect, as experimentally determined, is then tricated by any such method as that recently 0.46 +0.12=0.58 km./sec., compared to the used by Grebe and Bachem. theoretical 0.634. While the data are far too

RAYMOND T. BIRGE meager to draw any final conclusions, it is

UNIVERSITY OF CALIFORNIA worthy of notice that the results of all observers are truly consistent on really good A NEW HIGH TEMPERATURE RECORD FOR lines. The great discrepancy between St.

GROWTH John's and Grebe and Bachem's general A RECORD of growth of young joints of a averages has been the puzzling factor, thus prickly pear (Opuntia) at 50° C. and 51.5° C., far. The author believes that he has a partial and of the active elongation of etiolated stems explanation for this, and will present it in a of the same plant growing at 49° C. was publater paper, together with a list of lines which lished in 1917. Previously to that time Dr. are suitable for use, as far as condition (2) is J. M. McGee had found that the mature concerned.

joints of the same Opuntia might reach temIt might be added that, for the nine lines peratures of 55° C. in the open without quoted by Grebe and Bachem), 6 (a 3858.822 damage, which was a record for endurance of 10 Schwarzschild's results indicate a falling cur

the higher plants in air. rent, not a rising, as quoted by Grebe and Bachem,

In the repetition of the growth measurebut are too discordant to have any value. St. ments at the Desert Laboratory late in March, John's are very reliable.

1921, young joints which might reach temperatures of 49° C. in the sun in an unventi- conditions of ventilation and transpiration. lated glass house were heated further by the Readings of 54.5° C. to 55.5o C. were made use of electric grills. Temperatures were for a period of an hour and a half during taken by mercurial thermometers with bulbs which period the elongation was 0.2 mm. or of the clinical type thrust in to joints within near the maximum rate for the species and a few centimeters of the one being measured, was still continuing. One heater was removed but which had equivalent exposure.?

at 12:15 midday and ten minutes later the The elongation of the joints during this joint had fallen to 49.5° C. The cooling had youngest stage is directed by the temperature, resulted in a minute reverse movement of the and the retardations due to maximum night auxograph recording lever of a character transpiration and acidity which come in later which could only be attributed to the conare not yet manifest. The rate of elongation traction of the metal and clay of the setting. therefore is greatest in midday and early The temperature of the joints had fallen to afternoon. Such a joint showing a tempera- 32° C. by 3 P.M. with no noticeable diminution ture by the inserted thermometer of 13.5° C. of the rate, the maximum being taken to lie was subjected to the additional heating of the at some point over 40° C. electric grill at 1:30 P.M. At 2 P.M. the tem- A comparison of the thermometer with perature passed 51° C. with growth still in U. S. Bureau of Standards No. 7618 gave an progress, the rate but little lessened from that

error so small as to be negligible with regard of 1 mm. in 24 hours which it was showing to the above data. Furthermore the young at the beginning of the test. The tempera- joint continued its growth at a rate normal ture was now raised slowly until 3 P.M. the to its developmental stage. joint stood at 51.5° C., the maximum at which These and previously published measuregrowth had ever been observed in any seed ments establish the following points: plant. At 3:10 a temperature of 54.5° C. was 1. Growth in Opuntia may begin at 9° C. reached and five minutes later the readings and extend to 55° C. were 55.5o C. The joint was kept for an 2. Young joints of Opuntia may endure hour between 55° and 55.5o C. during which the maximum of 55° C. observed in mature time the auxograph tracing showed a retarda- joints in midsummer, for periods of an hour tion but not a stoppage of growth. The heat and a half, resuming elongation at lower was shut off, the temperature soon falling to temperatures with no perceptible after-effects. 42° C. and to 19° C. at 9 P.M., when the 3. A new high record for growth in Opuntia record assumed the character of that of the and for the higher plants of 55° C. (131° F.) preceding day of the same joint and of a has been established by these experiments. similar one standing near it.

4. The maximum rate of growth of Opuntia A repetition of the tests was made next day occurs between 37° C. and about 47° 49° C., at 10 A.M. when the joint stood at 33.5° C. under which conditions a biocolloid consistThe heaters were brought into action, the ing of 9 parts agar and 1 part protein underjoint reaching 55° at 10:45 A.M.

goes maximum swelling in water.2 ration stood in the sun and was under normal 5. The cell colloids of Opuntia include a

1 MacDougal, D. T., and H. A. Spoehr, “Growth large proportion of pentosans or mucilages, and Imbibition,” Proc. Amer. Phil. Soc., 56, 289- the colloidal condition of which is in general 352, 1917. McGee, J. M., “The Effect of Position less affected by the temperatures used than upon the Temperature and Dry Weight of Joints

albuminous substances. It is to be noted howof Opuntia,” Carnegie Inst. Wash. Year Book for

ever that bacterial cells, which are highly 1916, p. 73. MacDougal, D. T., “Hydration and

albuminous, may withstand high temperaGrowth,Carnegie Inst. Wash. Pub. 297, 1920. DeVries, H., “Matériaux p. l. connaisance d. 2 MacDougal, D. T., “The Relation of Growth l'influence d. 1 temperature s. 1. plantes,” Arch. and Swelling of Plants and Biocolloids to TemperaNéerlandaises, III., p. 3, 1870.

ture,Proc. Soc. Exper. Biol., 15, 48–50, 1917.

The prepa

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tures, such as those of boiling water. The presence of salts or other compounds may be accountable for the resistance of the proteins to high temperatures.

D. T. MACDOUGAL DESERT LABORATORY,

TUCSON, ARIZONA,

THE AMERICAN MATHEMATICAL

SOCIETY THE two hundred and fourteenth regular meeting of the American Mathematical Society was held at Columbia University, on Saturday, February 26, 1921, extending through the usual morning and afternoon sessions. The attendance included thirty-five members Ex-president H. B. Fine occupied the chair. One hundred and fifteen new members were elected, and twenty-four applications for membership in the society were received.

The council voted to accept the invitation to affiliate with it extended to the society by the American Association for the Advancement of Science,

Professor E. B. Van Vleck was appointed representative of the society in the division of physical sciences of the National Research Council, to succeed Professor H. S. White. The final report of the committee on membership and sales was presented by its chairman, Professor E. R. Hedrick; in all one hundred and thirty-two applications for membership have been received through this very efficient committee. Questions having arisen concerning dues of foreign members, concerning sales and exchanges of publications with foreign societies and libraries, and concerning individual or concerted efforts to aid foreign journals, a committee was appointed by the council to consider these and related problems.

A letter was read to the council from ex-secretary F. N. Cole donating to the society the sum which accompanied the testimonial tendered him at the preceding meeting of the society in recognition of his very distinguished services. It was voted that the council accept the gift and extend to Professor Cole its heartiest appreciation of his generosity; it was further voted that this fund shall constitute, and be designated as, the Cole Fund. A committee was appointed to consider the use to which the income can best be devoted. The council approved the suggestion that the present volume of the society's Bulletin be inscribed to Professor Cole.

A letter of felicitation was sent to Professor Mittag-Leffler, of Stockholm, on the occasion of the seventy-fifth anniversary of his birth.

The following papers were read at this meeting:

Coefficient of the general term in the expansion of a product of polynomials: L. H. RICE.

The mathematical theory of proportional representation, with a substitute for least squares: E. V. HUNTINGTON.

On the apportionment of representatives: F. W. OWENS.

On the polar equation of algebraic curves: ARNOLD EMCH.

Generalization of the concept of invariancy derived from a type of correspondence between functional domains. Second proof of the finiteness of formal binary concomitants modulo p: 0. E. GLENN.

Concerning the sum of a countable number of point sets: R. L. MOORE.

On the simplification of the structure of finite continuous groups with more than one two-parameter invariant subgroup: S. D. ZELDIN,

Periodic functions with a multiplication theorem: J. F. RITT.

Note on equal continuity: J. F. RITT.

Expressions for the Bernoulli function of order p: I. J. SCHWATT.

The expansion of a continued product: I. J. SCHWATT.

Method for the summation of a family of series: I. J. SCHWATT.

Note on the evaluation of a definite integral: I. J. SCHWATT.

A property of the Pellian equation with some results derived from it: JOHN MCDONNELL.

A necessary and sufficient condition that the sum of two bounded, closed and connected point sets should disconnect a plane: ANNA M. MUL

LIKIN.

Some empirical formulas in ballistics : T. H. GRONWALL.

Summation of a double series: T. H. GRONWALL.

A geometrical characterization of the paths of particles in the gravitational field of a mass at rest: L. P. EISENHART.

The equations of interior ballistics: A, A. BEN

NETT.

The next meetings of the society will be at Chicago on March 25 and 26, and at New York, in April,

R. G. D. RICHARDSON,

Secretary

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