ican mathematicians were among his students and later helped to develop in our country a deep and abiding interest in mathematical research. The lectures which constitute the present volume were given at is home to a small number of students during a period of about five years, and he had expected to revise them and then publish them as his last mathematical contribution. On account of illness he could not do this and therefore the present volume was prepared for the press by those who were entrusted with his unpublished papers. Fortunately the editors decided to make no important changes so that we have here the words of a mathematical statesman which should interest not only mathematicians but also others who are interested in the great cultural forces of our age.

The headings of the eight chapters into which the present volume is divided are as follows: Gauss; France and the École Polytechnique in the first decades of the nineteenth century; the establishment of Crelle's Journal and the blooming of pure mathematics in Germany; the development of algebraic geometry beyond Moebius, Plücker and Steiner; mechanics and mathematical physics in Germany and England until about 1880; the general theory of functions of complex variables by Riemann and Weierstrass; deeper insight into the essence of algebraic forms; group theory and function theory, especially automorphic functions.

These headings represent fundamental centers in the remarkable development of mathematics during the nineteenth century. They also point to the fact that Klein naturally emphasized the history of those developments in which he either took part or which are closely related to the subjects which he helped to advance. In particular, the theory of numbers, algebra and the theory of aggregates received relatively too little attention. This lack of completeness is, however, compensated by the confidence inspired by one who speaks about the history of a subject on which he himself is an authority. While some attention is paid to biographical sketches and other matters which are not strictly mathematical we find here also some of the most profound and far-reaching mathematical observations. The commanding but attractive personality of the author is exhibited in many places, and his unusually wide personal acquaintance with leading mathematicians and with their most important contributions adds greatly to the value of the work. As an instance of the type of some personal remarks we may note that in speaking about H. Poincaré it is noted on page 375 that he did not enter the field of applied mathematics in the proper sense of this term and hence his contributions may be regarded as some

SCIENTIFIC APPARATUS AND

LABORATORY METHODS

SYNTHETIC RESIN AS A MOUNTING
MEDIUM

IN the issue of SCIENCE for January 14, 1927, announcement was made of a new synthetic resin possessing physical and optical properties which made it particularly useful in microscopy. Having had experience with other compounds which at first seemed promising, yet later spoiled for one reason or another, the only doubt I had or expressed at the time the above-mentioned article was prepared concerned the stability of the product. It was first made on October 6, 1926, and a part of the original sample, as well as slides mounted therefrom, is in perfect condition on April 1, 1927. Evidently, the resin can be depended upon to keep unchanged for a period of many months; we have no reason to suspect that it will ever change.

In fluid form, this material has a refractive index of close to 1.70 for yellow light, and when hardened on the slide, it approaches 1.80, the exact figure not yet having been determined because it is far above the scale of any available refractometer.

A great deal of interest in this material has been shown by microscopists in many parts of the world as a result of the preliminary announcement in SCIENCE, and if the inquiries I have received can be used as a basis for forming an opinion, it certainly appears that there is a real desire in many branches for a better material than Canada balsam for a mounting medium.

For the benefit of all interested workers, I want to explain that I have developed the technique of handling the resin, only in the mounting of diatoms. It is so superior to other known resins for this purpose that one is tempted to call it ideal.

Whether methods of using it in other branches of microscopy can be developed or not remains to be determined by experiment. Thus far the best solvent we have found is aniline, but this does not necessarily mean that the last stage before mounting a preparation should consist of clearing in the solvent. Aniline is not very volatile; consequently a more protracted or higher temperature is needed to bring the resin to brittle hardness under the cover than would be the case could xylol or benzol be used as solvent. The hardened slides do not show a tendency to lose their

covers by chipping. Improvement in methods of manufacture are expected to produce a material with a greatly reduced yellow color, but it is not likely to ever be water-white. The experienced microscopist will readily detect the ease with which transmission of the green ray for which most objectives are corrected is effected.

Upon heating, the material becomes so fluid it readily passes through filter papers and this property makes it very superior in diatom-work because of the freedom of the slides of bubbles. Its high index of refraction is its most valuable property, of course, and it should make chitinous structures, such as insects, crustaceans, etc., readily visible without staining.

ings. A representative portion of one of the experiments is given in the accompanying table. This will give an idea of the responsiveness of the test. The refractive index tends to increase in inverse proportion to the vigor of the seedlings. When the refractive indices (x) are correlated with the seedling characters (y) of the entire series of 116 ears in this particular experiment, ry = .592.041 when y = per cent. germination; ry=.360.055, when y = height of seedling; and ry=.343.055 when y = green weight. Higher correlations have been obtained in other series.

Experiments are still in progress by the chemists, L. A. Penn and Paul Ruedrich, of Berkeley, California, in order to determine the best method of preparation of the resin and the chemical reactions involved. G. DALLAS HANNA CALIFORNIA ACADEMY OF SCIENCES, SAN FRANCISCO, CALIF.

Refractive

index

(Std. 30 germi- height greenweight

(mm)

(gm)

DURING the course of certain experiments with a large number of samples of sweet corn, it became essential to determine with a minimum of time and effort the relation between vigor and the condition of the distilled water in which it had been soaked. Some years ago, when the question of the toxicity of distilled water was under discussion, evidence was presented that the injurious effect produced on seedlings grown in distilled water was at least partially due to the extraction of electrolytes from the roots. These determinations were made in several instances by means of conductivity measurements. Apparently none of the investigators attempted to measure the effect of distilled water on dormant seeds. A number of experiments were undertaken along this line, but the Abbé refractometer was used instead of the hydrogen-ion concentration as the means of determining the relative quantities of solids leached from the seeds. The method is extremely simple, consisting merely of soaking 5 or 10 gm of seed in 50 cc of distilled water in well-stoppered bottles for fortyeight to seventy-two hours at a temperature of 30° C. Two or three drops of the liquid are all that is required for the reading. In order to check the test thousands of readings were taken of distilled water in which sweet corn seed had been immersed. In nearly all cases duplicate samples from the same ear were planted on the greenhouse bench and the growth of the seedlings compared with the instrument read

Early in the experiments it became apparent that high refractive indices were accompanied by the presence of dense suspensions of colloids. Upon reading these with a Leitz nephelometer it was at once apparent that in many respects the colloidal index of the leachings is superior to the refractive index as a messure of the potential vigor in sweet corn. The colloidal indices in the above table are typical. The standard used in these experiments consisted of 0.5 per cent. c.p. soluble starch dissolved in 0.5 per cent. sodium toluene para sulphochloramid.

=

It should be noted that the coefficients of correlation for the entire series are even higher than for the refractive indices. The values are r,, = .634.037 when y per cent. germination; ry=.680.034 when y height of seedlings; and r,, .693 ± .033 when y = green weight. The correlation between the refractive and colloidal indices is rxy = .713 ± .015. A considerable tendency exists for the coefficients of correlation to increase inversely as the percentage of germination in the case of the colloidal index. This is illustrated by the following:

SPECIAL ARTICLES EXCYSTATION IN VITRO OF HUMAN INTESTINAL PROTOZOA1

FOR many years it was believed that the cysts of intestinal protozoa would not excyst until subjected to the digestive juices peculiar to the normal host of the species. Recent experimental work, however, indicates that moisture and a temperature of about 37° C. for several hours are the only factors necessary to stimulate excystation in the intestinal protozoa of man. Darling2 (1913) noted the disappearance of cysts and the appearance of trophozoites in feces containing cysts of Endamoeba histolytica that were kept in a moist chamber. It is not at all certain, however, that the trophozoites observed came from the cysts, since amoebae of other species often appear in fecal material kept under similar conditions. Yorke and Adams3 (1926) observed the process of excystation in this species; Allen* (1926) describes

1 From the Laboratory of Protozoology, Johns Hopkins School of Hygiene and Public Health. The writer is greatly indebted to Mr. Conrad Bauer for his valuable assistance.

2 Darling, S. T., 1913. "Observations on the cyst of Entamoeba tetragena." Archiv. Int. Med., 11: 1-14.

3 Yorke, W. and Adams, A., 1926. "Observations on Entamoeba histolytica. I. Development of cysts, excystation and development of excysted amoebae, in vitro.'' Ann. Trop. Med. and Parasit., 20: 279-302.

4 Allen, E. A., 1926. "Excystment of Councilmania lafleuri Kofoid and Swezy in culture in vitro." Univ. Cal. Pub. Zool., 29: 175-178.

what she believes to have been excystation in the form named by Kofoid and Swezys (1921) Councilmania lafleuri; and Smith (1927) has observed, and shown to the writer, excystation in Iodamoeba williamsi. The writer is now able to add to this list Endamoeba coli, Endolimax nana and the flagellate Chilomastix mesnili; he has also observed early stages of what appears to be excystation in vitro in Giardia lamblia. The other intestinal protozoa of man are Trichomonas hominis and Endamoeba gingivalis, which have no cyst stage, and Embadomonas intestinalis, Tricercomonas intestinalis and Dientamoeba fragilis, which are rare species not easily obtained for study.

Endamoeba histolytica. Excystation in vitro in this species has been described by Yorke and Adams (1926). Material containing cysts was sealed under a cover glass and examined in a warm microscope chamber. Pseudopodia were formed inside of the cyst; then a break appeared in the cyst wall through which the amoeba escaped. Moisture and a temperature of about 37° C. seemed to be the essential factors in excystation. Cysts that had been in Locke-eggserum medium at 37° C. for two hours proved more satisfactory than unincubated specimens.

Councilmania lafleuri. Allen (1926) saw what she believed to be the last of eight amoebulae to escape from the cyst wall of this species. According to her observations the entire amoeba does not leave the cyst, but the eight amoebulae into which it divides pass out one by one through a pore in the cyst wall.

Iodamoeba williamsi. Excystation in this species has been observed by Septima C. Smith (1927). She found that cysts fifteen hours old, when placed in an incubator at 37° C. for two hours and then in a warm chamber at about 40° C. for three hours, would excyst in a saline medium. Minute pseudopodia were noted within the cyst; then followed a break in the wall and the escape of the amoeba. In some cases the amoeba emerged part way and then returned, escaping only after several passages back and forth. The newly excysted organisms were very active. She concluded that the stimuli necessary for excystation are moisture and a temperature of about 37° C. for several hours.

5 Kofoid, C. A. and Swezy, O., 1921. “On the free, encysted and budding stages of Councilmania lafleuri, a parasitic amoeba of the human intestine." Univ. Cal. Pub. Zool., 20: 169-198.

6 Smith, Septima C., 1927. "Excystation in Iodamoeba williamsi in vivo and in vitro." SCIENCE, 65: 69-70.

7 Hegner, Robert, 1927. "Excystation and infection in the rat with Giardia lamblia from man." Amer. Journ. Hyg. (in press).

Endamoeba coli. Excystation of E. coli was observed many times by the writer in material obtained by washing infected feces in water. This material either in water or in weak saline solution was sealed under a cover glass and placed on the stage of a microscope confined in a warm chamber. The protoplasm within the cyst is at first finely granular and the eight nuclei are usually clearly visible, but later the nuclei become invisible and a number of larger granules of various sizes appear. The first evidence of activity preceding excystation is the movement of the cytoplasm in the center of the cyst. No large free area exists between the cyst contents and the cyst wall such as described by Smith (1927) in Iodamoeba williamsi. Pseudopodia first appear through an opening in the cyst wall. This opening is small and the protoplasm streams through it rapidly in a thin strand. The amoeba does not leave the cyst wall at once, but usually, after from one half to three fourths of the protoplasm has escaped, movement begins in the opposite direction and most or all of the animal streams back again into the cyst. This egress and return of the protoplasm may occur as often as ten times before complete escape is effected and the liberated amoeba moves away from the deserted cyst wall.

After excystation the amoeba moves at first slowly but soon flows across the field by means of rapidly forming pseudopodia. These pseudopodia are somewhat similar to those of E. histolytica, being formed rapidly and more or less explosively and being at first free from granules although not so clear and hyaline as those of E. histolytica. In every case the entire contents of the cyst emerged as a single amoeba. Excysted amoebae were watched for more than six hours, but no division stages were observed.

Endolimax nana. Excystation could not be studied as easily in Endolimax nana as in Endamoeba coli because of its minute size. So far as could be observed, however, the process was similar in every respect. The first evidence of activity was movement in the cytoplasm; this was followed by a minute break in the cyst wall through which the cytoplasm protruded; then after flowing in and out several times the organism separated from the cyst wall as a single amoeba.

Chilomastix mesnili. Excystation of this flagellate was seen in only one case. The details were not clearly made out, but the essential features were observed. Movement of the protoplasm within the cyst was followed by a break in the wall at the anterior end and the rapid emergence of the organism, which soon took on approximately the shape of a typical trophozoite. One large cystostome was pres

ent. Whether the excysted specimen contained one or two nuclei was not determined. In this case the cyst was in a saline medium and excystation occurred after three hours and forty minutes at about 37° C.

Giardia lamblia. Complete excystation of Giardia lamblia in vitro has not been observed, but movement within the cyst can be brought about by the same method as that shown to be effective with other protozoa. Washed cysts from two to four days old were used. Material was sealed under a cover glass and kept in an incubator at 37° C. for two hours; it was then placed on the stage of a microscope in a warm chamber at approximately 39° C. Within from ten to fifteen minutes movement began in some of the cysts. The contents seemed to contract and expand, due probably to bending movements of the axostyle such as were observed in cysts recovered from the small intestine of the rat (Hegner, 1927). The protoplasm of the organism was seen to shrink away from the cyst wall and after from one to four hours became quiescent.

It seems safe to conclude from these observations that, as suggested above, moisture and a favorable temperature (about 37° C.) for a sufficient period (several hours) are the essential factors in excystation. It, therefore, follows that the digestive juices of the host that ingests the cysts of intestinal protozoa are unnecessary in bringing about excystation. They may be helpful, but on the other hand it is possible that they are harmful. If the latter is true, then the cyst wall probably protects the cysts from the secretions encountered in the stomach. In this connection it may be noted that no excystation nor protoplasmic movements were observed within the cysts of Giardia lamblia that were injected into the stomach of the rat, although cysts hatched in the small intestine of this animal (Hegner, 1927). Fur ther details of excystation in these intestinal protozos will be published in a later communication.

THE JOHNS HOPKINS SCHOOL

OF HYGIENE AND PUBLIC HEALTH

ROBERT HEGNER

ISOTOPES OF CALCIUM

THE writer has recently studied the selective reflection of several carbonates at about 6.5 microns. Polarized light was used so that bands due to vibrations along the different directions in the crystal would not be superimposed. In the case of calcite (CaCO3) three small maxima were observed. The wave lengths were 6.36 μ, 6.54 μ, and 6.62 μ. When several bands overlap, it is difficult to calculate the true intensity of the separate bands as there is no zero line of reference. However, using the band at 6.54 μ as the standard, the band at 6.36 μ is about

one twentieth as intense; also, the band at 6.62 μ is about one fifth as intense as the band at 6.54 μ. So it is likely that calcium is made up of isotopes with atomic weights of 39, 40 and 44 and of quantities in the ratio of one fifth, one, one twentieth, respectively. The atomic weights given would have the approximate separation as found for the bands and these atomic weights with the quantities named would give a mean atomic weight about 40. It is interesting to note that calcium has been studied for isotopes by Dempster, Aston2 and G. P. Thomson. Dempster found points which correspond to 40 and 44 and another set of points which correspond to atomic weight 39. However, he considered the 39 as due to potassium, which likely occurred as an impurity. Aston also studied calcium, but due to the fact that it did not produce anode rays easily, he did not find a line for calcium of atomic weight 44. Aston carefully excluded potassium from the mixture, but the line corresponding to atomic weight 39 was more intense than the 40 line. So the line at 39 was possibly a mixture of potassium and calcium. G. P. Thomson's work on calcium gives a broad line at 40 which was not resolved by his instrument. However, he states that there must be another line at 39 or 41 making calcium an isobar with potassium. So it is likely that calcium has an isotope of atomic weight 39. In addition to the above facts it appears that it would have been very difficult to detect the isotope of atomic weight 44 if the intensity were only one seventieth of that of atomic weight 40. It could not have been observed by the method of band spectra used by the writer. It seems probable, therefore, that the isotope Ca is present to a greater extent than one seventieth and that a mean atomic weight of 40.07 is made possible by the presence of Ca39.

UNIVERSITY OF NORTH CAROLINA

E. K. PLYLER

A PRE-CHATTANOOGA SINK HOLE1 THE Chattanooga shale is locally five to seven times the thickness generally observed in the region of the Gainesboro, Tennessee, quadrangle. This fifteen-minute quadrangle, ten miles south of the TennesseeKentucky line, was mapped by the Topographical Branch of the United States Geological Survey in 1925. Through it the Cumberland River swings in entrenched meanders four hundred feet below the

1 Physical Rev., 18, 421, 1921.

2 Aston, "Isotopes," p. 101.

& Phil. Mag., 42, 857, 1921.

1 Printed with the permission of the state geologist of Tennessee.

level of the dissected Highland Rim Plateau.2 The Fort Payne formation of lower Mississippian age is at the surface of the plateau throughout the area. Beneath the Fort Payne a green shale, varying in thickness from a few inches to one or two score feet, lies upon the Chattanooga shale. The Leipers, Catheys and Cannon strata of Ordovician age, together four hundred feet thick, are separated from the Chattanooga shale by a disconformity. The rocks of the region are gently arched in a northeastern extension of the Nashville Dome.

The writer spent three and a half months of the 1926 field season mapping the areal geology and structure of the Gainesboro quadrangle for the State Geological Survey of Tennessee. An interesting result of the summer's work was the discovery of an extraordinary local thickness of the Chattanooga shale. This body of shale is generally ten to fifty feet thick in the Nashville Basin and adjacent areas. According to general observation, the thickness does not vary more than five or ten feet in many miles.3 The writer found the thickness to exceed 149 feet on Flynn Creek, five miles south of Gainesboro. The shale is exposed in several places in the vicinity with seventy-five or ninety feet of strata visible in a continuous outcrop. It lies in an irregular closed depression or series of depressions in a limestone conglomerate-breccia which is at the same altitude as Leipers, Catheys and Cannon strata. The actual contact of the breccia with formations other than the shale was not seen. Some of the blocks in the breccia contain fossils common to the Leipers and Catheys, but the fossils do not determine with certainty the formations from which the blocks were derived. Some of the blocks differ in lithology from the preChattanooga strata heretofore observed in this general area. It is possible that a detailed and thorough study of all the blocks might yield information which would partially close the hiatus between the Leipers and Chattanooga deposits. The breccia is more than one hundred feet thick in some places.

2 Purdue, A. H., "General Oil and Gas Conditions of the Highland Rim Area in Tennessee," Resources of Tenn., Vol. 7, No. 4, pp. 220-228. 1917.

3 Butts, Chas., "Geology and Oil Possibilities of the Northern Part of Overton County, Tennessee, and of Adjoining Parts of Clay, Pickett and Fentress Counties,' Tenn. State Geol. Survey Bull., 24, pt. 2-A. 1919. Hayes, C. Willard, and Ulrich, O., U. S. Geol. Survey Geol. Atlas, Columbia folio (No. 95). 1903. Mather, Kirtley F., "Oil and Gas Resources of the Northeastern Part of Sumner County, Tennessee,'' Tenn. State Geol. Surv. Bull. 24, pt. 2-B. 1920. Miser, Hugh D., "Mineral Resources of the Waynesboro Quadrangle, Tennessee, "Tenn. State Geol. Survey Bull. 26. 1921.