HOW MANY FIGURES ARE SIGNIFICANT?

THE readers of SCIENCE are aware that varying practices are followed by the workers in the natural and social sciences regarding the number of decimal places kept and reported in their investigations. A definite and uniform practice would conduce to general understanding. Discussions with my colleagues regarding certain quantitative studies of my own which promised to be serious and worth-while have become mired around the decimal point. As a result of this I have determined upon a rule for my personal guidance which I believe may be of general utility.

Determine the probable error of the measure involved, by statistical means if possible, otherwise estimate it. Keep to the place indicated by the first figure of 1⁄2 the probable error.

As an illustration, suppose we calculate the mean and standard deviation of a certain series and find:

lation coefficient of .75248 from a population of 400. Its probable error, according to the usual formula, is .0146. One half the probable error equals .0073. Accordingly, the correlation coefficient should be published as equal of .752.

The argument underlying this rule is that one should not throw away data that are likely to inAuence judgment. A difference of 1 probable error indicates that the chances are 3 to 1 that the difference is of the sign indicated. This is scant evidence of significance but not entirely meaningless. A difference of one half of the probable error indicates that the chances are about 5 to 3 that the difference is of the sign indicated. For ordinary purposes this is of insignificant moment. Failure to keep more figures introduces a slight error, but keeping them introduces a much greater error in interpretation by suggesting an accuracy which does not exist. It is necessary to strike a balance and the rule suggested is offered as a reasonable compromise.

It is intended that it be applied to raw or original measures or observations as well as to derived constants such as averages, measures of variability, etc. It is to be expected that computation work preceding publication will be carried to at least one figure further than the final published result.

STANFORD UNIVERSITY

TRUMAN L. KELLEY

OPPORTUNITIES FOR SCIENCE TEACHERS IN NEW YORK HIGH SCHOOLS

A LETTER requesting information regarding oppor tunities for science teachers in the high schools of New York City was received by the writer some months ago from an associate professor in a large collegiate institution east of the Mississippi. The information furnished may be of interest to others and is outlined below. There is a real opportunity for important work, both in science education and in supplementary graduate work in science.

(1) There has been for some years a shortage of well-qualified teachers, especially of men for the boys' high schools. Three successive examinations in biology netted not more than three or four successful candidates, who were immediately appointed.

(2) The population of the New York City high schools stands at present at one hundred and ten thousand, and increases by thousands every year. All these ought to have several courses in science, and it appears that recognition of this fact is growing on the part of the administrative officials, and science work is entering a floodtide. At present between four and five hundred specially selected science teachers are required to offer the courses now given. (3) The salary of the regular high school teacher,

called "assistant teacher," ranges from nineteen hundred to thirty-seven hundred dollars. Credit is given in the initial salary for recognized outside teaching experience and graduate work. By a further examination for the license of "first assistant," a progression to forty-two hundred dollars is possible, with administrative duties as chairman of department. Such departments range in size from two or three to forty teachers. High schools range from one to eight thousand pupils. At the last count there were thirty-five secondary schools ranked as high schools, with more new ones in prospect.

(4) Opportunities for continued graduate work and research are probably not equalled or even approached elsewhere in the country. The educational problems constitute an intensely interesting and important field of work in themselves, and New York is headquarters for more kinds of pure and applied scientific research than anywhere else. The universities, professional schools, libraries, science foundations, botanic gardens, museums, industrial establishments, et al., all offer problems by the score, with facilities for the qualified investigator. For those who have not finished graduate study toward a degree, the universities offer important graduate courses on Saturdays.

(5) Full details regarding the stated examinations, etc., may be obtained by addressing the Board of Examiners, 500 Park Ave., New York City. Following are paragraphs taken from their circular of information, and giving some of the facts a prospective candidate for the examination would be interested to know.

(a) Teaching positions in New York City are secured by competitive examination, å part of which is written. These examinations usually held twice a year, in November or December, and in March or April, usually at a time when the New York City public schools are not in session.

College graduation and one year's teaching experience, or, in lieu of teaching experience, one year of postgraduate work which must include 60 hours in the methods of teaching the subject.

(b) It takes nearly a year for examiners to make proper evaluation of the candidates' references, scholarship and records of service so that persons applying for New York City positions who take the examination should not look for appointment any earlier than one year from the date of the written examination.

Copies of the last written examination question paper may be obtained, while they last, from the Board of Examiners, 500 Park Avenue, New York, upon request, en closing a stamped and self-addressed envelope.

STUYVESANT HIGH SCHOOL AND BROOKLYN BOTANIC GARDEN

RALPH C. BENEDICT

Instead of using a piece of iron pipe for the tank a heavy glass jar can be used, provided the pressure is not run too high. In an apparatus of this kind, described in detail by the writer in the April, 1914, issue of the Proceedings of the Society of American Foresters, a pressure of 30 pounds per square inch can safely be used.

The great advantage of the glass jar is, of course, that the material can be observed without opening the chamber. Hence, certain obvious precautions can be taken against too rapid release of pressure and attendant bubbling over of the celloidin or the celloidin becoming too low on account of an insufficient original supply.

The writer has also found that woody material can be satisfactorily imbedded by the pressure method. by using only a 10 per cent. solution of celloidin, provided a liberal supply is used to begin with. Thus, one avoids the necessity of any transfer of material to a higher concentration. Another way of hastening the process with tissues that can endure higher temperatures is to heat and cool the chamber alternately at intervals of several hours. The increased pressure should be applied particularly while the celloidin is cooling, so as to secure penetration into the cell cavities while the gases are contracting and condensing within.

FOREST PRODUCTS LABORATORY, MADISON, WISCONSIN

ARTHUR KOEHLER

A CURIOUS SURGICAL CASE

I HAVE received from Mr. Nisuke Takahasi, a teacher in a high school in Kumamoto, Japan, a specimen of a fish somewhat noted in Japanese surgery.

It is a fish two and four fifth inches (7.0 cm) long taken from a man's throat, in which it had become lodged. The specimen concerned is a common fresh water fish of the clear streams of Southern Japan, locally known as Oyarami or Kawamebaru, very closely related in fact as well as in appearance to some of our American freshwater sun-fishes (Centrarchidae). Its scientific name is Bryttosus kawamebari (Schlegel).

The specimen is virtually perfect, although apparently somewhat emaciated. How it was swallowed is not explained, but it is evident that its sharp dorsal spines would hold it in place once swallowed. The specimen was presented to Stanford University by Dr. Toyoji Nishiyama, of the Municipal Hospital at Kuverme, at the suggestion of Dr. Chiyomatsu Ishikawa, of the Imperial University of Tokyo. DAVID STARR JORDAN

STANFORD UNIVERSITY

SCIENTIFIC BOOKS

Human Origins, a Manual of Prehistory. By GEORGE GRANT MACCURDY, Ph.D. Vol. I, The Old Stone Age and the Dawn of Man and his Arts, 440 pages; Vol. II, The New Stone Age and the Ages of Bronze and Iron, 516 pages. D. Appleton and Company, New York.

A READER whose interest in the prehistoric archeology and ethnology of Europe is professional will scrutinize the qualifications of the author of any work on this subject before turning over the pages of the work itself. Such a reader will desire to know whether or not the author has a first-hand knowledge of his subject. What experience has he had in the excavation of archeological sites? Does he know the collections of prehistoric material in European museums? Is he competent to pronounce upon geological and paleontological questions? Is he a physical anthropologist? Unless he is satisfied with the qualifications of the author, the worker in the field of knowledge dealt with will decline to give serious consideration to his writings.

In the present instance the reader may proceed to the perusal of "Human Origins" with complete confidence that it is the output of a competent scientist writing within the field of his own special knowledge and experience. Dr. MacCurdy has been trained in the methods of European prehistoric archeology and in the technique of physical anthropology by the foremost Continental authorities in these subjects. For many years he himself has conducted excavations in prehistoric European sites; his writings have furnished American anthropologists with the latest information on progress of the science in Europe; he is one of the two or three Americans who are recognized abroad as authorities on European prehistoric archeology. Further, he brings to bear upon European questions his extensive experience in the archeology and physical anthropology of the New World.

To a teacher of European prehistory the outstanding merit of Dr. MacCurdy's work is its comprehensiveness. It deals with the entire prehistoric period. It does not leave the reader stranded on a terminal

moraine in the company of fossil men, extinct animals and chipped stone implements. With the exception of Déchelette's great work ("Manuel d'archéologie préhistorique, Celtique et Gallo-Romaine”), now somewhat out-of-date, "Human Origins" is the one satisfactory attempt to carry the prehistory of man in Europe through to the present era in an adequately detailed treatment.

The first volume deals with the Old Stone Age and fossil man. Here Dr. MacCurdy is at his best. Climatic and geographical conditions, prehistoric chronology, types of fossil men and animals, industries and arts of the various archeological periods-all these subjects are thoroughly discussed, but with due regard for their relative importance. A disproportionate amount of space is not allotted to any particular feature. MacCurdy does not build his book upon some one aspect of prehistory, subordinating all other subjects to that of his own specialized knowledge and interest. A few crucial points in this volume should be noted. The author accepts the Foxhall eoliths of the Pliocene period; he assigns the Acheulian industry to the Rissian glaciation and places the beginning of the Mousterian industry in the third interglacial (Riss-Würm) period; he regards the Piltdown mandible as human, but is not certain that it belongs with the associated brain-case fragments. The section on fossil man is concise but complete. In the opinion of the reviewer, Dr. MaeCurdy does not sufficiently consider the evidence pointing toward the existence of an essentially modern type of man in the Lower Paleolithic Age.

The second volume is devoted to the Mesolithie, Neolithic, Iron and Bronze Ages and to valuable appendices dealing with, the stratigraphy of paleolithic sites and with the distribution of paleolithic art and of prehistoric monuments. Appreciation of the inclusion in this work of a summary of the early metal periods has already been expressed. What the author has to say of the Bronze and Iron Ages is, so far as it goes, excellent. But of the 918 pages of text, plates and bibliography included in the two volumes, only 52 pages are devoted to the Bronze Age, and the Iron Ages are crowded into 71 pages. Yet from the historical, ethnological or archeological viewpoints these are the most important periods of European prehistory. Fossil man is accorded 136 pages of discussion and recent man receives a scant 7 pages. There is no adequate treatment of late prehistoric and proto-historic racial movements. The reviewer does not cavil at the thorough and detailed treatment of the Paleolithic Age to which Dr. MacCurdy has devoted the bulk of his work. He only regrets that the author did not extend his treatise sufficiently to satisfy also the acute academic need

for a full discussion of the later periods. Civilization, after all, is cumulative and the nearer the archeologist approaches to the historical period the more extensive his material becomes and the more numerous and vital are the problems which he must endeavor to solve.

"Human Origins" is the most useful manual of prehistory available to readers of English. It surpasses the work of Déchelette in its superior grasp of problems of physical anthropology. The illustrations of MacCurdy's work are also more numerous and better. The classical French work is, however, better balanced. The scant notice accorded to the archeology of the Eastern Mediterranean area is less excusable in a general manual of prehistory than in a work primarily concerned with the archeology of France. But, without a doubt, students of prehistory are to be congratulated upon the publication of this scholarly treatise which is the work of no amateur but of a dependable authority.

HARVARD UNIVERSITY

E. A. HOOTON

SPECIAL ARTICLES

ELECTRIC TRANSPORT OF FLUID ACROSS MAMMALIAN SEROUS MEMBRANES EXPERIMENTS performed during the past year have shown that the serosae of mammals are amphoteric membranes. If the membrane is bathed in dilute blood or buffer more alkaline than a certain critical hydrogen-ion concentration and traversed by an electric current, the liquid streams through the membrane toward the cathode. With buffers more acid than the reversal point, streaming is toward the anode. reversal in sign of the electrokinetic potential difference1 between the membrane pore walls and the liquid in the pores is thus indicated.

A

The mesenteries of anesthetized living dogs, cats and rabbits, the mesenteries and parietal pericardia and pleurae of the same species, post-mortem, and two human pericardia, post-mortem, have thus far been tested. These membranes are essentially sheets of connective tissue, bearing blood vessels, lymphatics and nerves, and in some instances, fat cells, lined on each surface by a single layer of pavement mesothelial cells. Intercellular fibers form the major bulk of the lean membranes; these are predominantly collagenous except in the pleural sheet between pericardium and diaphragm where elastin fibers may be present in large proportion.

The reversal point of a complex, amphoteric membrane may be defined as that concentration of H-ions

1 Freundlich, H., and Gyemant, A., Ztschr. f. physik. Chem., 1922, c, 182.

in a given solution within the pores of the membrane, traversed by an electric current, at which the total electroendosmotic current through the membrane is

zero.

=

The mean values of the reversal points with citratephosphate buffers for all tissues studied have been between pH 4.3 and pH = 5.3. By using buffers alternately more acid or alkaline than the reversal point the direction of liquid flow across any given membrane site may be reversed an indefinite number of times. The time interval required is only that taken for the requisite manipulation in changing buffers and making the runs.

The buffers used have been dilutions of McIlvaine's2 citric acid-sodium phosphate mixture and certain isotonic, physiologically balanced buffers. The latter were citrate-phosphate mixtures containing Na, K and Ca in the proportion of Ringer's solution, and made isotonic by the addition of glucose or of glycerin. The glycerin buffer was found preferable. The mean values of the reversal points for the several membranes when bathed in the hyptonic unbalanced buffer and in the isotonic, physiologically balanced buffers showed only small and inconstant differences.

The fat and lean membranes in each category similarly showed small if any difference in the positions of the mean reversal points.

The apparent reversal points for the mesenteries of living animals proved to be lower than those for the mesenteries post-mortem. This low value in the animals with functioning circulation has been ininterpreted as essentially due to admixture with the buffers of buffer salts from the blood. Distinct differences have not been detected between the reversal points of the membranes in the first compared with later hours or days post-mortem, with the possible exception of a small shift toward the acid range of the fat pericardia reversal points when tested several days post-mortem.

=

The approximate mean reversal points found with the citrate-phosphate buffers were as follows: for mesenteries of living animals, pH 4.4; for pleurae, post-mortem, pH = 4.6; for mesenteries, post-mortem, pH = 4.8; for lean and fat pericardia, postmortem, pH = 5.1. The mean reversal point estimated for the human pericardia was about pH = 5.0. The concentration of hydrogen-ions requisite for reversal of the membranes with these buffers containing polyvalent anions is greater than with an acetate buffer.

The ready reversibility of the membranes would seem to indicate that their charging, i.e., electrokinetic p. d., is ultimately dependent largely upon the dis

2 McIlvaine, T. C., J. Biol. Chem., 1921, xlix, 183.

SELACHIAN "DENTICLES" IN THE CAT1

It is now well known that the human lips at birth possess an inner zone beset with "long, soft, villus-like outgrowths." In a few weeks, these villi largely disappear, though the zone itself remains more or less distinctly marked throughout life. Denuded of their epithelium, Ruysch figured them as "papillae," in 1707. Luschka (1863) was the first to describe them with modern precision, and since then they have been the subject of important studies by Neustätter, Stieda, Ramm and others. The portion of the lip which bears the villi is clearly distinguishable to the naked eye, and the individual projections, with their vascular cores, may be seen on low magnification. Neustätter, in 1895, remarked that so far as his investigations showed, human lips alone are provided with this double zone- -the outer of which is smooth, and the inner, villous-and he rather fantastically ascribed the condition to the shortness of the nipples and flatness of the central area of the breasts in

women.

Thus human infants require a special "Greifapparat" for an airtight contact!

Rejecting this interpretation-of "non-skid" lips, as his assistant called them—and after reviewing the literature in the way here outlined, Dr. F. T. Lewis proposed a different interpretation (Buffalo meeting of the American Association of Anatomists, April 16, 1924). He showed photographs of the labial "villi" in man, and others of the teeth of the skate, both intact and in sections, and proposed to regard them as homologous structures. That is to say, he considered the human labial villi, notwithstanding their small size, their tendency to point outward and their lack of dentine, as actual denticles or potential selachian teeth. In the human oral region, then, in addition to the gill clefts, there would be another striking suggestion of the ichthyoid plan of develop

ment.

The present account is intended to report the finding of bilaterally arranged papilliform structures on

1 A study conducted as Medical Fellow of the National Research Council.

the inner surface of the upper lip in the newborn kitten. These are very clearly the equivalents of the villi or denticles of the human lip, though the inner zone which they form is not exposed at the oral margin; they are wholly within the lips.

On the upper lip of the kitten they are arranged in three groups in the specimens studied-a median group, and on either side, a lateral group.

The median group consists of a single row of four large incisor-like papillae, which might possibly be mistaken for teeth, but the well-defined dental ridge is further within the mouth, and these papillae have no connection with it. Of these four papillae those next the midline are the largest and measure 1.0 mm in height by 0.75 mm in width at the base. They are flattened in the same plane as the human incisors. Their free margins are somewhat rounded and are without serrations. The lateral members of this group are very similar though a little smaller.

On either side of the median group is a lateral group of from twenty to thirty smaller papillae, bluntly conical in shape and arranged in poorly defined rows. Those in one row may partially overlap the units in the next row. These papillae do not stand erect, but their tips are turned somewhat forward and toward the median line. Beyond the lateral groups, in the direction of the corners of the mouth, a portion of the lip is quite smooth.

The papillae in all the groups consist of connective tissue cores covered with a very thick epithelium, much thicker than the epidermis. In these respects they are like the papillae of the human lips, but they are neither so slender nor so vascular. No dentine has been observed.

The location of the villi would seem to preclude the possibility of their serving to strengthen the animal's grasp upon the nipple. Without assigning to these rather remarkable structures any function, I would regard them, provisionally at least, as “denticles," for superficially their resemblance to selachian teeth is very striking.

During the month that this report has been in press, 130 kittens and cats have been examined, and although the villi early disappear in man, in the cat they are found to be retained throughout life. Their number diminishes, and those of the median group become merely moundlike masses limited by furrows. In the lateral groups, however, the loss in number is accompanied by an increase in size, and the acquisition of a more definitely pointed character, in those which remain. They may attain a length of 2.75 mm. and a breadth of 1.25 mm. In general they point downward and outward, but instances are not rare in