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logical perfection of a consistent set of theories. He constructs the electromagnetic theory of light and must needs adhere to it on many occasions, yet with full knowledge that it can not be correct. He rejoices in the existence of the universal constant, h, and the appearance of the quantum, h”, in resonance and ionization potentials, in photoelectric X-ray phenomena, and in the theory of heat radiation, yet he can not be reconciled to the existence of the quantum in the phenomenon of the passage of light through a vacuum. He builds an atomic structure which will not only provide a clear picture, but will also furnish quantitative results in striking agreement with experiment; and yet he must, in his building, reject certain principles which elsewhere he adopts without hesitancy. He rejoices in the achievement of the general theory of relativity, which, unless proved untenable, gives a logical consistency at present-and probably for many, many years, unattainable by other means; yet in his constructive thinking he sometimes uses the ether which the general theory of relativity ignores, and he lives in his old Euclidean world which the present developments from this theory deny.
In short, the physicist can not be consistent. Moreover, he can not progress unless this inconsistency is a stimulus and not an annoyance. He must live as if in several compartments, enjoying in each one the consistency possible therein, and being not distressed but rather interested and invigorated by the failure to unite these compartments into one consistent whole. If he "believes," he must be inconsistent. If he progresses, he must adopt a set of dogmas in the small compartment in his immediate problem. If he follows with full sympathy modern progress in physics, he must have not one, but many dogmas, and these not wholly consistent with one another.
I refer not merely to the multiple-theory method of attack upon a problem, for the dogmas are not even altogether similar in kind, but more especially to the ability to appreciate thoroughly not only "constructive
theories," but also "theories of principle" (quoting from Einstein) It is not merely the approach from a different viewpoint in the same universe, but it is the ability to live in more than one universe.
All of this may be obvious, but yet, in point of fact, now and again there appears evidence that even physicists of note are pained by this rôle. They seem to resist by objections which do not aid in the extension of these compartments, or by a rebellion against the obviously advantageous policy of polydogmata.
G. W. STEWART
STATE UNIVERSITY OF IOWA
TOTEM POLES FOR MUSEUMS
FIFTY years ago some of the best totem poles of the Haida Indians of Queen Charlotte Islands cost the Indians several thousand dollars each. To-day many of these may be purchased for a dollar and a half or two dollars a foot. That is, an average totem pole can be purchased, crated and put aboard a steamer at Masset for about one hundred dollars.
Many of the Haida totem poles have disappeared. A few have been taken to museums where they are preserved; some have been burned; many have decayed. Several, seen during the past summer, at Yan opposite Masset, have recently been blown over by the wind. In a few years all will have disappeared unless means are taken to save specimens of this art for the future. However the other tribes having totem poles may feel at this date, the Haidas have come to the point of neglecting the poles and being willing to sell them. They are owned by families, and negotiations as with an estate are necessary for properly obtaining them.
This North Pacific art is one of the treasures of Canada and the United States. Examples of it should be preserved in each large city of the continent. It may not be generally known how easily this can be done.
In the summer the Haidas of Masset are busy fishing. In the spring they have less to do and some are in need of money. Mr. Alfred Adams or Mr. Henry Edensaw are trust
worthy Haidas of Masset, B. C., who are capable of corresponding and executing the purchase of a pole or poles, and of engaging other help and superintending the lowering and creating of poles, their transportation across the inlet from Yan to the wharf at Masset and their shipment to destination. The poles are very heavy and the cost of handling will be perhaps equal to the price of the poles. They are soft and their own weight will crush parts of the carvings unless they are properly crated. Some of the poles 50 to 60 feet in length may have to be cut in sections for shipment.
Here is an opportunity. Examples of this unique art now going to decay may be rescued, loaded and started on their way to safe-keeping in our museums at the rate of about one hundred dollars per specimen.
HARLAN I. SMITH
GEOLOGICAL SURVEY, OTTAWA, CANADA
TO KILL CATS FOR LABORATORY USE A QUICK and humane method of killing a cat or other small mammal in the laboratory is to put the animal under an open topped bell jar, i. e., a bell jar which has a small bottle-like neck at the top through which there is an opening. This mouth should be comparatively small, not over a half inch in diameter, and the neck should be at least an inch long. After the animal has been placed under the bell jar, a very small quantity of ether or chloroform is poured through the opening in the top, and it is then corked up. The liquid strikes the sides of the neck and immediately runs down in a thin film over the inner surface of the bell jar and evaporates into the chamber in two or three seconds. The enclosed animal shows its effects almost immediately, and dies in a very short time.
While it is not necessary, it is better to seal up the base of the bell jar because occasionally the animal falls down after it becomes unconscious, and its head comes in close proximity to the crack between the jar and the object on which it is placed, and it thus obtains sufficient air to delay its death. This can be pre
vented by wrapping a damp towel around the base so as to exclude the air. By placing the bell jar on a glass plate and sealing with vaseline, an airtight chamber can be made, but the advantage thus gained does not make up for the care necessary in order to avoid getting one's clothing in contact with the greased surfaces.
WASHBURN COLLEGE, TOPEKA, KANS.
ANTS AND SCIENTISTS
TO THE EDITOR OF SCIENCE: As a result of watching a colony of ants and attending a scientific meeting on the afternoon and evening of the same day, it seemed to me the two teeming hordes of excited workers-the insects and the scientists-had some queer traits in common, as:
1. How they work in ranks and cohorts, mutually attracted by some exciting discovery that a wandering member has stumbled upon, and that awakens the most astounding and intense interest.
2. How they immediately set to work to pull opposite ways, fight valiantly over their treasure, and heroically keep it up after they have amputated some of each others' legs and other appendages.
3. How they take up one thing, drag it about for a time, and then drop it for some other thing.
4. How they often expend enormous labor on something that isn't worth a darn; and here Mark Twain's story of the two ants and the grasshopper leg came to mind.
5. How their splendid industry is generally circular in direction; so that after long struggle, they get the thing back to the exact spot from which it started.
6. How they firmly believe that "they are the people" and refuse to admit or bother over bigger intelligences that are their interested observers and that can and sometimes do sweep them and their hills and runways and stores into oblivion.
7. How, measured by final results, they are nevertheless a wonderful body of workers;
and in tireless energy, patience and talent, stand out preeminent in their respective groups. ALBERT MANN
THE BRITISH NATURAL HISTORY MUSEUM
WE learn that there are at present vacancies in the entomological, zoological and geological departments of the Natural History Museum which have been open for several months, and that more vacancies are expected in the immediate future. The museum is one of the great national instruments for the collection, classification, and preservation of specimens of the animal and plants, the rocks and minerals, of the world. For the adequate performance of its duties, it must have a full staff of able and devoted specialists. It should require no defense on utilitarian grounds, for the advancement of natural knowledge of the kind to which it is devoted is recognized as a privilege by every civilized state. But there are plenty of utilitarian arguments. Take entomology alone: the number of living species of insects is estimated at over 2,000,000. The preserver of insect life on human life is continuous. As household pests, as carriers of disease, as enemies of stores or crops, they are every day being found to have an unexpected economic importance. It is to the experts and the collections of the Natural History Museum that we have to turn for the requisite information, and unless the museum has an adequate staff we turn in vain. The difficulty in filling posts with suitable men is partly financial. The present rate of pay for assistants in the second class is from £150 to £300, and in the first class from £300 to £500 a year, with a temporary war bonus. These salaries the "despair" of Professor Stanley Gardiner, whose cogent letter we publish in another column-are no longer sufficient to attract or to retain men of the right attainments, unless they happen to have private means. The smallness of the staff and its inevitable division into water-tight compartments makes promotion slow and capricious. These disadvantages are increased by an
antique privilege of the principal trustee, who nominates candidates for vacancies instead of advertising for them. It has frequently happened in the past that middle-aged mediocrities have been brought in and placed over the heads of the existing staff because of their acquaintance with a group in which some of the trustees are interested. The fact is that the mode of governance of the Natural History Museum is medieval. It should be separated from Bloomsbury and placed under a body of trustees selected not because they make a hobby of collecting bugs or butterflies, but because they have a wide knowledge of the scientific purposes which it is the business of the museum to subserve.-The London Times.
Geodesy, including Astronomic Observations, Gravity Measurements and Method of Least Squares. By GEORGE L. HOSMER. John Wiley and Sons. First edition, 1919, 377 pages, 6 X 9, 115 cuts.
This book is especially to be commended for the skill shown in the selection of illustrations, both photographs and drawings, and for the excellence of arrangement and printing of the text and tabular matter. These things contribute substantially to the satisfaction and comfort of the user.
Still more is the book to be commended for its positive qualities, which make it a distinct and valuable addition to that part of the literature of geodesy which serves to carry information and understanding from the extreme specialists who are developing the methods and extending the knowledge in these fields, to the students and the practising engineers who desire to get a well-balanced view of the whole field of geodesy quickly. The old well-known matters are restated well in effective grouping. The ideas, formulæ and tables most needed by the student and the practising engineer are selected from the great mass of available material with rare skill. The recent developments in geodesy are shown in true perspective with respect to old things, to a quite unusual extent for a text-book.
Among the comparative recent developments in geodesy that are especially well stated in the book are (1) the importance of determining the relative strength of different proposed chains of triangulation as fixed by the geometrical relations, and the methods for quickly doing so; (2) the relation between the average length of the lines in a triangulation and the rapidity, economy, and accuracy of that triangulation and its convenience to the user; (3) the advantages of the light and rapidly built towers such as are now used in the Coast and Geodetic Survey; (4) the advantages of the transit micrometer on portable instruments for determining time accurately; (5) the application of the interferometer to determination of the flexure of the support of a pendulum used to determine the relative values of gravity at different points. These things are stated forcefully and with good judgment as to their relation to older ideas and methods.
Though he has looked carefully for errors of omission, the reviewer, who has a background of experience which naturally tends to make him keenly critical, finds only three that are, in his opinion, important.
1. On its best direction theodolites the Coast and Geodetic Survey uses two sets of double parallel lines in the micrometer microscopes with which the horizontal circle is read, the two sets being so placed that the observer moves the micrometer screw only one turn between a forward and the corresponding backward reading, instead of five turns. This is a time-saving convenience which also increases the accuracy, and surely should have been mentioned in the book.
2. The necessity of tracing back the adopted field length of a base measuring tape to the standard meter and the methods of doing so are inadequately treated in the book. The developments of the past twenty years have made it clear that one must concentrate much more keenly on this part of the work than the book indicates.
3. The area method of computing the figure of the earth from geodetic and astronomic observations is barely referred to on page 204 without explanation. In view of the fact that
this method gives a much higher degree of accuracy from the same observations than the traditional arc method, it certainly deserves a page of general exposition in the book, even if it is possibly too difficult for the student to grasp in full. The student and the engineer should know that the more accurate method exists, should know its general character, and in a general way why it is more accurate than the arc method.
The author of the book has shown such ability to see with the eye of an expert, and to exercise the judgment of a practicing geodetic engineer, that one may confidently expect that even these three omissions will not occur in a second edition.
JOHN F. HAYFORD
CONCERNING APPLICATION OF THE PROBABLE ERROR IN CASES OF EXTREMELY ASYMMETRICAL FREQUENCY CURVES
In a study of the fecal pollution of shellfish, Dr. James Johnstone1 raises an important question: that of determining the most probable value of a measure from a series whose frequency distribution is highly asymmetrical. In such instances it is evident, although prevailing practise contradicts the statement, that it is illegitimate to apply the probable error in the usual manner. For such application presupposes a symmetrical (Gaussian) distribution, and, since a wide range of biological measurements is characterized by an asymmetrical distribution, the matter merits consideration.
Dr. Johnstone lists the following counts of colonies of bacteria growing on twenty plates, each having been incubated a standard length of time after being inoculated with 1 c.c. of an emulsion, in 250 c.c. of water, of five muscles collected at random from the polluted area: 7, 24, 40, 15, 22, 20, 17, 9, 16, 29, 7, 9, 10, 26, 15, 11, 21, 17, 10, and 41. Dr. Johnstone assumes each count to be an estimate of the number of bacteria per c.c. of the emul
1"The Probable Error of a Bacteriological Analysis," Rept. Lanc. Sea-Fish. Lab., 1919, No. XXVII., p. 64-85.
Logarithm 0.505-0.704 0.705-0.904
Although Dr. Johnstone discusses this distribution, and, by employing Galton's graphical method, determines certain constants, he fails to answer the question he raises.
In cases of this kind it seems as though the simplest procedure is to find some function of the measurements whose frequency distribution is Gaussian, and apply the probable error to that function. The reason is that an asymmetrical distribution implies that some influence other than "chance" is operative, and substitution of a function whose distribution is Gaussian enables their separation. In the particular case at hand, and it is typical of many within the province of biology, this function is the logarithm. This is easily demonstrated by grouping the logarithms of the counts with respect to a deviation of 0.1 from their mean (=1.2046) as follows:
Frequency . 0
The arithmetic mean of the logarithms (1.2046) is the logarithm of the geometric
mean of the counts (16.02), the geometric mean, by definition, being the twentieth root of the product of the twenty counts. Accordingly, the Gaussian distribution of the logarithms shows that the counts cluster in approximately constant ratio about their geometric mean, or, to express it otherwise, that variations in the count are compensatory in the geometric mean. This signifies that variation in the count is not primarily attributable to errors in sampling and that each count is not an estimate of the number of bacteria present per c.c. in a homogeneous emulsion, but rather that conditions favoring the propagation of bacteria fluctuated in an "accidental" way either during the period in which the twenty samples were removed from the emulsion, or from place to place within the emulsion, or both. Whether or not this interpretation be correct, the logarithmic frequency distribution demonstrates that something of like nature occurred. In any case the most probable number of bacteria per c.c. corresponding to the most typical condition of the emulsion is the geometric mean of the counts (16.02); and, in the same sense, 250 X 16.024,005 is, of course, the most probable number of bacteria in the whole emulsion.
The reliability of this estimate may be approximated by applying the probable error to the logarithms. The standard deviation of the logarithms, σ, is 0.224, the probable error, or, better, the "probable departure" from the logarithm of a single count is 0.6745 σ=
0.1511 and the probable departure from the logarithmic mean is 0.1511/20±0.0337. It follows from tabulated values of the probability integral that, had the entire 250 c.c. been examined, it is as likely that the logarithmic mean would have been within 1.2046 0.0337 as that it would have been outside these limits, while the odds are about 4.6 to 1 that it would have been within 1.20462(0.0337), about 22 to 1 that it would have been within 1.2046±3(0.0337), and nearly 142 to 1 that it would have been within 1.20464(0.0337). The numbers corresponding to these logarithms are the limit