mals, man has become the most wonderful living thing on earth, separated by a great gulf from his next of kin, and yet, in spite of his high degree, afflicted with more diseases than any other animal and beset by at least as many tormenting parasites. Inexperienced in his early history, his mind steadily advanced until to-day he contemplates all nature with a yearning to know its mysteries. The changes in the germ-cell sufficing to evolve him are as inscrutable to his reason as the constitution of matter and the interstellar ether, the nature and origin of the cosmical forces and of chemical affinity, the conditions obtaining on other worlds revolving about untold millions of other suns, or the origin, nature and meaning of life itself. But we ardently desire to know these things, to peer out into unfathomable space and to speculate upon the meaning of our existence and the unknowable as we perceive it all about us in the universe. Under such circumstances are we to live but a short time on earth and then be consigned to everlasting oblivion? In contemplating the real significance of the word eternal or everlasting, which must refer to infinity-a duration of time so inconceivable that a number of years expressed in pica type encircling the entire globe would be as naught when compared with it-our reason would appear to answer in the affirmative. But, as a species-sapiens-of the genus Homo, we can never know. We seem to be but intellectual atoms floating in an infinity of space and time. THOS. L. CASEY.

ST. LOUIS,

August 3, 1905.

SPECIAL ARTICLES.

THE SPEARMAN CORRELATION FORMULA.

SOME time ago C. Spearman published a formula for calculating the true correlation by the Pearson formula for observations in themselves variable.1 This method has been used by several psychologists without a full understanding of the way in which Spearman arrived at the method. Such a use of the

1 C. Spearman, American Journal of Psychology, January, 1904.

in which σ represents the true variability that determines the true correlation in the Pearson formula. The whole problem in practise is to find the value of v.

Spearman says that the true correlation may be obtained by dividing the average correlation for the various trials of the two tests by the square root of the product of the correlations for the successive trials for each test. Let,

xy=the average product of the deviations for the corresponding single trials in two tests. (pq), the same for t, and t2 of the first test. (pq), the same for t, and t2 of the second test.

v, and

=

the true variabilities of individuals in the two tests.

Thus the formula assumes that the successive observations upon the same individual, or t, and t, are constituents of the same norm in The conformity to the exponential law. method is simply a way of eliminating v from the expression. The assumption upon which the whole rests is that [pq] will be constant no matter what the magnitude of v.

Now, in tests as taken in psychological laboratories it is evident that some change in the norm results with each successive trial. In all tests we find practise, warming-up, etc., as factors leading us to consider the successive t's as ordinates of a curve whose abscissa represents units of time. In practise, at least, we assume a type of curve toward which all individuals tend. The individual curves are variants in the group defined by the type curve. The same conditions are found in growth of stature. It has been shown that individuals tend to the same curve of growth. Also that when an individual varies greatly from the type curve at one period of time he is likely to vary less at another. This implies that the individual tends to fill a space type in a time type so far as his physical growth is concerned. If this is true we should expect to find the same relations with respect to the form of any organ.

I have at hand data for measurements of the alveolar arch with reference to the median plane of the body. These measurements were taken as ordinates of the curve as defined by the teeth. This gives us the same general geometric conditions as were found in curves of growth. Now, before going on with the data let us consider the problem as that of a correlation between the ordinates of individual curves, varying from the type curve according to the exponential law.

We may assume that OM represents any curve. Let t, be the first observed trial or ordinate; t, the second. Now, no matter what the value of t, may be, there must be a correlation between t, and t, because of their geometric relations. Also, there may be a relation between (t,-t) and t

Let

2

2 Franz Boas, Report of the Commissioner of Education for 1896-7.

n-l

-0.27

In this table I have correlated the smallest dimension with each of the successively large dimensions as indicated by t. [x] is taken as a constant; σ, appears to be constant. The correlation of t and P varies for different points in the curve OM, in such manner that two points may be found for which the correlation is zero. [xp] varies with the magnitude of [P], which in this curve is dependent upon the distance between t, and t.

I have no good data for a psychophysical test. The only available data, at this writing, are the reaction times in the Columbia University tests. To preserve the form of the preceding table the fifth reaction was taken as the point of departure. Thus:

The result is similar to that in the foregoing. [xp] is negative with respect to consecutive trials. I have not calculated the values for all of the five trials because reaction time is not a good case; the distributions being asymmetrical, a disturbing factor is present. This will require special investigation.

These few observations lead to the following hypothesis: When a geometric form is taken as the type of biological activity the correlation between one dimension, taken as fixed, and its variation from another dimension will range indefinitely as positive or negative according to the geometric relations between the points from which the measurements are made. When two dimensions are correlated the degree of correlation will be increased or decreased by virtue of the equalization between the above correlation and the correlation between the parts common to both.

The method used by Spearman to determine the true correlation for psychological tests in which t, and t, seem to represent ordinates of a similar curve, assumes that [pq] will be constant for the successive trials. Turning to our last formula and substituting

stant when t, and t, are of the same type. We have shown above that the method of observation will sometimes result in a geometrical relation between t, and t, causing [pq] to vary. Whenever this occurs the method fails.

CLARK WISSLER.

TREATMENT OF SIMPLE HARMONIC MOTION.

THE very great importance of simple harmonic motion in the physical world demands very careful consideration of the method of presenting and treating it for students beginning the work in advanced physics.

From the books on physics which I have at hand, I have selected fourteen which are used by a large portion of American students for their first study of simple harmonic motion. Eleven of these present and define simple harmonic motion merely as the projection on a diameter of uniform circular motion, deriving equations and other definitions by use of this uniform circular motion. Some of them scarcely suggest the question whether there really is such motion; much less, under what conditions or by what law of force it would occur.

1hree of the fourteen texts give simple harmonic motion a dynamic definition, presenting it as produced by a force acting toward and varying as the distance from a center. But even these three, in treatment, make the auxiliary circle very prominent.

An experience of a good many years with large numbers of students leads me to believe that in the minds of very many the auxiliary circle with its functions and circular motion 'looms larger than the actual simple harmonic motion. It seems to me highly desirable to dispense with the auxiliary circle in both definition and treatment.

The definition should be dynamic. This dynamic definition should be drawn from experiments.

The treatment should be a problem, a study of the motion caused by a force acting by the law found in the experiments.

I offer the following as an illustration of treating simple harmonic motion as above suggested; and for students not using calculus.

Experiments. One or more on each, flexure,

Take qr perpendicular to cq, a√h on some scale (which need not be known).

On qr make the right triangle qsr, r= 0. Then qsa\/h sin = velocity at p in the simple harmonic motion.

Let T the period, the time of a complete vibration, from e to e' and back to e; and let t any portion of time.

If cq is given a uniform angular velocity 2π/T, that is, is made to vary uniformly with time, the component of q's motion parallel to p's path will at every instant equal the motion of p. The linear velocity of q, 2a/T, is equal to the constant a\h. is at

1 Unit mass was taken to simplify work in getting the form of the equations. The relation of mass to simple harmonic motion should be determined and put in the formula. Though only two or three of the text-books under consideration make any allusion, even, to mass.

THE BRITISH ASSOCIATION AND AFFILIATED AND CORRESPONDING SOCIETIES. THE report of the council of the British Association presented at the South African meeting the following resolution, from the conference of delegates, was referred to the council by the general committee for consideration and action, if desirable:

(i.) That a committee be appointed, consisting of members of the council of the association, together with representatives of the corresponding societies, to consider the present relation between the British Association and local scientific societies.

(ii.) That the committee be empowered to make suggestions to the council with a view to the greater utilization of the connection between the association and the affiliated societies, and the extension of affiliation to other societies who are at present excluded under regulation 1.

This resolution, having been referred to a committee, consisting of Dr. E. H. Griffiths, Sir Norman Lockyer, Professor Meldola, Mr. F. W. Rudler, Mr. W. Whitaker and the general officers, to consider and report thereon to the council, the committee made the following recommendations:

I. (i) "That any society which undertakes local scientific investigation and publishes the results may become a society affiliated to the British Association.

(ii.) "That the delegates of such societies shall be members of the general committee.

(iii.) "That any society formed for the purpose of encouraging the study of science, which has existed for three years and numbers not fewer that fifty members, may become a society associated with the British Association.

(iv.) "That all associated societies shall have the right to appoint a delegate to attend that annual conference, and that such delegates shall have all the rights of those appointed by the affiliated societies, except that of membership of the general committee."

II. The committee further recommend that the council request the corresponding societies committee

(i.) "To collect information as to the societies of the United Kingdom who might become associated societies under rule 1.

(ii.) "To consider and report on the question of 'A Journal of Corresponding Societies' referred to in Principal Griffith's Report."

III. The committee also recommend

66

(iii.) That any society formed for the purpose of encouraging the study of science, which has existed for three years and numbers not fewer than fifty members, may become a society associated with the British Association.

(iv.) "That all associated societies shall have the right to appoint a delegate to attend the annual conference, and that such delegates shall be members or associates of the British Association, and shall have all the rights of those appointed by the affiliated societies, except that of membership of the general committee.

II. "That the corresponding societies committee be requested to collect information as to the societies of the United Kingdom who might become associated societies under rule I. (corresponding societies).

III. "That in nominating a chairman of the conference of delegates, rule VIII. (corresponding societies) be allowed to stand."

THE NEW MUNICH CLINIC.

THE completion of the Clinic in Munich for nervous and mental diseases marks an important epoch in the progress of humanity, no less than in the history of medicine. From the time when William Griesinger, forty years ago, planned the first modern hospital for the insane, the leading authorities in Germany have labored to perfect the plans and organization of institutions of this class, with the result that the Munich Hospital will serve for years to come as a model to be copied by other nations. Whether the clinic is judged by the opportunities it affords for the observation and treatment of nervous and mental diseases, by the provision it makes for the instruction of students or by the facilities it offers to those engaged in the scientific study of the brain, it stands unique. Without detracting from the remarkable advances made during the past fifty years in surgery, pathology and bacteriology, it may be affirmed that no greater progress has been recorded in the history of medicine than has occurred in psychiatry during the period that began when Pinel, in the wards of the Salpêtrière first removed the chains from the insane, and that culminated in Germany in the movement that has rendered possible the completion of the Munich Hospital. Nearly forty years have passed since university and state authorities in Germany, influenced largely by the teaching of Griesinger, realized that the study of the brain, with a view not only to the discovery of the means for the prevention of insanity, but also to determine the most efficient methods of increasing the power to think and act normally, includes the discussion of many problems as important to mankind as the enquiry concerning the origin and spread of infectious diseases or the growth of tumors. The plans for the hospital in question are not entirely of recent creation; they represent the experience gained in the construction of twenty-two hospitals of similar type which exist in the German empire, and of which not a single example is yet to be found in an Englishspeaking country.

of the new University

As an excellent general description of this