=

it will appear that the error introduced by assuming that e-221-22 is negligible since, for z = 1/10 this error at its maximum is only as 0.99-0.99005 to 0.99, or 5 parts in 99,000 with respect to 1— P, and on the whole, even less than this; and it is the values of 1-P, smaller than those obtainable from the usual tables, in which we are here interested. The values of this table check with those in the usual tables, as far as the latter go, and also (in the extreme cases, especially where hx = 5.0, 5.5 and 6.0) with the values given in the original work of Burgess.

where E is the probable error and the quadratic mean error. A

Interpolations will be fairly accurate to the fourth place if proper account be taken of the second difference.

3 Burgess, Trans. Roy. Soc. Edinb., XXXIX., p. 257 ff. "On the Definite Integral (2/π) f。'e-11dt

with Extended Tables of Values.''

POLARIZATION OF SOUND

THE term polarization, applied to a wave motion, is generally associated only with transverse waves, more especially with light-waves, as referring to a state in which certain qualities are different in certain directions at right angles to one another and to the direction of propagation. By its origin, however, the term may be used with the same justification for longitudinal waves exhibiting qualities that are different in different directions, irrespective of the nature of such qualities and the relation of the various directions to each other.

It is thus proper to speak of a polarization of sound when conditions prevail under which a quality like its pitch is of opposite character to opposite sides of a fixed plane or axis.

Such conditions may be brought about by putting the source, which for the sake of simplicity is supposed to produce a sustained sound of uniform pitch, through certain movements. It is well known that when such a source is in motion the pitch of the sound emitted into space will be a function both of the direction of the movement and its speed.

p denoting the pitch observed, q the pitch produced, the velocity of sound, and u the speed component of the movement in the direction of the observer, with due consideration of its sign.

If the source, instead of being moved at uniform speed in one direction, is made to perform a harmonic oscillatory movement at right angles to a plane P, and symmetrical to it, then the resulting sound will be of uniform pitch only at points located in this plane, assuming the extent of the movement to be small as compared with the distance to the point of observation. To either side of the plane the pitch will be undulating, the undulations reaching their maximum amplitude at points directly in line with the movement.

While the undulations will be of the same amplitude at any two points symmetrically located with respect to the plane, they will be opposite in phase and, therefore, of opposite character. Accordingly, if the source is made to emit sound while to one side of the plane only, i.e., during alternate half oscillations, then, by the above formula, the resulting sounds will be of descending pitch to that side of the plane, while to the opposite side of it the same sounds will be of ascending pitch. The sound may thus be said to have been polarized with respect to the plane P.

If the oscillatory movement of the source is substituted by a rotation at uniform speed about an axis A, results of a similar nature are obtained. In this instance, however, the resulting sound will be of uniform pitch only

ARTHUR D. HIRSCHFELDER, Saligenin in two to four per cent. solution is a practical local anesthetic not only for minor but also for major surgical operations such as thyroidectomies and laparotomies, and for caudal anesthesia; in 4 to 8 per cent. solution it is particularly useful in anesthesia of the male and female urethra for cystoscopy. Quigley and Hirschfelder have shown in a series of phenyl carbinols that substitution for one of the inactive hydrogens of the carbinols lessens the anesthetic action and substitution of both causes it to be lost. Ethyl, propyl, n-butyl, iso amyl and benzyl ethers of saligenin were prepared from potassium saligenate and the corresponding halide. They all numb the tongue like cocaine, the butyl ether most, but all also produce a stinging sensation as well. Emulsions made with acacia lower the blood pressure on intravenous in rabbits, the benzyl ether producing the most lasting effects. The mono acetic, di benzoic and mono benzoic esters of saligenin have been prepared, as well as the acetate and salicylate of bromsaligenin.

Molecular magnitude and physiological action: OLIVER KAMM. Molecular volume data were utilized to predict the relative acute toxicities of monohydroxy alcohols belonging to several different homologous series. Benzyl alcohol and its homologues were found to agree with predicted values.

Preparation and hydrolysis of benzyl esters: E. H. VOLWILER. Benzyl benzoate as an antispasmodic has come into increasingly general use since it was first suggested by Macht. With the purpose of finding the benzyl esters best adapted as antispasmodics, a number of other benzyl esters, both new and old, were prepared and their hydrolysis rates determined. The rates of hydrolysis of these benzyl esters increase in the following order: salicylate, benzoate, stearate, cinnamate, acetate, succinate, and fumarate. Benzyl acetylsalicylate, a new compound melting at 26°, was prepared; its rate of hydrolysis is very rapid, due to the presence of the acetyl group. It is therapeutically the most active of all the benzyl esters investigated.

Arsphenamine: Some factors which influence its colloidal properties: A. E. SHERNDAL. When the pentavalent aryl arsenic acids are reduced to the trivalent arseno compounds, their well marked crystalloidal characteristics are suddenly replaced by decidedly colloidal tendencies. This may be, caused by the formation of large complex molecu

lar aggregates. Arsphenamine in dry form shows marked colloidal properties, which vary in degree with the method of preparation. Precipitation from ionized solutions tends to increase these colloidal tendencies, while anhydrous non-electrolytes tend to reduce them to a minimum, as shown by experiment. These variable colloidal charac teristics are paralleled by differences in the disperse state of acid and alkaline arsphenamine solutions, and may account for hitherto unexplained toxic and biologic phenomena exhibited by such solutions.

Laboratory tests vs. clinical results: ROBERT P. FISCHELIS. A discussion of the need for clinical evidence of the value of medicinal products and how such evidence may be obtained. The author included a discussion of the necessity for drawing proper conclusions from laboratory tests, as compared with clinical results.

Vanillin glyceride: FRANCIS D. DODGE. A crystalline deposit which had formed after a time in a flavoring mixture composed essentially of va nillin, glycerin and alcohol was found to be a compound of vanillin and glycerin, apparently analogous to the benzol-glyceride described by Fischer. The compound is obtained more readily with acid catalysts (hydrochloric or sulfuric acids) and when purified melts at 159°. It is very slightly soluble in water or ether, more readily in alcohol, and may be recrystallized from hot alcohol. It is soluble in aqueous potassium hydroxide, and is reprecipitated by acids. The compound is hydrolyzed by hot water, yielding vanillin and glycerin in equivalent amounts. It is also very quickly hydrolyzed in acid solutions, so that the preparation requires much care. For purification, the crude crystals are dissolved in the calculated amount of 0.5N KOH, and reprecipitated by somewhat less than the theoretical amount of acid. The compound thus obtained forms thin plates, which are stable in dry air. Under the microscope, the crystals show, in convergent polarized light, an orthorhombic interference figure, and are thus easily distinguished from the monoclinic needles of vanillin. The formula is probably:

THE NATURE OF MAN 1

A FEW years ago, as you may remember, Élie Metchnikoff published a book entitled "The Nature of Man: Studies in Optimistic Philosophy." If you have read that interesting work, you know that it is chiefly concerned with the great problem of death-with the problem, that is, of adjusting human emotions and human understanding satisfactorily to the common doom of living creatures. In Metchnikoff's view that problem has been mainly responsible for the existence of religions and philosophies. In his belief religions and philosophies have not been able to deal with the problem satisfactorily; but their failure, says he, is no reason for despair; for it is his conviction-and here we see why he deemed his study to be one in optimistic philosophy-that the problem can be satisfactorily solved by science and in particular by the science of biology, for the process of dying is one of the processes of life. And so his book aims at being an important contribution to what may be called the science or the philosophy of death.

I hope that this address upon "The Nature of Man " may appear to you, as it appears to me, to be, likewise, a study, or the result of a study, in optimistic philosophy. It is not of death, however, that I intend to speak, but of life. I desire to look towards the possibility to contemplate the possibility-of a valid philosophy, or a science, of human life.

The core of my message is a certain concept -a concept regarding the essential nature of man. The concept is, I believe, both new and important strictly new, if I be not mistaken, and tremendously important. This judgment I may express with propriety because the idea 1 Address at the annual meeting of the Phi Beta Kappa Society, Columbia University, May 31, 1921.