ing a very small correction for capillary depression) is the difference between the pressure at the base of the tube and the pressure corresponding to the liquid column extending upward from the base to the level in question. The pressure is thus always least at the top of the system, and greatest at the bottom. At the base of the tube the pressure remains practically unchanged throughout an experiment, being equivalent to the atmospheric pressure acting on the surface of the mercury in the reservoir, increased by a small value to account for the depth of the tubeopening below the mercury surface. But the pressure at any higher level, which is always smaller than that at the base of the tube, becomes still smaller as water lost above is replaced below by the much heavier mercury, and this decrease continues until the mercury-water boundary attains the level in question, after which the pressure in the mercury at that level remains constant with still further elongation of the mercury column. The pressure at the mercurywater boundary becomes continually smaller as this boundary ascends, becoming zero when the column of mercury just balances the opposed external pressure —that is, when the height of the mercury column in the tube just corresponds to the maintained pressure at the base. At this time the pressure at every level in the mercury is positive, being greatest at the bottom and zero at the top of the mercury column, and the pressure at every level in the water is negative, this negative value being of course numerically greatest at the top of the system and zero at the mercury-water boundary. The water is then all in a state of tension; it is taut, like a vertically suspended rope or wire. The water adheres to the nearly rigid glass, rubber and porcelain walls and to the mercury below. As still more water is lost by evaporation from the cylinder and the mercury column continues to elongate upward, the upper portion of this column also passes into a state of tension and we have a demonstration of the transmission of traction through the upper portion of the mercury as well as through all of the water. The taut mercury adheres to the water above and to the very thin water film that intervenes everywhere between mercury and glass and this film adheres to the glass, thus acting as an adhesive cementing mercury and glass together.

The essential pressure relations outlined above may be stated algebraically as follows, all pressure values being expressed as heights of equivalent mercury columns, in centimeters.

It is clearly negative, and there is tension at the give level, if the expression in the parenthesis is greate than B+b. B is the atmospheric pressure on th mercury surface in the reservoir outside of the tub (usually the current barometer reading), while b is th depth to which the tube projects downward into th mercury in the reservoir. H is the vertical length the mercury column between the base of the tube an the given level, while h is the vertical length of th water column below the given level, between it an the water-mercury boundary below. D is a small val due to capillary depression. (It may be taken 0.8 cm. for a tube of 1.5 mm. bore.) If the level co sidered is below the water-mercury boundary, then is zero. If the level considered is at this boundar then h remains zero and H is the total vertical leng of the mercury column in the tube, measured fr the lower end of the latter. If the given level is the top of the system, then H remains as in the la case and h is the total height of the water colur measured from the water-mercury boundary to t top. To illustrate, if B is 75.5 cm., b is 2 cm., H 125 cm., h is 20 cm., and D is 0.8 cm., then P = 75.5 2- (125 +20 +0.8) 77.5-145.8=-68.3 em. T negative pressure at the given level, which is 143 c above the level of the mercury in the reservoir in t case, is equivalent to 68.3 cm. of a mercury colum or about nine tenths of an atmosphere. This is measure of the tension or traction at the given lev (It should be noted that the expression "negat pressure" is sometimes erroneously used to der simply decreased positive pressure, a positive press lower than that of the surroundings.)

=

In an experiment of this kind the liquid column the system eventually breaks in every case, sometin in the water (in cylinder or tube) and sometimes the mercury. When rupture of the column oce before the pressure at the highest point of the sys has become negative, then the experiment is a fail in respect to the demonstration of traction and lic tension (for none is developed in such a cas although it does successfully demonstrate what been called the "suction power" of evaporation. suction developed at any level in the system is t equivalent to the (positive) value of P, as found means of the equation. It is of course greatest at top of the system.

An experiment to show the "suction power" evaporation from a fine-pored membrane is regu's performed in laboratory courses in plant physiol and is generally described and figured in the te books of that science. The arrangement is essent:" like that of the Askenasy experiment. No diffieu" are involved and the mercury column gradually e gates and reaches a height of 60 or even 70 cm.

many cases, but (unless proper precautions have been successfully taken to make this really an Askenasy experiment) the liquid column breaks before the pressure at the top has become negative in sign. Every Askenasy experiment demonstrates suction before any tension is developed and it demonstrates both suction (below) and liquid tension (above) when the pressure at the top is negative.

It is this suction experiment that was referred to by Dr. C. A. Arndt (SCIENCE for May 21, 1926, page 527), who seems to have failed to realize that traction and liquid tension can not begin until after the possibilities of ordinary suction have already been exhausted. This author was apparently not dealing with the Askenasy experiment at all. His "superior His "superior results" are to be taken as bearing upon the suction experiment only, being consequently just failures for The Askenasy experiment. Without additional data (barometric pressure, length of water column above the mercury in the system, and bore of tube) even the "greatest total height" given, 28 inches, is not in itself evidence of liquid tension, although the smallness of the difference between this value and the normal barometer reading (about 30 inches for Philadelphia) indicates that the pressure in the top of the system was as low as one or two inches of mercury. Shorter mercury columns of ten or twenty inches, uch as Dr. Arndt mentions, surely represent failures as far as the demonstration of tension by the Askenasy nethod is concerned. From Dr. Arndt's printed statement and also from correspondence with him it s clear that the pressure on the surface of the merury in the reservoir was the current barometric pres

ure.

Plant physiology requires as careful thinking as do he physical sciences, and students of plant water relations should be led to distinguish clearly between action and traction. In the case of suction the longating or moving column of liquid is under the etion of two opposing external forces, one larger han the other but both tending to compress the iquid and shorten the column. In the case of tracjon also there are two external opposing forces, but oth tend to overcome the cohesion of the liquid and tretch the column. In the first case the liquid column slightly compressed, in the other it is slightly tretched (tension). In suction the liquid is pushed and in traction it is pulled up. For a demonstraon of suction alone it is not necessary to exercise my special care in setting up the apparatus, but pecial treatment is generally necessary if any tension traction is to be developed.

BURTON E. LIVINGSTON GRACE LUBIN

LABORATORY OF PLANT PHYSIOLOGY, JOHNS HOPKINS UNIVERSITY

SIMPLE SEISMIC MEASUREMENTS

THE measurement of earthquake acceleration maxima by observation of the fall of vertical columns was proposed more than forty years ago. The condition that a properly directed horizontal acceleration should be sufficient to overturn a simple rectangular parallelopiped was stated by Professor C. D. West as a = gb/h, where h is the height and b the breadth of the paralellopiped, and g is the gravitational acceleration. This relation results at once if one equates the inertial moment about a lower edge of the parallelopiped to the gravitational moment about the same edge. By observation after a quake of the status of a number of parallelopipeds having different ratios. b/h an estimate of the magnitude of the maximum acceleration was to have been obtained. But upon testing this method by experiment Milne1 and Omori2 found West's formula to be inapplicable to earthquake-like accelerations. Discrepancies as high as 35 and 40 per cent., some positive and some negative, were recorded.

There seem to have been two reasons for this disagreement. The acceleration of West's formula-or rather any acceleration in excess of it-although undoubtedly sufficient to start the overthrow will not bring it to completion if the duration of the acceleration be too brief. Seismic accelerations are not constant accelerations but are of an alternating nature and may rise to maxima much higher than that expressed by the above equation and yet die away so quickly that the complete overthrow does not take place. On the other hand, the alternating character of the acceleration may in some cases result in the upset of the parallelopiped through the development of resonant oscillations, even though West's acceleration is never attained. In this case the elasticity of the paralellopiped and of its foundation play an important part. These errors, though opposite in sense, can not be expected to annul each other, and a discrepant result, difficult at present to predict, will in general remain.

West's equation, in short, does not apply to the case of an object overturned by an acceleration of alternating or oscillatory character because it was never formulated to fit such conditions. It correctly defines the minimum acceleration, however attained, at which the object will start to turn over. But only for special cases, such as that of a constant acceleration, does the formula state the acceleration competent to complete the overthrow.

The theoretical treatment of an object overthrown by simple harmonic motion does not appear to have been presented. Galitzin dismisses the matter with the observation that the problem offers real difficul1 J. Milne, Trans. Seis. Soc. Japan, Vol. 8, 1885. 2 J. Milne and F. Omori, Seis. Journ., Vol. 1, 1893.

ties. The difficulties are substantially reduced however by the assumption that the stability is such that the object rotates through only a small angle (tan =0) before coming to a position of instability. This assumption fortunately does not impair the application of the results to actual earthquake accelerations up to the intensity ranked by Cancani as "Very disastrous." The geometrical form of the object considered is of no real importance and we may drop all restrictions of this kind and assume only a rigid body stably supported by a horizontal axis somewhat lower than its center of mass, and a brace or stop of some kind which prevents rotation under the action of gravity. The object thus described will be referred to as a bar. The angle made by a vertical and the perpendicular dropped from the center of mass of the bar upon the axis of rotation will be called .

Now it may be shown that the bar will just be thrown down by a horizontal simple harmonic motion directed at right angles to its axis if the maximum acceleration of the motion has the value

In this equation R is the radius of gyration of the bar, L the distance from the center of mass to the axis of rotation and T the period of the oscillation. The derivation of the equation is too lengthy to be appropriately presented here and it must suffice to state that it has been deduced by rigorous methods and completely verified by experiment.

The experimental work was conducted upon an oscillating table capable of horizontal simple harmonic motion of adjustable period and amplitude. Every variable quantity represented in the above equation was varied through wide limits, and of over five hundred observations every one conformed to the equation within the leeway of two or three per cent., which the uncertainties of observation permitted.

It is worth noticing that with an infinitely long period of oscillation-and therefore with constant acceleration-the equation reduces to a=g, which is West's formula stated in a slightly different way.

A series of similar bars of suitable form, mounted at a variety of angles of inclination so that an earthquake would cause some to fall and leave others standing, would yield important information about the nature of the oscillatory horizontal movement. But it is evident from the equation that a knowledge of the critical angle dividing the fallen from the standing bars will not in general suffice to determine the maximum acceleration, since the acceleration is a function both of this angle and of the period of oscillation. The influence of the period can only be suppressed by making the whole second term under the

radical sign a small quantity, even for short periods. Experiment shows that this may be done by a suitable choice of the form and dimensions of the bar, so successfully, at least, that for all oscillations with periods greater than one fourth of a second the maximum acceleration is fully determined by the critical angle, with an error which can not be greater than six per cent. and which is much less in nearly all cases. It is probably not worth while at present to strive for greater accuracy at this point, since the errors resulting from the assumption that the earth motion is simple harmonic have not been investigated.

The problem may be approached in another way. Referring again to the equation one sees that a knowledge of the critical angle, as obtained by observing a given set of bars, gives an equation in which a and T alone are unknown. From a second set of bars, different from the first in R or L, another critical angle is observed, giving another relation between a and T. The two equations are independent and to gether suffice to determine both a and T. With the acceleration and period known the corresponding amplitude is of course readily computed. These de terminations are subject to three errors only. The first is the error in determining the critical angles it may be made as small as desired by the use of a larger number of bars. The second is the error in volved in the assumption that is small; this i entirely negligible for quakes of small intensity and rises only to about one per cent., with very disastrou quakes. The third error is that of the assumption that in the neighborhood of the maximum acceleration the earth motion is simple harmonic. Assumption of this kind have often been made, but never, so fa as known, critically investigated. It is impossible a the present time to make a numerical statement o the exactitude of this assumption, but its validity be comes of less and less importance for present pur poses as the radius of gyration of the bars is dimin ished. It appears probable to the writer that error of this sort in the determination of maximum accelera tion can be kept below five per cent.

It appears possible therefore to make importan earthquake measurements with extremely simple an inexpensive apparatus. Through the courteous co operation of Dr. T. A. Jaggar instruments are soo to be located upon the island of Hawaii, a regio which by reason of frequent local quakes should serv admirably as a proving ground for seismometrics devices. A more complete paper upon these subject will be published in the near future.

DEPARTMENT OF PHYSICS, UNIVERSITY OF HAWAII, HONOLULU, T. H.

PAUL KIRKPATRICK

MINERAL METABOLISM IN ADULT MAN

MR. GUY W. CLARK in the studies here presented, selected as subjects of the experiments, inmates of the California State Prison at San Quentin. Expert medical and dental examination of the men was always available and the ever present element of "Custodial Control" was a factor in causing the men to abide by the restrictions for the entire experimental period. This paper is an outstanding contribution to the discussion of essentials of diet.

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ATOMIC FORM

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The Theory of Atomic Form assumes that the Atom of each Element possesses a geometric solid form to which it owes its characteristic qualities. A definite form called a "Carbonoid" is ascribed to the Carbon Atom, and carbonoid aggregates are shown to correspond in character with the Carbon Skeletons of Organic Molecules, and to accord with the crystalline structure of Graphite. ... A remarkable explanation of the forms of optically-active isomers is furnished, and interesting views are suggested on the probable structure of molecules in which optical relations are of primary importance.

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