quakes it appeared that the motion at the bottom of the pit was very much less than that observed on the surface, while for small disturbances the difference between the surface and pit records was too small to be measurable. In 1886 a pit 18 feet in depth was sunk through dry compact earth at the Imperial University in Tokio, at the bottom of which seismometers were established on a brick pavement. These seismometers and others in the Seismological Laboratory a few yards distant when placed side by side gave records which were identical. The work was commenced by Professor S. Sekiya, and continued by myself, and the records obtained have now been subjected to a careful analysis by Mr. F. Omori, a graduate of the University, who has taken from ten to thirty waves in thirty different earthquakes and for each of these waves calculated its amplitude, period, maximum velocity, and maximum acceleration. Of these thirty disturbances, for each of which diagrams were obtained on the surface and in the pit, three were strong and twenty-seven were feeble. For each set of calculations referring to a particular earthquake average values were obtained, and the average for these average values was as follows:

1. Ratio of Quantities Observed on the Surface to those Observed in the Pit.

From the above it appears that for small disturbances the motion on the surface is slightly greater than it is in the pit; further, from an inspection of the diagrams, it is seen that those from the pit are always smoother than those from the surface. In severe earthquakes Mr. Omori points out that this latter character is strongly marked.

The ripples referred to appear amongst the waves in the early part of a disturbance, and, as Mr. Omori suggests, may be the continuation of the minute motions which are sometimes recorded in diagrams before the true earthquake itself has commenced.

A conclusion of some importance, which is confirmed by the above observations, is that buildings which rise from a basement or which are surrounded by an open area receive less motion than those which rise from the surface.

Observations on the vertical component of motion are now being made in the pit.

THE OVERTURNING AND FRACTURING OF BRICK AND OTHER COLUMNS.

During the past year a long series of experiments was carried out to determine the accelerations necessary to overturn or fracture columns of various descriptions. The columns were placed or fixed upon a truck which could be moved back and forth through a range and with a period comparable with what might occur in a severe earthquake. Each back and forth motion was recorded on a band of paper running at a uniform speed in a direction at right angles to the direction of motion of the truck. At the instant the column overturned or was fractured a mark was made on the paper, so that the particular wave which was being drawn when overthrow or fracture occurred could be identified.

On the assumption of simple harmonic motion, calling the period of this wave T and its amplitude a, which were quantities measurable on the diagram, the maximum velocity V, or and the maximum ac

V2

Σπα

T'

celeration, or could be calculated. These quantities were compared

a

with quantities dependent on the dimensions, density, and strength of the columns experimented upon. The object of the experiments was to furnish those who have to build in earthquake countries with data respecting the quantity of motion which certain forms of structure might be expected to withstand.

On October 15, 1884, we recorded in Tokio a maximum acceleration of 210 mm. per sec. per sec., whilst on February 22, 1880, when Yokohama was considerably damaged, such records as were obtained apparently indicated 360 mm. per sec. per sec. A maximum range of motion of 100 mm. and a period of 2 seconds implies a maximum acceleration of 450 mm. per sec. per sec. As it is possible that this quantity might be exceeded, structures in earthquake countries ought at least to be able to withstand three times as much.

For various reasons, of which the following are important, it seems impossible to absolutely determine the quantity of motion necessary to overturn a body of given dimensions.

1. The body may be set in motion and be rocking with a definite period and amplitude when it receives the final impulse which determines its overthrow.

2. Bodies, like columns, standing on end have a period of oscillation varying with the arc through which they rock.

3. An earthquake seldom, if ever, consists of a single sudden move

ment, but of a series of movements, which continually vary in amplitude and period.

4. A series of earthquake waves is often accompanied by a series of superimposed waves.

OVERTURNING.

The theoretical investigation of the overturning of a body like a column, which, although incomplete, has yielded results comparable with those obtained from experiment, is due to my colleague, Professor C. D. West. The result may be expressed as follows:

Let f the acceleration in feet per sec. per sec. which may cause overturning,

y=the height of the centre of gravity of the column,

x=the horizontal distance of the centre of gravity of the column from the edge about which it may turn,

g=the acceleration due to gravity.

Experiments showed that the quantity f, which may be calculated from the dimensions of a body, is closely related to the maximum acceleration, or which the body experienced at the time of over

turning.

V2

a

a

When the period of motion is short ƒ and closely approximate, but when the period is great (say two seconds) ƒ may be 30 per cent. V2 greater than

a

FRACTURING.

A theoretically-derived formula, which showed a close relationship with the results of experiment, was

where a the acceleration necessary to produce fracture;

Fo the force of cohesion, or force per unit surface, which, when gradually applied, is sufficient to produce fracture;

A area of base fractured;

B=thickness of the column;

f=height of centre of gravity above the fractured base; W weight of the portion broken off.

Values for Fo varying between 41 and 14.8 lbs. per square inch were determined by pulling portions of the brick and mortar columns asunder in a testing machine.

Corresponding to these different values of F° different values of a were

obtained.

Out of fourteen columns which were broken, in twelve cases the values obtained for a, when F°-14.8 lbs., were fairly comparable with the quan

tity V2/a. In two cases where fracture may have occurred at a bad joint the quantity V2/a was more near to a when F-4.1 lbs.

As an illustration of the practical application of the above investigation, let us assume that the greatest maximum acceleration to be expected is 1,000 mm. per sec. per sec., which is a quantity four times greater than anything yet recorded in Tokio, and then determine the height to which a brick column 2 feet square may be built above its foundations and be able to withstand this motion.

If a is the height required and w the weight of one cubic inch of brickwork=0608 lbs., then by substitution we derive from the above formula

A detailed account of the relationship of this formula to the formula previously employed, together with an account of the experiments, is being offered by myself and Mr. F. Omori, a graduate of the Imperial University, to the Institution of Civil Engineers.

For assistance in carrying out the experiments my thanks are due to Mr. D. Larrien, who provided the truck and rails on which the experiments were made; Mr. K. Tatsuno, Professor of Architecture, who designed and built the walls and columns; the authorities of the University, who provided the workshop and workmen, to Mr. Y. Yamagawa, who superintended the electrical appliances; and, finally, to my colleagues, who from time to time rendered valuable assistance.

EARTHQUAKES IN CONNECTION WITH ELECTRIC AND MAGNETIC PHENOMENA.

1. Magnetic Phenomena.

The conclusion to be derived from the notes relating to magnetic phenomena and earthquakes published in the Report for last year was that, for Tokio at least, the records of the Magnetic Observatory, which is continually being shaken by earthquakes, only show disturbances which may be the result of mechanically-produced movements. Since then I have read an account of the experiment of M. Mourreaux, chief of the Magnetic Observatory of Parc Saint-Maur, near Paris. Having had his instruments disturbed at the time of earthquakes, M. Mourreaux suspended on the same stand as the magnetograph a copper bar having the same form as the magnetic one. The bifilar suspension for the copper bar was made identical with that used for the magnet, and the movements of each were recorded photographically.

With three earthquakes the records for the magnet were disturbed, whilst the records for the copper bar were not disturbed. This experiment has been discussed by G. Agamemnone ('Atti della Reale Accademia dei Lincei,' vol. vi., January 5, 1890), who points out that for various reasons the period of the copper bar and the magnet must be different, and, therefore, by a given movement one might be caused to move whilst the other remained at rest-a conclusion with which the present writer

concurs.

Near an active volcano, where masses of magnetic matter may be

shifted or altered in temperature, changes in magnetic elements may possibly be observed, but, so far as observation and experiment have hitherto gone, we are inclined to the opinion that ordinary earthquakes are in no way connected with magnetic phenomena.

2. Electric Phenomena.

In the Report for last year I gave the results of a comparison of the records of several hundreds of earthquakes, and the photographic records of atmospheric electricity from a Mascart electrometer. The observations were made at the Meteorological Observatory in Tokio. A result arrived at was that at the time of many earthquakes, especially when Tokio was near the epicentrum, the air often became electro-negative. In a detailed paper on this same subject (Trans. Seis. Soc.,' vol. xv. p. 160) it is stated that these results must only be regarded as tentative,' and as during the past year I have discovered a source of error in Mascart's instrument, this remark must not be overlooked. Sometimes, even in exceedingly dry weather, the instrument rapidly loses its sensitiveness, and, if the mirror be displaced, it does not quickly return to zero. reason does not appear to reside in the fibre nor always in the acid, for, if the wire dipping in the acid and attached to the needle and mirror be taken out and washed, the sensitiveness is regained. Now the acid is being changed weekly and the wire washed. The results which have already been recorded having an explanation in mechanical movements must still be regarded as tentative.

The

Second Report of the Committee, consisting of LORD RAYLEIGH, Sir WILLIAM THOMSON, Professor CAYLEY, Professor B. PRICE, Dr. J. W. L. GLAISHER, Professor A. G. GREENHILL, Professor W. M. HICKS, and Professor A. LODGE (Secretary), appointed for the purpose of calculating Tables of certain Mathematical Functions, and, if necessary, of taking steps to carry out the Calculations, and to publish the results in an accessible form. THE first Report was in 1889. Since then values of Io(x) have been calculated from x=0 to x=6·10 at intervals of 01, and considerable progress has been made in still further expanding this table, making the interval 001. This will enable values of Io() for intermediate values of a to be read off by the help of first differences only.

Progress has been made towards the calculations of I1(x) for values of differing by the interval 01, or, if desired, 001. The method adopted is that of calculating the successive differential coefficients of (a) for the values of a given in the 1889 Report by means of the formula

and its derivatives, and interpolating by means of Taylor's Theorem. The Committee have asked for a grant of 151., to enable them to employ a professional calculator to help in the continuation of the work. 1891.

K