Gyroscopes as adjuncts to the solution of these problems have not hitherto proved themselves successful.

On the assumption that the earth-waves in alluvium were harmonic in character and symmetrical in form, in the Report for 1892 it was shown that they might be 20 feet in length; and, knowing their length and period, the velocity of propagation was determined. Even should these waves have lengths several times this amount, some knowledge of their form might be obtained by simultaneously measuring the difference in movement between, say, the heads of a line of stakes at right angles to the direction of the advancing waves and different points of a wire or rod parallel to such a line, but only held in position at its two extremities.

I am led to mention these latter experiments as indications of the important problems which seismologists have yet before them.

LIST OF EARTHQUAKES RECORDED IN JAPAN IN FEBRUARY 1893.

The list of earthquakes appended to this section of the Report is given as an example of a catalogue which might be compiled from the material which since 1885 has been accumulating at the Central Meteorological Observatory in Tokio.

The approximate centre of a disturbance is indicated by its latitude and longitude, while the energy of the disturbance may approximately be deduced from the figures which show in geographical miles the diameter of the area shaken.

Hitherto investigations respecting seismic activity, the periodicity of earthquakes, &c., have been based upon catalogues where only the number of shocks have been recorded, and where the disturbances of one seismic area have been inextricably mixed with those from another.

With a catalogue like the one suggested it would be possible to investigate the rate at which seismic activity is decreasing or increasing either in a given area or in Japan as a whole, giving values to the shocks proportional to the area they had shaken. It would assist us in determining whether there is any relationship between the frequency of earthquakes in neighbouring areas. Inasmuch as many earthquakes seem to be the result of sudden fractures or yieldings taking place during the process of rock-crumpling, it does not seem unlikely that the relief of strain along one axis should be altogether without effect upon neighbouring axes where folding may also be in operation. One interesting investigation of the records of a district which has very kindly been made by Mr. F. Ŏmori has been to plot the shocks which succeeded the great disturbance of 1891 as a curve, the co-ordinates of which are equal intervals of time and the number of shocks occurring during these intervals.

It will be remembered that the immediate cause of the disturbance was the formation of a large fault which can be traced some forty or fifty miles, together with several minor faults. During the seven months which followed the great shock no less than 3,000 shocks were recorded. How many have been recorded up to date has not been calculated, but from the appended list for the month of February, that is sixteen months after the first shock, sixty-two disturbances were noted.

The curve representing this decrease in activity closely approximates to a rectangular hyperbola, which now, with an average of two shocks per day, is becoming asymptotic.

With the law of decrease deduced from these records Mr. Ōmori

calculates that it will take about thirty years for the district to regain its original stability. The records for the Kumamoto earthquake, which took place in July 1889, show a like result, but with a rate of decrease directly proportional to the intensity of, or the area shaken by, the primary disturbance.

One curious fact connected with the extinction of the Nagoya earthquake is that the district of greatest visible faulting, where valleys were compressed and mountains were lowered, seems to have reached a fair state of quiescence, while the most active settlement, or the district where an extension of faulting is now taking place, is at the S.E. extremity of the main line of original disturbance-a few miles N.E. from Nagoya in Niwa-gun (N. lat. 35° 20', and E. long. 136° 50').

Not only would the publication of the catalogue here indicated furnish material very much better than that which has been hitherto attainable for the continuation of investigations like those made by Perrey, Mallet, and other seismologists, but we should have materials for investigations which would be entirely new.

Earthquakes recorded in Japan in February 1893.

NOTE. The reason that the diameter of the area shaken by many shocks is given as three miles is because the shock was only recorded at one place, and from investigations on areas disturbed by small shocks this number may be taken as approximately correct (see On a Seismic Survey made in Tokio,' Trans. Seis. Soc., vol. x.).

OVERTURNING AND FRACTURING OF MASONRY AND OTHER COLUMNS.

In the Twelfth Report (1892) it was stated that the form of a wall or pier which, rather than snapping at its base, would, when subjected to horizontal reciprocating motion, be as likely to snap at any one horizontal section as at any other had been determined.

A brick building with walls approximating to this form has been designed and built by Professor K. Tatsumo on the University compound. Mr. C. A. W. Pownall, M.I.C.E., has constructed brick piers for the bridges on the Usui Pass, some of which are 110 feet high with similar sections.

An experiment relating to overturning which is in progress is to determine the relationship between the dimensions of a body and the amplitude of motion which will fail to overturn the same, no matter how short the period of motion may be.

PUBLICATION OF A SEISMOLOGICAL JOURNAL.

In consequence of many persons who took an active interest in seismology having left Japan, because work which formerly found a place in the publication of the Seismological Society now finds a place elsewhere, and for other reasons, the Seismological Society, which between 1880 and 1892 had published sixteen volumes, ceased its existence. As a certain amount of work still continues in order to bring this before those who are interested in seismology, a seismological journal has been published and the first volume already issued.

Bibliography of Spectroscopy.-Report of the Committee, consisting of Professor H. MCLEOD (Chairman), Professor W. C. ROBERTSAUSTEN (Secretary), Mr. H. G. MADAN, and Dr. D. H. NAGEL. THE collection and verification of titles of papers on spectroscopy have been continued during the past year, and it is expected that another instalment will be ready for printing at the next meeting.

Mathematical Functions.-Report of the Committee, consisting of Lord RAYLEIGH (Chairman), Lord KELVIN, Professor CAYLEY, Professor B. PRICE, Mr. 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 of the Committee was in 1889 (at Newcastle-on-Tyne), when they published tables of I(a) for integral values of n from 0 to 11, from 0 to 60, at intervals of 02; L(x) being defined by

The present tables of I,(a) are from x=0 to 5·100, at intervals of '001, and are given to nine decimal places, the last figure being approximate. They have been calculated by means of Taylor's Theorem, the successive derived functions being obtained by use of the formula

and of the formulæ derivable from this by successive differentiations. The values of these derived functions were checked by double calculation of the values of I(a) halfway between those given in the 1889 table; thus, for example, I(23) was calculated as I1(2·2+0·1) and also as I1(2·4-0·1). This important check confirmed at the same time the values of I(x) which were given in the 1889 table, so that certainly the tables now given are free from any systematic error. When the present tables were finished, accidental errors were discovered and corrected by taking out first and second differences, and then, finally, the printed tables were checked by continuous addition of the first differences on Edmondson's calculating machine. It is confidently hoped, therefore, that the tables are free from serious error.

Tables of I(a) have also been calculated, and are in a forward state, but are not quite ready for printing this year.

It is proposed to have the tables republished in book form when com