382 



NATURE 



{Feb. 14, I i 



work of seismologists has been in the study of individual dis- 

 turbances for the purpose of determining the principal elements 

 of motion, amplitude, period, direction, and speed of transmis- 

 sion. In this study much has been learned. From the nature 

 of the case we are almost absolutely restricted to an investigation 

 of surface phenomena, and we are soon forced to admit that 

 what goes on at the surface cannot accurately represent what is 

 going on below. Among other reasons for this conclusion we 

 have, HDtably, the greatly varying results obtained from the 

 same disturbance at points comparatively very near to each 

 other. The amplitude at one point may be two or three times 

 that at another a few hundred feet away, and not only this, but 

 the periodic times do not agree, and when the maximum 

 acceleration is applied to the disturbance, its so-called intensity 

 or destructiveness will vary greatly within a small area. As a 

 matter of fact, it has long been known that such variations in 

 destructive power do occur in nearly all earthquakes. Not only 

 do the above elements vary, but the speed of transmission, when I 

 once the surface is reached, is undoubtedly not constant, although i 

 we have no reason to believe that it is not approximately so in | 

 the rocks through which it is, in the main, transmitted. Most | 

 of these irregularities are doubtless due to the non-elastic cha- 

 racter of the materials lying near the surface and to their lack of 

 homogeneity. In spite of their appearance in the phenomena of 

 the surface, it is difficult, if not impossible, to believe that they 

 exist in the rocks below. It is more reasonable to assume that 

 during an earthquake the waves of transmission are, in the main, 

 and until the surface is reached, somewhat regular in their form 

 and approximately constant in certain of their elements. It 

 may also be assumed that in amplitude and periodic time the 

 subterranean wave, although doubtless much less than the surface- 

 wave, cannot differ from it enormously, so that elements of motion 

 obtained by seismometric observations upon the surface may be 

 applied within certain limits' to the investigation of the energy 

 involved, the results being considered as rough approximations. 



On these assumptions the following calculations have been 

 made : — 



Let A be the area of a portion of a wave-front, and / a length 

 measured at right angles to A. Then formula (5) above, which 

 shows the energy per second across unit area, multiplied by 



—- will evidently express the energy required to generate the 



waves existing at any moment in the volume /A. That is 



27rWV A/ 

 f'- ' V 



m {m = mass of volume /A) 



Imv-i^ 



That is to say, the work consumed in generating waves of har- 

 monic type is the same as would be required to give the maximum 

 velocity to the whole mass through which thie waves extend.^ 

 Sir William Thomson, who was probably the first to apply this 

 principle, in his calculation of the mechanical value of a cubic 

 mile of sunlight, concludes that in the case of a complex radia- 

 tion this value is more likely to reach twice that of the above 

 expression. 



On the assumption that the maximum velocity of the particle 

 is known, we may now apply this formula to the calculation of 

 the energy involved in an earthquake. For this purpose I have 

 selected, first, the Japanese earthquake of January 15, 1887, 

 which disturbed over 30,000 square miles of territory, and the 

 elements of which were well recorded on the Tokio seismo- 

 graphs. Assuming a mass of 150 pounds per cubic foot, and taking 

 a cubic mile as the volume to be considered, I find that to put 

 it in vibration required the expenditure of 2,500,000,000 foot- 

 pounds of ei ergy, and this might be called the "mechanical 

 value of a cubic mile of earthquake." Assuming that an area of 

 100 miles square, with a mean depth of one mile, was thus in 

 vibration at any one instant of time, which is not improbable 

 considering the known rate of transmission and the long duration 

 of the earthquake, the amount of energy thus represented would ; 

 be 25 X 10^- foot-pounds. This energy might be generated by 1 

 the fall, under the action of-gravity, of a cube of rock 1000 ftet [ 



I LordRaylfiah, "Theory of Sound," vol. ii. p. 17. Sir William Thomson 

 bn_^The Possible Density of the Luminous Mediun:." j 



on each edge, the mass of which would be 75,ooo,ooq t(5i^s< 

 through a vertical distance of about 166 feet. 



It would be interesting to apply this method to the Charleston 

 earthquake of August 31, 1886. Unfortunately no seismographic 

 records were made, and the elements of motion are largely 

 matters of conjecture. Messrs. Button and Hayden, in the 

 report already referred to, express the opinion that in some 

 localities the displacement must have been as much as 10 inches 

 or I foot. This seems to me improbable, but it may be safe to 

 say that over a considerable area it was as much as i inch. 

 Nothing is known with certainty as to the period of the oscilla- 

 tions, but as it generally increases with the magnitude of the 

 disturbance, it would probably not hi grossly incorrect to call it 

 two seconds. Assuming these magnitudes, I find the energy of 

 a cubic mile of the Charleston earthquake, taken near enough 

 to the epicentrum to be disturbed as above, to be equal to 

 24,000,000,000 foot-pounds. The speed of transmission of this 

 disturbance has been pretty well determined, by Newcomb and 

 Button, to be approximately three miles per second, so that a 

 cubic mile would be disturbed in one-third of a second. To do 

 this would require 130,000,000 horse-power. Assuming as 

 before that an area about the epicentrum 100 miles square was 

 thus disturbed, the energy involved would be 24 x lo^^ foot- 

 pounds, and the rate of its expenditure would be that of 

 1,300,000,000,000 horse-power. 



All of these numbers can only be regarded as gross approxi- 

 mations. They probably indicate the order of magnitudes- in- 

 volved, and may be useful until more trustworthy data are 

 furnished. 



THE ROYAL HORTICULTURAL SOCIETY. 

 'FHE annual general meeting of the Royal Horticultural 

 Society was held on Tuesday, February 12, at the offices, 

 117 Victoria Street, S. W. The Society is to be heartily con- 

 gratulated on the great improvement which has taken place 

 in its aff'airs since it quitted the Gardens at South Kensington 

 this time last year. From the Report of the Council, and the 

 speech of Sir Trevor Lawrence, Bart., M.P., President, in 

 moving its adoption, we glean the following particulars. Buring 

 the past year 657 Fellows have joined the Society, 81 have 

 resigned, and 48 died, the total number of Fellows on the books 

 being now 1636. The total income from all sources, inde- 

 pendent of the " Bonation " account (^1125 55. ), was £z'^'^l 

 8j. dd. ; the total expenditure, £'i\\2 i\s. \d., showing a surplus 

 of .^204 I4J-. 2d. On January i, 1888, there was a debit 

 balance of ;^"ii52, which has been cleared off by the transfer of 

 ofyiC755 1^- ^'■i- '^'"oni the " Bonation " account, and ^^396 \2s. 6d. 

 from current revenue. The total expenditure on the maintenance of 

 the Society's Gardens at Chiswick was,^^ 1501 6s. Sd., the receipts 

 from the sale of produce, ;^737 7s. 6d., brought up by minor 

 items tO;(^8io 4^-. 31/., making the net cost of the Gardens to the 

 Society -^691 2s. ^d. The income for 1889 is estimated at 

 ^3000, and the expenditure at£iig$o. The President referred 

 to the great value to the Society of the services of Mr. Byer, 

 F.R.S., Birector of the Royal Gardens, Kew, and Mr. H. 

 Veitch, who were retiring from the Council owing to the pressure 

 of other engagements, and of Mr. Wilson, F.R.S., and Br. 

 Hogg, who were retiring after having served the Society well 

 and faithfully during very many year?. He also paid a well- 

 deserved tribute to the energy, ability, judgment, and devotion 

 to their duties, of the Honorary Secretary, the Rev. W. Wilks, 

 and the Treasurer, Mr. B. Morris, Assistant-Birector of the 

 Royal Gardens, Kew. Buring the past year numerous very in- 

 teresting exhibitions have been held in connection with the fort- 

 nightly meetings of the Society in the Brill Hall of the London 

 Scottish Volunteers, James's Street, Buckingham Gate. A mag- 

 nificent show was held on May 17 and 18, in the Gardens of the 

 Inner Temple, by the permission of the Treasurer and Benchers, 

 in which, for the first time in the history of such displays, atten- 

 tion was drawn to the excellent horticultural work being done 

 by the market growers of the London district. A conference 

 on apples and pears, held at Chiswick from October 16 to 

 20, attracted great attention, and the papers read and the 

 discussions raised as to the circumstances and conditions 

 requisite for the successful cultivation of these fruits in the 

 British Isles were of great value. The Society propose 

 to hold this year, in addition to a great show in the Temple 

 Gardens on May 30 and 31, ar.d its usual bi-monthly exhibi- 



