Feb. 14, 1889] 



NATURE 



381 



ranean cause of the same. But modern seismology proposes to 

 measure the intensity of an earthquake and to express its value 

 numerically. It is worth while, therefore, to inquire in what 

 sense the term may be used with precision, and what may be 

 accepted as its mathematical equivalent. Evidently it may 

 mean, and in fact it has been made by different writers to mean, 

 the measure of the surface destruction ; the energy per unit area 

 of wave-front of a single earthquake wave; the rate at which 

 energy is transmitted across unit area of a plane parallel to the 

 wave-front ; and the total energy expended in the production of 

 the original disturbance. The use of well-constructed seismo- 

 graphs has furnished us, within a few years, a good deal of fairly 

 trustworthy information relating to certain elements of earthquake 

 motion, notably the amplitude and period of vibration and the 

 velocity of transmission, by means of which, and aided by a few 

 not very violent assumptions, some of the above quantities may 

 be calculated. They are not identical, numerically or other- 

 wise, and it is manifestly improper to apply the word intensity 

 to all of them. 



An earthquake wave is generally assumed to be the result of 

 an harmonic vibration. While this supposition is not strictly 

 correct, it is probably not so far erroneous as to materially 

 vitiate the results which follow. 



If then— 

 a = maximum displacement, 

 / = periodic time, 



"', = maximum velocity of particle, 



V = velocity of wave transmission, 



d — density of material through which transmission occurs, 

 the following are easily obtained : — 



(l) Maximum velocity, z'^ = . 



(2) Maximum acceleration, ^' = '^^^^. 



a f- 



(3) Energy of unit volume with velocity, z\ — \dv-f 



(4) Energy of wave per unit area of wave-front = 



(5) Energy per second across unit area of plane parallel to 

 wave-front (rate of transmission) 



Zir-a-d 



2it"-a"'dY 



It is well known that Mallett and others of the earlier seismo- 

 logists attempted to find a mathematical expression which should 

 represent the so-called "intensity" of the shock, by means of 

 the velocity of projection of loose bodies as determined by their 

 range, and also through the dimensions of bodies which would 

 be overturned by the shock. The maximum velocity of the 

 earth might be ascertained by the first method with fair 

 accuracy ; the second method is nearly, if not quite, worthless 

 in practice, and both are decidedly inferior in design and opera- 

 tion to the modern seismograph, which gives the principal 

 elements of the motion directly. 



In a paper by Profs. Milne and Gray, Philosophical Maga- 

 zine, November l88l, the following occurs : — "The intensity 

 of a shock is evidently best estimated from the maximum 

 velocity of translation produced in a body during an earth- 

 quake. This is evidently the element according to which the 

 destructive power is to be measured, it being proportional to 

 the maximum kinetic energy of the bodies on the earth's surface 

 relative to that surface during the shock." Now this state- 

 ment is inconsistent with that which immediately follows, and 



with their mathematical expression, which is I« , equivalent 



to the second expression given above. This inconsistency was 

 doubtless quickly and first detected by the authors, and in a 

 copy of the paper received from them I find interlinear correc- 

 tions in the paragraph quoted above in virtue of which the 

 words "rate of change of" are substituted for the word 

 "maximum" where it first occurs, and "acceleration" for 

 the words "kinetic energy," thus bringing it into agreement 

 with the remainder of the discussion, and at the same time 

 unquestionably better representing the opinion of the authors, 

 who in all subsequent publications have used the maximum 

 acceleration to represent the intensity as shown in the over- 

 turning, shattering, and projecting power of the shock. 

 V * 

 The same expression, _L , is used as a measure of intensity 



by Prof. Holden in his paper on "Earthquake Intensities in 

 San Francisco" {Atnerican Journal of Science, vol. xxv. p. 427) 

 where he defines it as " intensity of shock defined mechanically 

 = destructive effect = the maximum acceleration due to the 

 impulse." He asserts that "the researches of the Japanese 

 seismologists have abundantly shown that the destruction of 

 buildings, Ike, is proportional to the acceleration produced by 

 the earthquake shock itself, in a mass connected with the earth's 

 surface." This statement is hardly justifiable, at least up to the 

 present time. In the Report of the British Association for 

 1885, the Committee appointed by the Association for the pur- 

 pose of investigating the earthquake phenomena of Japan, con- 

 sisting of Messrs. Etheridge, Gray, and Milne, describe among 

 other seismic experiments one which consisted in determining 

 the quantity to be calculated from an earthquake diagram 

 which would give a measure of the overturning or shattering 

 power of a disturbance. The result of this investigation seemed 

 to show that the acceleration, which by calculation from the 

 dimensions of the columns was necessary for overturning, was 



something between the mean acceleration, represented by '^, and 



the maximum acceleration, ^. 

 a 



The actual destruction caused by an earthquake wave is 

 undoubtedly a function of many variables, but it seems 

 tolerably certain that maximum acceleration is the leading 

 factor, and at the present time no better measure can be found. 

 It appears to me, however, that it is unwise to apply ihe term 

 "intensity" or "intensity of shock" to this quantity, which 

 might be called the " destructiveness " of the wave, or perhaps 

 its " destructivity," as indicating a little more clearly the power 

 to destroy. 



Button and Hayden, in their "Abstract of the Results of 

 the Investigation of the Charleston Earthquake," presented to 

 the National Academy of Sciences on April 19, 1887, define 

 intensity as the "amount of energy per unit area of wave- 

 front," but, in the subsequent discussion, use it almost con- 

 tinually as a measure of surface destruction. Upon the first 

 definition they have based a very interesting and novel method 

 for determining the depth of the focus ; but in the application of 

 the method to the Charleston earthquake they have used the 

 word in its other and very different sense. A reference to the 

 formulae given above will show that one of these quantities is 

 inversely as the square of the distance from the origin, as 

 assumed by them in the development of their method, while the 

 other, used in its application, is not so proportional, and this 

 must be admitted to be fatal to their deductions. 



In the discussion of a somewhat analogous case, Lord 

 Rayleigh says ("Theory of Sound," vol. ii. p. 16), "The 

 rate at which energy is transmitted across unit of area 

 of a plane parallel to the front of a progressive wave may 

 be regarded as the mechanical measure of the intensity of 

 the radiation." The algebraic expression for this quality, 

 as shown above, is, of course, similar to that of the quan- 

 tity last considered, differing from it only in the power of 

 "/" in the denominator. Both are very important expressions ; 

 neither is very closely related -to "surface destruction," and the 

 latter is unquestionably a suitable measure of the " intensity of 

 an earthquake " in the most important sense. 



It thus appears that at least four measures for earthquake in- 

 tensities are and have been in use, which are expressed mathe- 

 matically in terms of amplitude, period, velocity of transmission, 

 and density of medium in formulae (l) (2) (4) (5) above. To 

 show more forcibly the necessity of placing some restrictions 

 upon the use of the word, I have compaied the "intensities " of 

 two earthquakes, using each of the four expressions. The dis- 

 turbances compared are those of May 6 and May 11, 1884, at 

 Tokio, Japan, the observations being made by Prof. Milne 

 (Trans. Seis. Soc. Japan, vol. x. p. 27). The same instrument, 

 located in the same place, was used in both, and the interval 

 of time between the two is so small as to forbid any important 

 change in the conditions. That of May 6 is called "A," and 

 that of May 11, " B," The results are as follows : — 



B ... (I) (2) (4) (5) 

 A ... I -I 17 o'9 I '3 



from which it is evident that much depends on the measure of 

 intensity adopted. 



As stated at the beginning of this paper, the more recent 



