<0 



!) 7-1. Meoiiurt'meitt of carihqvake^ by rrferenct to (heir EJecf^ on Biiildhif/.i. 



Attcmytts have been made to infer the eliaraeter (if earth<jiiakc iiiotiuiis from 

 the traces which destructive ^hwks leave hcliind tliciii, in fiactnird walls, pro- 

 jeete<l fragments, overturned columns, etc. The two laruje volumes in which 

 ^lallet has described the great Neapolitan cartlnjuake ut' 1S57* are in «rreat part 

 filled with calculations of this kind. So far as these refer to tlic direction of the 

 principal movement (on the supjiosition that there was a princiial movement 

 with a definite direction), they arc not without value; but in ajiplyinu: his 

 nietisurcments of projection and overthrow to the determination of the greatest 

 velocity of dis|)lacement, ^fallet has throughout niadf an a.«sumption which 

 entirely vitiates his results. The assumption, already alluded to in s])caking of 

 standing columns (§ (54), is that the body which suffers overthrow docs so in 

 conse(juence of a suildeii change of momentum witii respect to tlie ground, and 

 that the momentum so actpiircd is left free to do its woik, in causing the body to 

 fall, without further interference. In other words, it is a.ssumcd either that the 

 motion of the ground begins ijuite .-uddenly, and then continues (until the liody 

 falls) with a uniform velocity — the velocity which is calculated- by Mallet's 

 ' formula-; : or (■l.'-e that, having communicated this velocity to tln^ Ixxly, the 

 ground :?uddenly stops, and stays at rest until the body falls. It need scarcely be 

 jioiuted <iut, after the results given in Chapter V, how wide of the facts this 

 assumption is. And it is difficult ti> «;e how any observations of bodies projected 

 or overthrown can be of the smallest use as data from which to determine 



earthipiakc motions, when these have the extraordinary mplcxitv which 



ab.solute measurements have shown them to po.ssess in Ja]ian. 



Mallet's treatment of fracture<l .structures is even more un.satisfactory, and, 

 in<Ieetl, involves a distinct error. Taking the case of a coliiinn wliiili is fractured 

 at a horizontal plane tlirongh the base by a horizontal impulse, he e(|uatcs the 

 momentum nudtiplied by the height of the centre of gravity, witli the moment 

 of resistance of the section to rujiture. It is, liowevi.-r, the greatest rate of 

 acceleration, and not the greatest velocity, which determines whether fracture 

 .shall take |>lacc. If wc assume the column to break without .-iensible bending, 

 so that the act of rupture (which is to be clearlv ilistinguisbed from the over- 

 tlirow which may or may not follow it) occuis with s<'nsible iiwtantaneousne.ss, 

 we should e<piale the moment of the re.-i.4tance to acceleration with the moment 

 of resistance to ru]iture. (falling 71/ the ma.ss above the fraclureil section, u the 

 acceleration, /* tiie height of the centre of gravity aiiovc the section, / the monx'nl 

 of inertia of the wction about a horizontal ceiilial axis perpend icidar lo tlic 

 tiinction of acceleration, Ij the shoitcst perpendicidar di.-tance of (iiis axis from 

 the edge of the s<'ction, and /the modulus of rupture, we have 



M..U= ^^ . or "= jijf^h- 



* The Fint Princi|ilea of Obncrvaliunul Sciimology, Londuii, I8G2. 



