Fare. — Milne Earthquake Diagram. 415 



from (1). Hence 



d^ 1_ d 1 (tr+l)1 d n 



dz* r"+* d6 F(T + 1 z r'+*+2 ' ~V\ dd F(r + l + 1 

 or, elevating one order, 



di ( 1 d \ 1 o-! d 



dz' \f*T dO P( 7 = >~+^T (o--!)! ^ F(r + % ( a ) 



which is the first of the two relations. 



The second is established in a precisely similar manner. 

 Thus 



d d l d l d 



dx dz 1 "~ dz 1 dx a 



By means of (4) the left-hand side becomes 

 d d i d o- ! 



Ax rfiT "' P " = < " !)' dx (^-1)7 r ' _i V " ~ ' 



from (2). For the right-hand side we have, using (2), 

 d i d d l / d 



TT- r °" Per = 



(,— |p.-i) 



dz 1 dx dz 1 



Hence 



rfar 1 \ dO / (o--- *)! d<9 



or, elevating one order, 



d^ ( d \ (o- - - 1) ! . d 



which is the second relation. 



( d \ . (o- + 1) ! . d 



Art. LIU. — On the Interpretation of Milne Earthquake 



Diagram. 



By C. Coleridge Farr, D.Sc 



• Read before the Philosophical Institute of Canterbury, 26th November, 



1902.] 



Plate L. 



The question as to whether a horizontal pendulum seismo- 

 graph acts as a clinograph, or whether its records must in part 

 be ascribed to horizontal movement of the earth's surface, has 

 received discussion by Milne,* Omori.f and others, whose 



* Nattire, vol. lxv., p. 202, and B.A. Reports. 



f Publications of the Earthquakes Investigation Committee, No. 5, 

 Tokyo, 1900, p. 45 et seq. 



