364 Mr. F. Y. Edgeworth on 



knife-edge u x comes in front of the vertical plane through n x ; 

 and, since the lower point of attachment of the compensating 

 spring t Y is far below w 1? a couple is introduced which com- 

 pensates for the greater upward force. The same is the case 

 in the reverse order, when the lever is deflected upwards. 

 Hence if the pull exerted by t Y and the other conditions 

 mentioned below be properly adjusted, the horizontal lever 

 may be made to have any desired period of free oscillation. 

 In actual practice some positive stability must be given to 

 the lever in order that its position of equilibrium may be 

 definite ; but its period may be made so great that, even if 

 oscillations of considerable amplitude in its own period are 

 set up, they will be so slow compared with those of the earth- 

 quake, that the undulating line so drawn will still be practi- 

 cally straight, so far as the earthquake record is concerned. 

 In order to insure good compensation, the condition must be 

 fulfilled that the rate of variation of the compensating couple 

 is always the same as that of the supporting couple. If 

 this be not the case, the pendulum must either be left with 

 excessive positive stability for small deflections, or it will be 

 continually liable to become unstable by the compensating 

 couple becoming too great when the deflection exceeds a cer- 

 tain limit. In the present instance, let the modulus of the 

 supporting spring be M, the arm at which it acts a ; let the 

 modulus of the compensating spring be M 1? and the distance 

 between n Y and u\ be a x . Then for a deflection of the lever 

 equal to we have, on the supposition that the length of the 

 supporting spring and link is great compared with a x , for the 

 return couple Ma 2 cos sin — M^ 2 cos sin — M iy 8sin 0, 

 where ft + a x is the total elongation of the spring for the hori- 

 zontal position of the lever. Now our condition necessitates 

 /3 being either zero or negative; and in order to keep within 

 this condition the length of the unstretched spring and link 

 are made to reach a little above n x , and the height of u x is 

 made adjustable, so that M^ 2 can be adjusted to be as near 

 Ma 2 as may be desired. 



XLI. On Discordant Observations. By F. Y. Edgeworth, 

 M.A., Lecturer at King's College, London*. 



DISCORDANT observations may be defined as those which 

 present the appearance of differing in respect of their 

 law of frequency from other observations with which they are 

 combined. In the treatment of such observations there is 

 great diversity between authorities ; but this discordance of 

 * Communicated by the Author. 



