148 Prof. F. Y. Edgeworth on the 



further Note on Vibration, C. P. S. May 1920, where 

 the complete solution requires the elliptic function, as 

 explained above. These are the vibrations in the ideal case 

 where terms varying as % 2 , «r 3 are added to the leading term 

 ri 2 x of simple rectilinear vibration. 



But these vibrations can be visualized and studied in 

 reality in the various projections of pendulum motion, in the 

 extension to the more general case where the axle is fixed on 

 a whirling arm, as in Watt's governor, the gyrocompass, or* 

 the Gilbert barogyroscope ; and a complete solution has been 

 given in the Report to the Aeronautical Committee on Gyro- 

 scopic Theory, 1914, Chapter VIII ; while the verification 

 by differentiation and integration has provided exercises in 

 ' Applications of the Elliptic Function/ 1892. 



Stroboscopic vision will convert these rectilinear vibra- 

 tions into the central orbits considered above, but with 

 = mt, so that the shape of the curve is seen, but not the 

 velocity in the orbit. 



Staple Inn. 



Nov. 5, 1920. 



XI. The Genesis of the Law of Error*. 

 By Prof. F. Y. Edgeworth, F.B.A. f 



PROFESSOR SAMPSON'S courteous reference to some 

 remarks of mine upon this subject deserved an earlier 

 acknowledgment. I would have sooner expressed apprecia- 

 tion of his criticisms, but that I wished to finish the article 

 which has appeared in the September number of this Magazine.. 

 I hoped to be able to speak more to the purpose about the 

 law of error J after considering its application to a leading- 

 branch of Physical Science. 



The points at which new light may be expected from 

 Prof. Sampson's original reflections may be introduced by a 



* Communicated by the Author. 



t Referring to the article on this subject by Prof. P. A. Sampson in 

 the Philosophical Magazine for October 1919. 



| The term ''error " designates according- to the context either error 

 proper, i. e. deviations of an observation from the physical quantity 

 which is observed, or generally deviation from an average. The law o"f 

 error (or the normal lawj designates the function (l/c^^exp— a; 2 c 2 

 considered as approximately representing the frequencv-distribution of 

 an aggregate ; the first approximation, further approximations beino- 

 furnished by a series descending in powers of 1/yO/. where n is the 

 number of independent items in the aggregate. 



