490 Mr. W. G. Gregory on a Method of 



single observations the curve of error would perhaps be 

 something like fig. 14. 



Fig. 14. 



14. As a final example, suppose we are trying to place a 

 small round body in a given position in a plane. Here the 

 law of error will depend on our manner of testing the adjust- 

 ment : whether we merely look up and down and from side 

 to side to get two (very nearly independent) judgments of 

 the corresponding coordinates, or whether we examine the 

 object from every point of view to make sure that no error 

 can be detected. The case may be illustrated mechanically 

 by supposing two pendulums supported one on gimbals, the 

 other after the manner of Foucault's pendulum ; appropriate 

 laws of friction being assumed. The law of error will further 

 depend on whether we follow the method of § 12 or of § 13. 



If we were trying to drive a billiard ball from one given 

 position so as to make it come to rest in another given 

 position (without rebounds), the errors of direction and of 

 distance would, if small, be very nearly independent ; the 

 latter coordinate being probably subject to much greater 

 variation. 



We are led, then, to the following conclusions: — The law 

 of error in a set of observations depends on the nature of each 

 special case ; and what may be called the probable law of 

 error is determined by our knowledge of the conditions. 

 The combination of three or more sources of error of com- 

 parable importance gives in general a law of frequency not 

 seriously differing from that of Laplace ; so that the method 

 of least squares will be practically the most advantageous, 

 except where a single source of error with a very different 

 law is predominant above all the rest. 



LVIII. On a Method of Driving Tuning-Forks Electrically 

 By W. G. Gregory, M.A., Demonstrator in Physics at the 

 Royal Indian Engineering College, Coopers Hill*. 



IN the ordinary method of driving tuning-forks by elec- 

 tricity, the battery circuit is completed just before the end 

 of the stroke and broken again soon after the commencement 

 of the return motion. Thus the fork receives its impulse at a 

 * Communicated by the Physical Society : read November 1, 1889. 



