[ 159 J 



ISP 



' 



V. On the Vibration* in the Field round a Theoretical Hertzian Oscillator. 

 /?// KARL PEARSON, F.R.S., ami ALICE LEE, B.A., B.Sc., University College, London. 



Received January 2, Read January 19, Revised May 14, 1899. 



[PLATES 1-7.] 



CONTENTS. 



SECTION. PAK. 



1. Introductory 159 



2. General theory of a damped oscillator suddenly started 1GO 



3. Determination of the Q-f unction and method of calculating the wave-diagrams ... 161 



4. Electric and magnetic forces 164 



5. Wave-speed of magnetic force 167 



G. Discussion of method of resolving electric force 169 



7. Wave-speed of component axial electric force and of total radial electric force . ... 171 



8. Wave-speed of component transverse electric force and of total force peqxsndicular to 



oscillator axis 172 



9. Remarks on electric force in equatorial plane 178 



10. Wave-speed of integral force of induction . 178 



11. Graphic method of determining phase 179 



\'2. Wave-speed of total transverse electric force and of electric force in equatorial plane . 179 



13. Explanation of diagram of phases for the waves in Sections 7, 8, 10 and 12 .... 183 



14. Conclusions 187 



(1.) Although HERTZ realised very fully* that his oscillator did not give " perfectly 

 regular and long continued sine-oscillations," and although BjERKNEst determined so 

 long ago as 1891 the general form of the damping, it does not appear that HERTZ'S 

 original investigation of the nature of the vibrations in the field round one of his 

 oscillators has hitherto been modified. Indeed, his diagrams of the wave motion have 

 been copied into more than one text-book,]: and have usually been taken to represent 

 what actually goes on in the surrounding field. Actually not only the diagrams, but 



" "On very rapid Electric Oscillations," ' Wiod. Aniial.,' vol. 31, p. 421, ' Electric Waves,' p. 49. 

 t ' Wied. Annal.,' vol. 44, pp. 74, 513-526. The damping of the oscillation in four or five periods is 

 very marked. 



{ For example, ANDREW GRAY, ' Absolute Measurements in Electricity and Magnetism.' vol. 2, p. 734. 



3.11.99 



