.270 Prof. L. Natanson on the Molecular Theory 



from a gradual mode of procedure in performing the calcu- 

 lations I have confined myself, in this communication, to 

 the consideration of some simpler aspects of the problems 

 at issue. Thus we shall avoid, as far as we can, analytical 

 intricacies, and the meaning and bearing of the fundamental 

 principles involved will become apparent. 



The effect of small particles in diverting portions of 

 incident light from its regular course was investigated by 

 Lord Rayleigh in a series* of admirable papers. It would 

 carry us too far into scientific history to give an account of 

 his work as well as of later inquiries)" that fall more or less 

 directly within our province; but I desire to repeat here th<» 

 acknowledgment, made more than once in the course of 

 the papers, of my indebtedness to Lord Eayleigh/s writings. 

 I also desire to take this opportunity of referring to 

 Mr. W. Esmarclfs paper cited below; with this author I 

 find myself in closest contact and agreement in respect of 

 many conclusions. 



§ 1. Let us consider a linear simple vibrator maintained 

 in vibration by the operation of a train of incident electro- 

 magnetic waves. It is natural to begin the calculations bv 

 considering the expression of the secondary field that diverges 

 from the vibrator. An effective method of working it out is 

 as follows. Let V(<r , y , z ) be one of the points occupied 

 bv the vibrator, M (.?.', //, z) any point where the secondary 

 field is to be estimated. If we introduce an auxiliary 

 vector M* whose components ty x (x, i/, z, t), ^0', jA ~, 0, 

 "SP^.i', y, z, t) satisfy equations of type 



y^=c 2 V^ (la) 



c being the velocity of propagation in vacuo, the secondary 



* Phil. Map-. (4) vol. xli. pp. 107, 274, 447 (1871) ; (5) vol. xii. p. 81 

 (1881) : (5) vol. xlvii. p. 375 ^1899). ' Scientific Papers,' vol. i. pp. 87, 

 104, 518; vol. iv. p. 397. 



t G. Sap-nac, Becueil de Travaux offerts a H. A. Zorentz, p. 377 (1900). 

 Lord Kelvin, Baltimore Lectures, p. 301 (1904). M. Planck, Sitz.- 

 Ber. d. Kgl.-Pr. Akad, d. Wiss. for 1904, p. 748. L. Mandelstam, 

 Anvalen der Physik, vol. xxiii. p. 626 (1907). A. Schuster, l Introduction 

 to the Theory of Optics,' 2nd edit., p. 325 (1909). A. Einstein, Annalen 

 der Physik, vol. xxxiii. p. 1275 (1910). H. A. Lorentz, K. Akad. v. Wet. 

 te Amsterdam, Proceedings, vol. xiii. (1) p. 92 (1910). P. Langevin, 

 Bulletin d. Seances de la Soc. Prang, de Physique, p. 80* (1910). Pes Idees 

 Modernes sur la Constitution de la Matiere, p. 97 (1913). L. Vessot King-, 

 Phil. Transactions Koy. Soc. of London, A. vol. ccxii. p. 375 (1913). 

 W. Esmarch, Annalen der Physik, vol. xlii. p. 1257 (1913). (*This paper 

 only came under my notice after my first communication on the present 

 subject was already printed.) 





