[ 157 ] 



XVII. On the Pressiwe of liadiation. By T. H. Havelock, 

 B.A.J M.Sc.y Scholar of St. Jolui's Colleje and Isaac 

 Newton Student in tlie Unicersitfj of Cambvidye *. 



SINCE Maxwell's sngoestion of the existence of a pressure 

 due to radiation f, interesting theoretical applications 

 have been made in the thermodynamics of radiation + ; and 

 more recently the pressure has been demonstrated experi- 

 mentally by Lebedew §. 



These circumstances lead to a consideration of the theory 

 of the pressure^ and this naturally depends upon the view 

 taken of the mechanical action in the electric field. This has 

 been supposed by some || to be expressible explicitly in terms 

 of stress, but in the following ^York we use the analysis given 

 bv Larmor 1[. We consider first the simpler case of waves 

 along a stretched string, and then proceed to electrical 

 radiation. The leading idea is that the pressure of the 

 waves, or at least the part which can be measured as 

 mechanical action, is the average efl:ect of a bodily force 

 integrated through an absorbing medium ; in other words, 

 the pressure is primarily due to absorption of energy, and 

 this operates by introducing a difference of phase between 

 the electric and magnetic factors in the expression for the 

 mechanical force. 



Waves along a String. 



§ 1. We begin by considering the transverse vibrations 

 of a stretched string, unlimited in length along the axis of x; 

 W being the mean constant tension, y the displacement and 6 

 the inclination to Ox of an element of the string. If F be 

 the force per unit length along 0.3? on an element hx, we 

 have 



= ^^^ I - 1'^ |-^ + terms of higher order V . (1) 



* Communicated bv Prof. J. J. Tliomson, F.R.S. 



t Maxwell, El. and Mao-, vol. ii. § 792. 



X Raylei.irh, Phil. Mao^l902, vol. iii. p. 338. 



§ Lebedew, Ann. der Phys'ik, 1901, vol. vi. p. 433. 



II Goldhammer, Ann. der Phys. 1901, vol. iv. p. 834. 



1] Larmor, Phil. Trans. 1897, A 190, p. 253. 



