On Non-Newtonian Mechanical Systems <Sfc. 943 



These are the formulas given in the British Association 

 Report. 



So far as tabulation will ordinarily be required, it will be 

 sufficient in general, even for only moderate values of x or m 

 (^>10 or m > 10) to take the first terms of T and t only, if a 

 three-figure accuracy is required. The order of accuracy 

 possessed by the formulas is similar to that of the ordinary 

 semi convergent expression for Jo(V) where x is real. 



The first approximations may be written 



l m (x) = (27r^cosh/S)-V^ osh ^-^ sinh0 > ) 

 K m (x) = Tr^TTxcoshpyie-^^P-P^V /' ( ^ 



w here fi is defined by m = x sinh j3. 



A useful substitution in the final formulas has been sug- 

 gested to me by Prof. Alfred Lodge. If an angle 6 be 

 chosen such that 



x = m tan 0, 

 then 



£ = m(sec0-f log € tan-|0), .... (18) 



and this logarithm has already been exhaustively tabulated. 

 Thus the tabulation of the Bessel functions may be performed 

 very rapidly, and this applies also when the higher approxi- 

 mations are used. 



CVI. On N on- Newtonian Mechanical Systems, and Planck's 

 Theory of Radiation. By J. H. Jeans, M.A., F..R.S* 



1. T])LANCK'S treatment of the radiation problem, 

 Jl introducing as it does the conception of an in- 

 divisible atom of energy, and consequent discontinuity of 

 motion, has led to the consideration of types of physical 

 processes which were until recently unthought of, and are to 

 many still unthinkable. The theory put forward by Planck 

 would probably become acceptable to many if it could be 

 stated physically in terms of continuous motion, or mathe- 

 matically in terms of differential equations. Larmor f has 

 recently made an extremely interesting suggestion as to how 

 it might perhaps be possible to do this, but has not so far 

 carried out the analysis necessary to determine whether his 

 suggestion leads to a solution of the difficulty or nof. 



The question discussed in the present paper includes that 



* Communicated by the Author. 



t Bakerian Lecture, 1909, Proc. Roy. Soc. A. vol. lxxxiii. and Phil. 

 Mag. xx. p. 350. 



