304 M. P. Rudski on the 



coefficient of self-induction as 47ra(L — 2), which agrees with 

 (9) in the principal term. 



In the same way we may find the coefficient for a super- 

 ficial current in the wire. For (Phil. Mag. ibid.) if q is the 

 total quantity of the superficial current, we have the value of 

 Gx at E equal to 



2 ,[a(L-2)-£(2L-l) +I J(L + ^)] ( 



while from the value of the potential we find the normal flux 

 of force through the upper half of the anchor-ring equal to 



Hence the Coefficient of Self-induction is 



7T 



{4a(L-2)+2c(L + !) + I J(4L+ll)}, . (10 ) 



which is somewhat greater than the value (9) for a steady 

 current. 



XXVI. Note on the Thermodynamics of the Sun, 

 By M. P. Kudski, Odessa*. 



IT has been advanced by Helmholtzf that the contraction 

 of the sun may be the principal source of the energy of 

 that celestial body. He seems to believe that the temperature 

 of a radiating and contracting sun may be rising. On the 

 other hand, Lord Kelvin % esteems such a behaviour highly 

 improbable. 



A. Hitter § states a theorem, that the temperature of a 

 gaseous celestial body when emitting heat must be rising. 

 But this theorem is based on the supposition that the body is 

 in an adiabatic state, contrary to the other supposition that it 

 is losing heat. Mr. Lane || has obtained similar results, but 

 the method he has arrived at is unknown to me. 



My purpose is to illustrate the assertion of Lord Kelvin, 

 and to define in a certain manner the meaning of the word 

 contraction in the special case which we are considering. 



Consider, first, a small body, such as we are observing on 



* Communicated by the Author. 



•j- Populm-e Vortrdge, B. i. pp. 45 & 76. 



% Nat. Phil, part ii. (2nd edit.) p. 490. 



§ Anwendungen der mech. Warmeth. auf kosmolog. Probleme. Ha- 

 nover, 1879, p. 20. 



|| Huggins, Address, Report Brit. Assoc. 1891, p. 18. Mr. Huggins 

 does not quote the book or journal. 



