100 Mr. A. E. II. Love. Note on ths present [Jan. 15, 



tilled with a uniform glow whenever the discharge passed through 

 tin- primary circuit, but, when the electrostatic induction was shielded 

 off by pieces of wet thin blotting paper connected to earth, no glow 

 could be observed, though the wet blotting paper is not a sufficiently 

 good conductor to shield off electromagnetic induction. 



The maximum integral electromotive force round the secondary is 

 shown to be VM/L, where V is the difference between the potentials 

 of the coatings of the jar before discharge, L the coefficient of self-in- 

 duction of the primary circuit, and M the coefficient of mutual induc- 

 tion between the circuits. Though in my experiments this was 

 greater than the electromotive force requisite for a discharge through 

 gas at the same density between terminals separated by the length of 

 the tube, not the faintest glow could be detected. A.11 ray efforts to 

 get a discharge through the secondary have so far been unsuccessful,* 

 and I feel sure that the ease of getting a discharge without electrodes, 

 say by the motion of the upper regions of the earth's atmosphere 

 across the lines of magnetic force, has been much over-estimated. 

 Until, however, we have got a discharge without electrodes through 

 nothing but the gas itself, we are unable to say whether the passage 

 of the discharge from the positive to the negative electrode which 

 occurs in gases is a consequence of having matter in two states in the 

 path of the discharge, or whether it is an example of a more general 

 law, that, whenever tubes of electrostatic induction shorten in a con- 

 ducting circuit, they do so in the direction of the electric displacement. 



In conclusion, I have much pleasure in thanking Mr. Bartlett and 

 Mr. Everett for the assistance they have given me in the course of 

 this investigation. 



II. " Note on the Present State of the Theory of Thin Elastic 

 Shells." By A. E. H. LOVE, M.A., St. John's College, 

 Cambridge. Communicated by LORD RAYLEIGH, Sec. R.S. 

 Received January 3, 1&91. 



In a paper read before the Royal Society in February, 1888, and 

 published in ' Phil. Trans.,' A, of that year, I advanced a theory of 

 the mode of deformation that takes place when a thin shell is vibrat- 

 ing. The theory was founded on the form of the potential energy 

 function, obtained by a method adapted from that of Kirchhoff for 

 plates. It appears that, in case there are no surface-stresses on the 

 faces of the shell, this function consists of two terms, of which one 

 contains a certain function W 2 and the thickness 2h as factors, and 



* Since this paper was sent in to the Royal Society, I have succeeded in getting 

 a discharge without electrodes through a tube about 45 cm. in circumference. The 

 discharge did not exhibit any signs of stratification. -Jan. 23, 1891. 



