307 



sidence of electricity in the wire when any one key is touched, and 

 to let the different strengths of current, in one direction or the other, 

 be produced by the different keys. Thus without a condensed code, 

 thirty words per minute could be telegraphed through subterranean 

 or submarine lines of 500 miles ; and from thirty to fifty or sixty 

 words per minute through such lines, of lengths of from 500 miles to 

 100 miles. 



The rate of from fifty to sixty words per minute could be attained 

 through almost any length of air line, were it not for the defects of 

 insulation to which such lines are exposed. If the imperfection of 

 the insulation remained constant, or only varied slowly from day to 

 day with the humidity of the atmosphere, the method I have indi- 

 cated might probably, with suitable adjustments, be made successful ; 

 and I think it possible that it may be found to answer for air lines of 

 hundreds of miles' length. But in a short air line, the strengths of 

 the currents received, at one extremity, from graduated operations 

 performed at the other, might suddenly, in the middle of a message, 

 become so much changed as to throw all the indications into con- 

 fusion, in consequence of a shower of rain, or a trickling of water 

 along a spider's web. 



VI. " On the Equation of Laplace's Functions/' &c. By W. F. 

 DONKIN, M.A., F.R.S., F.R.A.S., Savilian Professor of 

 Astronomy, Oxford. Received December 3, 1856. 



(Abstract.) 

 The equation " _|_ ^ 4. _ =6$ when transformed by putting 



#=? sin0cos0, y r sin0 sin <f>, s=rcosd, may be written in the 

 form 



and if u=u Q +u l r+u 2 r 2 + ... +u n r n + ..., we find on substituting this 

 value in (1), and equating to zero the coefficient of r n , that u n satisfies 

 the equation 



VOL. VIII. 2 B 



