OP ELECTEIC SIGNALS THEOEGH SEBMAEINE CABLES. 
1015 
Erplanation of Table XVI. 
Table XVI., given to the author by Professor W. Thomsoit, will now be shortly 
explained. The author will not enter into any detailed explanation of the theory by 
which the results contained in the Table were obtained, as these results are the direct 
mathematical consequences of the equations given in the papers already alluded to, and 
as Professor TnoMSOif will probably himself publish the full mathematical development 
of the theory. 
The first column headed 0 contains a series of “times” occupied by the full periods 
of electric operations, each of which, when continually repeated, produces a succession of 
equal and similar rises and falls in the received current, or of “ dots” as they have been 
hitherto called in this paper. The series begins with the shorter and ends with the 
longer times, or, in other words, begins with the more rapid and ends with the slower 
speeds. The numbers in the first column are numbers measuring the times of the periods 
in terms of a certain quantity a. taken as unity. The actual time in seconds occupied 
by each period or cycle of electric operations corresponding to the series in the first 
column is equal to the numbers entered there multiplied into a. This quantity a is 
equal to f^-*logt (lO^), where 
c = the electrostatical capacity of the insulated wire per unit of length in absolute 
electrostatic measure ; 
k = the resistance of the conductor per unit of length in absolute electrostatic 
measure ; 
I = the length of the conductor. 
a varies therefore for every cable and for every length of the same cable. The 
meaning of this quantity will be best explained by the following extract from a letter of 
Professor Thomson’s to the author : — 
“ a, in definite absolute measure, means the tenth part of the time in seconds in which 
a simple harmonic electrification established in the wire and left to itself (two ends to 
earth) would subside to i^th of its amount. Thus in the time a, an harmonic electri- 
fication subsides to of its amount. The subsidence here spoken of is the gradual 
IQio 
loss of charge by conduction out through the ends to earth.” 
Now let the electrical operation producing the dot be a simple harmonic variation of the 
potential at one end while the other is connected to earth e. let V= A sin where 
V= the varying potential, A= a constant, and ^ = any function of the whole period^. 
Then, measiu’ed as a fraction of the maximum current which would be received if the 
maximum potential A were constantly maintained at the sending end of the cable, the 
difierence between the maximum and minimum received current will be the reciprocal 
of the number entered in the third column ; or translating this into the language used in 
