of Edinburgh, Session 1879 - 80 . 699 
which are sufficient for the numerals and all the letters contained 
in the Morse alphabet, less by one. These symbols we suppose 
assigned to the letters according to their frequency of occurrence as 
given in that alphabet. 
In the case of the Morse system we have only three states of the 
agent ; the third of the above states is not, or cannot be, made use 
of. As one is required for the purpose of spacing, only two are 
left to form symbols. To form equivalents for the 39 symbols 
spoken of above, it requires 2 permutations of one signal, 4 
permutations of two signals, 8 permutations of three, 15 of four, 
and 10 of five. Thus in the former case 102 signals are required 
to form the alphabet, in the latter 144. 
If the elementary signals of the Morse system are made to 
depend on a difference in quantity, then the above qualitative 
system possesses other two advantages. Its signals, as they differ in 
quality, can each be made to occupy the minimum time necessary 
for a signal to he observed, whereas in the other case the longer 
signal occupies thrice the time of the shorter ; secondly, elementary 
signals differing in quantity require, though belonging to the same 
letter, to be separated by an interval, whereas those differing in 
quality do not. 
By assuming that each of the qualitative signals can be sent in 
the same period of time as the short signals, also that the time 
required in the Morse quantitative system for the space between 
the elements of a letter is equal to that period, and the time required 
for a space between the letters to thrice that period, I have been 
able to calculate the relative times required by the two systems to 
sigual the words London, Edinburgh, Dublin. The respective 
ratios are 2*8, 2*6, and 2 ‘9. We may therefore conclude, assuming 
that the other advantages and disadvantages neutralise one another, 
that a message can be signalled 2 ’6 times as quick by the qualita- 
tive alphabet described as by the Morse (quantitative) alphabet. 
The four-state alphabet would allow one elementary sign to be 
invariably associated with the right hand, and the other elementary 
sign with the left hand, and the compound elementary sign with 
both together. The effect of this would be that a person who had 
learned to signal by means of any one agent, would have almost 
equal facility in signalling with any other. 
