332 Mr. BaBpaceE on the Influence of Signs 
To any person acquainted with the notation belonging to the 
calculus, it is instantly intelligible; yet if it were written out at 
length, the letters « and y would be each repeated 257 times, the 
letter y would be found 512 times, whilst the expression would 
also contain 257 commas and 512 pairs of parentheses; thus 
comprising in the whole 2307 symbols; and it may be added 
that it would require a much longer time to understand the 
meaning of the equation written out at length, than it would to 
find its general solution. 
The power which we possess by the aid of symbols of com- 
pressing into small compass the several steps of a chain of reason- 
ing, whilst it contributes greatly to abridge the time which our 
enquiries would otherwise occupy, in difficult cases influences the 
accuracy of our conclusions: for from the distance which is some- 
times interposed between the beginning and the end of a chain 
of reasoning, although the separate parts are sufficiently clear, 
the whole is often obscure. This observation furnishes another 
ground for the preference of algebraical over geometrical reason- 
ing, and is one which had not escaped the notice of Lagrange. 
““Chaque membre de phrase est claire et trés intelligible a le 
considerer seul, mais le tout est si long qu’on a souvent oublié le 
commencement quand on arrive a l’endroit ou Je sens est complet.” 
The closer the succession between two ideas which the mind 
compares, provided those ideas are clearly perceived, the more 
accurate will be the judgement that results; and the rapidity of 
forming this judgement, which is a matter of great importance, 
inasmuch as the quantity of knowledge we can acquire in a great 
measure depends on it, will be proportionably encreased. 
M. Degerando has clearly stated this advantage in comparing the 
decimal arithmetic with that of the Romans. “ La rapidité d’une 
operation intellectuelle est toujours en raison inverse des efforts 
qu’on demande a l’attention et a la memoire. Cette operation 
