Pascal and P. de Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Theorie analytique (1812) is to the best mathematicians a work requiring most arduous study.
The particular sizes and descriptions of wires used are dependent upon the character of the " circuits " the longer and more important circuits requiring the heavier wire.
At offices where the work is heavier than can be dealt with by the A B C apparatus, the " Single Needle " instrument has been very largely employed; it has the advantage of slight Single liability to derangement, and of requiring very little adjustment.
It differs from the open circuit in only requiring one battery (although, as in the figure, half of it is often placed at each end), in having the re circuit ceiving instrument between the line and the key, and in having the battery continuously to the line.
In this, as Most important cables, such as those of the Eastern Telegraph and the other with the earth; but it differed from other methods in requiring no " artificial " or balancing cable.