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The Telephone, invented by Mr Graham Bell, is an instrument by means of which any sounds, musical notes or spoken sentences, sounded into an instrument at the sending end of a telegraphic wire may be reproduced at the receiving end. The theory of the Telephone is two-fold. First, the mechanical theory of the nature of sounds and of speech; and secondly, the theory of the action of the instrument. The first part is well known. All sounds consist of a succession of waves propagated through the air, the rate and intensity of their succession determining the nature of the sound, in pitch, loudness, and tone. If the same succession of waves as a speaker makes in using his voice can be reproduced in the air in contact with the ear of any other person, by any means whatever, the latter person will hear a fac-simile of the sound uttered by the former.

The plans and calculations in this paper are now more than two years old, but the author has only lately, by the kindness of Professor Tait, found opportunity to carry them out in practice.A discussion is given of the different methods of applying the telephone to accurate measurement, and mention is made of the points which the author thinks have been missed by most of those who have worked in this way hitherto.A common principle runs through all telephonic null methods, viz., that the balance may be dependent on the frequency of the interrupted current or may be independent of it. In the latter case there are in general more than one condition of balance, and in the former case, although one will very often suffice, two may occasionally be necessary. In the former class of cases we get relations between electric quantities of the same dimension, in the latter relations between quantities of different dimensions, e.g., between coefficients of induction and resistances: so that when the frequency is known we can find a coefficient of induction in terms of a resistance, and so on.