The object which the author had in view in pursuing the investigations alluded to in the following paper was to discover some form of voltaic battery which should have a perfectly constant electromotive force, and should maintain a uniform difference of electric potential between its poles. This want has been much felt by electricians; and the utility of such an investigation may be best shown by a brief reference to the recent history of electrical measurement. In September 1861 a paper was read by the author before the British Association for the Advancement of Science advocating the adoption of a series of standard units of electrical measurement, and pointing out the mutual relations which should exist between such units. The subject was independently supported in Committee by Sir William Thomson, F. R. S., and the result was the appointment of a “ Committee on Standards of Electrical Resistance,” and a grant of money was set aside for the purposes of the Committee.