and Laplace for the flow of heat. In fact Ohm does this throughout his book, and in a passage, unfortunately omitted by the English translator, he explains the analogy and acknowledges his debt.
2. After discussing the three principles Ohm applies them to a simple circuit of uniform section and material, in order to obtain a graphical representation of the potential gradient (Gefalle) and its discontinuities.
3. Applications to linear circuits of different material and varying section, with a generalization of the graphical method.
4. Equation for determining the potential at any point, consisting of an algebraic interpretation of the foregoing graphical method.
5. Relation of current strength to the potential gradient. This is Ohm's law expressed in terms of current, electromotive-force and "reduced length" or resistance. It is this statement of the law which is frequently, though wrongly, taken as the earliest expression of the law.
6. Applications of the conceptions of potential gradient and reduced length to special cases.
7. The effect upon the current strength of varying the resistance.
8. Properties of thermo-electric and hydro-electric circuits.
9. The effect upon the electromotive-force and resistance of the number of elements of a battery.
10. Adjustment of the resistance for the best action of a galvanoscope.
11. Divided circuits.
12. The decomposing power of an electric current.
The second part of the book is mathematical in character and need not be outlined here.
Discussion and Summary.—We are now in a position to summarize Dr. Ohm's work in the establishment of the laws of conduction, and to place his experimental work of 1825-26 in proper perspective with respect to his theoretical work of 1827. In doing this it will be necessary first to trace the development of ideas in Ohm's mind, and second to see how the scientific public received the same knowledge.
In tracing this development in the case of Ohm one must infer that the order of appearance of his various published papers marks the stages of growth of his own knowledge. Following this suggestion we find, first, that Dr. Ohm published in 1825 an incorrect empirical formula based upon inadequate experimental data. This paper would seem to show signs of undue haste caused perhaps by a fear that some other worker, Becquerel for example, might anticipate him. If this premature publication can not be placed to his credit his prompt acknowledgment of the error must be. Second, after further experimentation he announced the true law in 1826, in somewhat different form from that in which it is familiar to modern students. In the third place, he framed certain hypotheses from which the law could be deduced. This he does in his book of 1827. In doing this and in elaborating the law and in extending it to a large number of practical cases, Ohm leaves the reader to infer that he starts from the hypotheses and not from
