610 THE POPULAR SCIENCE MONTHLY 



and Laplace for the flow of heat. In fact Ohm does this throughout 

 his book, and in a passage, unfortunately omitted by the English trans- 

 lator, he explains the analogy and acknowledges his debt. 



2. After discussing the three principles Ohm applies them to a simple cir- 

 cuit of uniform section and material, in order to obtain a graphical representa- 

 tion 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 neces- 

 sary 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 pre- 

 mature publication can not be placed to his credit his prompt acknowl- 

 edgment 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 



