124 BULLETIN OF THE BUREAU OF FISHERIES 



8. The electrodes should be from 2 to 12 inches above the bottom of the stream. 

 This distance depends upon the spacing of the electrodes and upon the character of 

 the stream bed. 



The voltage gradient along the line of centers between two parallel cylindrical 

 electrodes (which is the locus of the maximum voltage gradients) in an electrolyte 

 of uniform resistivity, such as the water of streams, can be calculated by the use of 

 the following equation: 



9 = 



fr+x,,S-2.)-xf»f[^ + ^(|)^J 



Where 



^ = the voltage gradient in volts per inch at distance x from the surface of 

 the electrode. 

 £'n = the voltage to neutral (one-half electrode voltage for a single-phase 

 circuit) root mean square values of the alternating voltages were used in 

 this investigation. 

 5 = the spacing, in inches, between electrode centers. 

 r = the radius, in inches, of the electrodes. 

 x = the distance, in inches, from the surface of the electrode at which the 



voltage gradient g is to be calculated. 

 « = 2.7183, the base of Naperian logarithms. 

 To facilitate the electrical calculation of fish screens and to show how the various 

 factors, such as electrode diameter and spacing, influence the voltage gradient. 

 Figures 12 to 21, inclusive, were calculated and plotted. Figure 12 is the plot 

 of the lines of current flow and equipotential surfaces for two standard 6-inch pipe 

 electrodes, spaced 24 inches, center to center. In Figure 13, 1 and 2 are the voltage- 

 gradient curves along the line of centers for J^-inch and 6-inch standard-pipe elec- 

 trodes. These curves clearly show the importance of using large-diameter electrodes 

 for improving the voltage gradient. Figures 14 and 15 show the variation of the 

 maximum and minimum voltage gradients along the line of centers for various elec- 

 trode spacings. Figures 16 to 21, inclusive, show the variation of voltage gradient 

 along the line of centers, with electrode diameter for 18, 24, 30, 36, 42, and 48 inch 

 electrode spacing, center to center. The diameters plotted in these curves are actual 

 outside diameters and not nominal pipe sizes; however, the various sizes of pipe 

 electrodes are designated by the standard nominal internal diameter by which they 



are known to the trade. 



CONCLUSIONS 



The following conclusions were reached from this investigation : 

 1. A very simple relation exists between the minimum voltage gradient required 

 to paralyze fish and their length, which can be expressed by the equation 



3.70 F 



where g = voltage gradient in volts per inch, TF= water-resistivity correction factor, 

 and L = length of fish in inches. 



