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The theory of echo formation provides formulas relating echo energy to physical characteristics of the target. Single-target theory (applicable to counting isolated fish) is extended to the multiple-target case relevant to schooling fish. An echo-integrator equation relates fish density to echo energy integrated over a time gate corresponding to the depth channel of interest. Parameters include the equivalent beam angle, the expected backscattering cross section per fish, equipment sensitivity, and a time-varied-gain correction factor. Variation of environmental factors (sound speed and absorption) affects the parameter values. More important is the variation of biological factors (fish behavior and physiology) which affects backscattering cross section and target strength. Verification of the echo-integrator equation, depending upon the linearity principle concerning the addition of signals from randomly distributed multiple targets, is discussed in the fisheries context. The swimbladder is the dominant sound reflector in fish having one. Accordingly, fish targets may be classified as (a) bladder closed, (b) bladder open, or (c) no bladder. Within each category, fish of the same size have similar target strengths. Target strength variation with fish size, water depth, and time is discussed. Experimental target strengths are well scattered even for nominally similar fish. Nevertheless, useful information about fish stocks can be obtained through careful application of acoustical techniques.