The quantitative determination of nerve‐cell populations of brain structures after degeneration of the cell bodies following the placement of appropriate lesions constitutes a powerful method of determining structural relations in brain. The features of the ultrasonic method of lesion production that make it particularly useful in such studies are briefly reviewed, and lesions in specific structures pertinent to the quantitative study of the mammillary complex of cat brain are illustrated. The reproducibility, for the methods presently employed, of neuronpopulation ratios for related structures now under investigation is discussed, and the use of such data to determine neuronal circuitry relations is illustrated by a specific example. This presentation does not require prior neuroanatomic knowledge as a basis for its understanding. Its purpose is to illustrate the principles of deciphering quantitative relations of connections between sets of nerve cells and this can be achieved without prior knowledge of the system to which the methods are applied.