A discussion is given of ion chambers in which a series of electrodes carry layers of solid detecting material. Counters of this type require low operating voltages, and can easily be miniaturized. Formulas are given for the correct layer thicknesses and for the neutron counting efficiency. The equations are applied to boron 10, and it is shown that there is a permissible tolerance of about 50 percent on the thickness of a boron layer, and a very considerable tolerance on the assumed values of the disintegration product ranges. Curves are given relating the optimum boron layer thicknesses and the efficiency to the number of layers. A miniature instrument is described having a sensitive volume of 0.4 cm3. It operates at a thermal neutron efficiency of 24 percent with a collecting voltage of 70.