An artificial neutron source located within a subcritical reactor at a position that is asymmetric with respect to a line or a plane of symmetry will give rise to a neutron flux shape that is itself asymmetric. The ratio of counting rates from two counters at different locations will then depend on the degree of subcriticality of the reactor, and this ratio can be used to infer the effective multiplication constant (λ0) of the system provided certain auxiliary parameters, which must be either computed or obtained by experimental calibration, are known. This situation is analyzed theoretically and some simple numerical experiments are presented which suggest that the auxiliary parameters (which themselves depend on the degree of shutdown) may be taken as constants in some cases.