Abstract A thermionic projection diode with an aluminized fluorescent screen was used to determine the average and point-by-point Richardson constants for the  zone of W and Mo filamentary single crystals. Errors due to secondary emission of electrons at the anode were corrected by data collected in a separate experiment. An apparent functional relationship between measured values of φ R ∗ and a R ∗ is discussed in terms of a patch theory which departs from previous patch theories by the introduction of the fundamental patch. In terms of this theory, micropatches are composed of fundamental patches, and the micropatch distribution on an emitter determines the compensation between the Richardson constants. For filamentary single crystals of W and Mo, a Gaussian distribution of micropatches was found to establish the observed compensation between φ R ∗ and A R ∗. The Gaussian micropatch distributions are centered on the work function of a fictitious apparent patch and the width of the Gaussian increases with atomic roughness of the emitting surfaces. The suggestion is made that the micropatch effect may be the dominant factor in the point-by-point variation in emission constants measured over a filamentary single crystal.