Known quantities of test objects approximating the parameters of cortical synapses were embedded in known volumes of a transparent embedding medium. The material was cut in slabs of appropriate thickness. The mean trace length (d) of the profiles of the test objects was measured and the number of profiles per unit area (NA) was calculated. Various stereological formulae were applied to these data to determine the number of test objects per unit volume (NV). For large numbers of those test objects most closely approximating the parameters of cortical synapses, the formula NV = NA/d and the DeHoff and Rhines formula ('61) for polydispersed circular disks NV = 8NAZ/ pi 2 (where Z is the mean of the reciprocals of the trace lengths) gave accurate results (error less than or equal to 5%). Other popular formulae and procedures were not as accurate and underestimated their number by as much as 32%.