Theoretical expressions relating the distribution of apparent seamount¿ heights per unti length of ship track to the distribution of actual seamount heights per unit area of seafloor are derived for both narrow-beam and wide-beam echo sounders. The shapes of seamounts are approximated as truncated right-circular cones of constant slope &egr;, height-to-radius ratio &xgr;, and flatness f; i.e., a seamount of basal radius r has a height h=&xgr;r, a flat top of radius fr, and a slope angle of ϕ=arctan &egr;. The set of all seamounts in a given physicographic province is assumed to be a Poissonian ensemble specified by a function v(R), the average number of seamounts per unit for which r≥R. A simple choice for the size distribution of seamounts, and one shown to be consistent with data in the eastern Pacific, is to specify that it decays exponentially with R:v(R)=v0exp (-αR). In the case of a profile of length L taken in water of depth D with a wide-beam echo sounder (half beam width>ϕ), the shallow-slope, deep-water approximation (&egr;≪1, &egr;/α≪D) yields that the expected number of seamounts with apparent heights h¿≥H¿ is N¿(H,L)=2<α-1+(&egr;D/2) +(fH¿/&xgr;)>Lv0e-H/&xgr;. We apply this samplying theory to apparent-height data measured from 44,020 km of wide-beam profiles on Pacific crust of post-Mesozoic age. Although the spatial distribution of seamounts in the eastern Pacific is certainly not Poissonian, the abundance statistics do not involve spatial correlations, and we show they are robust with respect to deviations from the Poisson model, provided the statistics are interpreted as averages over the area actually sampled by the track lines. The observed falloff of apparent heights in the eastern Pacific is very nearly exponental, justifying our use of an exponential model of seamount size distribution. The shape parameters are estimated from multibeam surveys of Pacific seamoutns, an analysis of 30 features in the height range 200-4000 m yields &xgr;=0.21¿0.028. Using these parametrs, we obtain v0=(4.0¿1.1)¿10-9 m-2 and α=(6.3¿0.8)¿10-4 m-1. These values imply that per 106 km2 in the eastern Pacific there are 1600¿400 seamounts with summit heights greater than 300 m and 200¿60 greater than 1000 m; integrated over the entire size distribution, seamounts occupy about 6% of the seafloor area and constitute about 0.4% of the oceanic crustal volume. Our estimates of seamount abundance are appreciably greater than those of most other authors, a discrepance we attribute primarily to the samplying bias of previous studies, which generally used uncorrected map counts. The hypothesis is corroborated by a comparison of our statistics with map count data for seamounts of heights exceeding 2000 m compiled for the eastern central Pacific from the Scripps charts; about 3000 m the map counts are consistent with the predictions of the exponential model, but below this height they are biased to low values.