We report the first detection of extragalactic HCN and HCO+ J = 4 -->
3 emission at lambda = 850 mu m. Because their critical densities (n s
imilar to 10(7) cm(-3)) and excitation energies (E(u) similar to 45 K)
are large, these lines trace dense, warm gas. We have detected HCN J
= 4 --> 3 toward NGC 253, NGC 4945, and IC 342 and report a sensitive
upper limit toward M82. We have also detected HCO+ J = 4 --> 3 in both
NGC 253 and M82. The HCN J = 4 --> 3/J = 1 --> 0 intensity ratio, whi
ch is larger for higher gas densities, is at least 12 times larger in
NGC 253 than that in M82. Single-component gas excitation model calcul
ations for NGC 253 show that, averaged over the central 300 pc, the mo
lecular gas is warm (T greater than or similar to 50 K) and dense (n s
imilar to 5 x 10(5) m(-3)). For M82, the lower HCN J = 4 --> 3/J = 1 -
-> 0 line ratio requires an average gas density at least 10 times smal
ler. In both M82 and NGC 253, the J = 4 --> 3/J = 1 --> 0 line ratios
peak at the nucleus. Consequently, molecular gas is densest in the cen
tral 300 pc. The submillimeter HCN and HCO+ lines reveal large differe
nces in the dense gas properties, despite similar CO and far-infrared
luminosities.