We report an evidence of order due to quadrupolar pair interactions, taking
place along the rare-earth (R) series of RPd3S4 slightly above their dipol
ar magnetic order. Specific-heat measurements proved that the R ions in the
se bronzes possess highly degenerate ground states, which may cause large o
rbital effects at low temperatures. The magnetic ordering temperatures much
exceed those predicted by the de Gennes scaling at both ends of the R seri
es. The fact suggests that orbital effects dominate over the ordinary excha
nge-type dipolar interactions. The presumed quadrupolar ordering temperatur
es, on the ether hand, scale with the squared Stevens factor along the R se
ries, indicating that quadrupolar pail interactions via conduction electron
s are responsible for the ordering.