Three large stacks of nuclear emulsions were exposed during 1964–66 on high-altitude balloons launched from Fort Churchill, Canada; Texas, U.S.A.; and Hyderabad, India. These stacks have been used to study the energy spectrum of the cosmic-ray nuclei of calcium and heavier (the so-called VH nuclei). These measurements result in integral intensity values for energies greater than 7.1, 1.58, and 1.00 GeV per nucleon, together with differential intensities over the range [Formula: see text] MeV per nucleon. Differential intensities were also found for lighter nuclei over varying energy ranges. The differential spectrum observed has a maximum value of about 1.6 × 10−3 nuclei/m2 sr s MeV per nucleon around [Formula: see text] MeV per nucleon and falls off at both higher and lower energies. These values are based on the observation of a total of some 1 600 VH nuclei. The energy spectrum has been compared with that observed at similar times for the helium nuclei in order to study the influences of ionization energy losses during propagation of these high-Z nuclei. These observations are interpreted as implying that if the source spectra of the VH nuclei and the helium nuclei are similar, then the VH nuclei have traversed less than 1 g/cm2 of matter while ionization energy loss has been the dominant acceleration term.