The capabilities of the apparatus for measuring the thermal conductivity of multilayer insulations, powders, fibers, and foams are pointed out, and the details of the construction are summarized. The vacuum system and instrumentation are briefly described. Special attention is devoted to a method of controlling the pressure of the gas above the boiling cryogenic liquid and to an automatic method of measuring small boil-off rates. Calibration of the apparatus, reproducibility of test results, and the effects of guarding of the exposed edges of the specimen are discussed.