A critical review is given of those factors which may be accompanied by variations in brain weight, viz. sex, body size, age of death, nutritional state in early life, source of the sample, occupational group, cause of death, lapse of time after death, temperature after death, anatomical level of severance, presence or absence of cerebrospinal fluid, of meninges, and of blood-vessels. Valid comparisons between the brain-weight of human populations should take all, or several, of these variables into account; however, published studies have not done so, despite claims to the contrary. The ideal sample is from subjects who have died suddenly without prior disease: while three such samples are on record for Europeans, none has been recorded for Negroes. The brain-weight of healthy Negroes is not known. Most published interracial comparisons are invalid. The histological, chemical and functional counterparts of big and small brains in modern man are not known. Published interracial comparisons of thickness of the cerebral cortex and, particularly, of its supragranular layer, are technically invalid: there is no acceptable proof that the cortex of Negroes is thinner in whole, or in any layer, than that of Europeans. It is concluded that vast claims have been based on insubstantial evidence.