Data from the Statistical Report on School Health and Hygiene were used to identify the entire process of the power of height p in the weight-for-height index W/H(p). The appropriate power of height p was determined by clarifying the allometric relationship, giving an index of relative weight, which is highly correlated with weight but uncorrelated with height for age. The procedure is equivalent to fitting a straight line on a log-log scale to the tabulated weights by height in different age groups. The p values show directional changes from 5 to 17 years of age in both sexes. The optimal p value is approximately 2 in preschool children but increases gradually to over 3 at 10 years in males and 11 years in females, and then falls back to 2 after puberty. The largest p value occurs 18 months earlier in females than in males, and the pattern is the same in the present samples and American samples. Because there are remarkable changes between 12 to 14 years in females and 14 to 16 years in males, the general weight-for-height indices with the precise power of height are preferable at these ages. A fixed power 3.0 is suggested for children between 3 and 12 years irrespective of sex or race.