The Pelidisi System

In The Big Show in Bololand: The American Relief Expedition to Soviet Russia in the Famine of 1921, Bertrand M. Patenaud writes of a system to identify the children most in need of help, the Pelidisi system:

This was the creation of a Viennese medical doctor, Professor Clemens Pirquet, who served as chairman of the Austrian equivalent of the [Russian-managed relief committee]. Pirquet devised a formula for determining the degree of undernourishment in children up to the age of fifteen. The measurement was the cubic root of the tenfold weight of the body divided by that body's sitting height. For adults the average would be 100, for children 94.5--anything below that signified undernourishment.

On the face of it, this is confusing. The cube of 100 is 1,000,000: so for units x of weight and y of height we need a body weight of 100,000x for height 1y. Unfortunately, the units are not stated. But presumably, since Pirquet was Austrian, they are taken from the metric system. Nor is "sitting height" defined. One can make sense of this by assuming that

• weight is stated in grams
• height is given as centimeters from the ground, or anyway the seat
• we aim at  numerator/denominator = 1, then multiply by 100

For a person weighing 100 kg, 10 * the weight in grams will be 1 million, the cube root one hundred. That just works out with a seated height of 1 meter, 100 centimeters, which one might expect of a man 6'7" tall. Men that height play basketball at 220 lb without anyone supposing that they are starved. Still the numbers look about right.

An article in the Journal of the Royal Army Medical Corps gave the formula as stated, and also committed itself to the statement that "the cube of the sitting height in centimetres is about ten times the body weight in grammes." Again, assuming that for sitting height we sit on the ground or measure from the seat, my sitting height is around 90 cm: I would be considered adequately nourished at around 72 kg, roughly my weight on graduating from college. A person 5' tall might have 75 cm sitting height. Then that person should weigh around 42 kg, call it 93 lb.