Simple empirical formulae for expressing the lineal growth of the human fetus

In the quantitative study of the growth of the human body there is often need for simple and accurate formulæ for expressing the relation between body-length and prenatal age. Empirical formulæ for lineal growth in the fetal period (3 lunar months to birth) have been published by Hassee 1 , Henry and Bastien 2 , and Scammorn 3 . No one of these is entirely satisfactory, for the first gives results which are not in accord with modern findings regarding prenatal lineal growth, the second is highly complicated, and the third is primarily for use in estimating the length from the age, whereas one usually desires to determine the age from the length. Practicable formulæ of this kind should fulfill the following conditions: (a) They should express age in terms of body-length for the entire fetal period (3 months to birth). (b) They should give a close fit to reliable data on the subject. (c) They should be in simple form, which will permit their application with ordinary arithmetic without the use of tables of special functions and the like. With these conditions in mind the following formulæ have been developed on the basis of the data of Mall 4 .

When Mall's observations are placed in graphic form they approximate a parabola having the general form: T = a + bL + cL², where T is the age in fetal or lunar months (calculated from the first day of the last menstruation), L is the total or crown-heel length in cm., and a, b and c are constants. The specific formula for expressing this relations is:

This may be simplified to:

For estimating the crown-heel length from the age, the formula may be transformed into :

These formulæ may also be modified for further use. According to Mall, the cohabitation age averages 10 clays less than the menstrual age which is estimated from the first day of the last menstruation, and the individual deviations from this average are quite small. Therefore, the formula for menstrual age may be modified to

to express the cohabitation age.