“Three Dimension” Graphs for Correlating “Age-Weight-Gland” Relationships

Abstract

In biometric studies of rats, it is desirable at times to compare simultaneously and graphically (1) Various organs by weight with (2) age and (3) body weight of the animal. By ordinary two dimension graphs, relationships between any 2 of these data can be well illustrated, but only by “three dimension” graphs is it possible to illustrate simultaneously the interrelationship of all 3–age, body-weight and weight of any given organ.

The construction of such graphs is simple (Chart 1) : Ordinate AB forms with abscissae BC and BD an angle of 120°. AB represents age, the only constant uniform with all rats; BC body-weight and BD gland-weight. The “age-weight” is easily plotted, the line B₁C₁ paralleling BC and forming an angle of 120° (AB₁C₁). Gland-weight is plotted from B₁ (corresponding to age) on line AB to D₁ (representing gland-weight), which point must be on a line perpendicular to AB projected from C₁ (corresponding to body-weight).

For normal rats all lines representing “age-body-weight” (B₁C₁) will parallel abscissa BC and form angles of 120° with ordinate AB, differing only in length. The lines representing “age-gland-weight” (B₁D₁) will vary in length and will parallel BD only when the increase in weight of the gland, with respect to age is directly proportional to the increase in body weight. If the gland is small for the age, angle D₂B₁A will be greater than 120° and line D₂B₁ short. If the gland is large, then line D₃B₁ will be longer and angle D₃B₁A more acute.