# A Mathematical Model for Odors Applied to Binary Odor Mixtures

To begin, we shall distinguish the“odor” attached to any substance, even if it is not detectable, from the “perceived odor” of a substance resulting from the composition of the “odor” of said substance and the “odor” of the environment in which it is immersed (generally air), which we suppose even though it may be odorless.

In the following, we represent the odor of a substance with the vector of a fixed origin O, and we represent the odor of the environment with the vector of origin O supported by the axis . Let be the vector that represents the odor of substance A, and the vector that represents that of the surrounding environment. The perceived odor of substance A will be represented with the vector . The intensity of the perceived odor of A will be noted down ψΑ = length of vector .All of the perceived odors of A, whatever their intensities, will be represented with vectors , whose extremity A’ is on half-line passing through O such that =λ. If another substance B exists in the same environment, the perceived odor resulting from the presence of A and B will be represented with a vector (1).

It may be observed that ; that is, it is the vectors representing the odors that are actually added, and not those representing the perceived odors (in Berglund’s model the vectors representing the perceived odors were added).