Prolonged sine

The law of the prolonged sine was observed when measuring the strength of the reaction of the plant stems and roots in response to turning from their usual vertical orientation.

The prolonged sine law was observed when measuring the dependence of the bending speed from the angle of reorientation.

It was observed that deviation from the desired growth direction by more than the 90 degrees causes further increase of the bending speed.

Poul Larsen in 1962 [1][2] proposed, that the intensity of the gravitropic reaction (bending rate) is proportional to where α is the angle of reorientation, g - gravity vector and constants a and b are determined experimentally.

[3] Following the popular hypothesis of the mechanism of the plant spatial orientation, the bending from the horizontal position is caused by some small heavy particles that after turning put pressure on the side cell (statocyte) wall, irritating some systems and activating the bending process.