The law of the prolonged
sine
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opp ...
was observed when measuring strength of the reaction of the plant stems and roots in response to turning from their usual vertical orientation. Such organisms maintained their usual vertical growth, and, if turned, start bending back toward the vertical. The prolonged sine law was observed when measuring the dependence of the bending speed from the angle of reorientation.
The observed law
It was observed that deviation from the desired growth direction by more than the 90 degrees causes further increase of the bending speed. After turning the 135 degrees the reoriented
plant
Plants are predominantly Photosynthesis, photosynthetic eukaryotes of the Kingdom (biology), kingdom Plantae. Historically, the plant kingdom encompassed all living things that were not animals, and included algae and fungi; however, all curr ...
or
fungi
A fungus (plural, : fungi or funguses) is any member of the group of Eukaryote, eukaryotic organisms that includes microorganisms such as yeasts and Mold (fungus), molds, as well as the more familiar mushrooms. These organisms are classified ...
understands that it is places "head down" and bends faster than turned by just 45 degrees. Poul Larsen in 1962 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.
[Сила тяжести в процессах роста растений / А. И. Меркис; Отв. ред. Г.Б. Максимов. - М. : Наука, 1990. - 185 с. : ил., граф., табл. - Библиогр.: с. 169-184. - ]
Significance
Following the popular
hypothesis
A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can testable, test it. Scientists generally base scientific hypotheses on prev ...
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 the pressure on the side
cell
Cell most often refers to:
* Cell (biology), the functional basic unit of life
Cell may also refer to:
Locations
* Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
(
statocyte Statocytes are gravity-sensing ( gravitropic) cells in higher plants. They contain amyloplasts-statoliths – starch-filled amyloplastic organelle
In cell biology, an organelle is a specialized subunit, usually within a cell, that has a specific ...
) wall, irritating some system and activating the bending process. The pressure of such particle to the cell was would be proportional to the sine of the reorientation angle, being maximal at 90° reorientation. It would be equal for the reorientations by both 45° and 135°. The prolonged sine law concludes that there are very significant deviations from such a predicted reaction.
References
{{DEFAULTSORT:Prolonged Sine
Plant physiology