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 opposite th ...
was observed when measuring the 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 the eukaryotes that form the Kingdom (biology), kingdom Plantae; they are predominantly Photosynthesis, photosynthetic. This means that they obtain their energy from sunlight, using chloroplasts derived from endosymbiosis with c ...
or
fungi
A fungus (: fungi , , , or ; or funguses) is any member of the group of eukaryotic organisms that includes microorganisms such as yeasts and mold (fungus), molds, as well as the more familiar mushrooms. These organisms are classified as one ...
understands that it is placed "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 (: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess o ...
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. The pressure of such particle to the cell 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
Plant physiology
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