en>Brirush: /* Equivalent formulations */ Added modularity theorem, some references

2013-11-15T17:28:03Z

Equivalent formulations: Added modularity theorem, some references

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[[File:Snowytreecricket.JPG|thumb|The tree cricket ''Oecanthus fultoni'']]'''Dolbear's law''' states the relationship between the air [[temperature]] and the rate at which crickets chirp.<ref name=frings57/><ref name=frings62/> It was formulated by [[Amos Dolbear]] and published in 1897 in an article called "The Cricket as a Thermometer."<ref name=dolbear>{{cite journal |last1=Dolbear |first1=Amos |year=1897 |title=The cricket as a thermometer |journal=The American Naturalist |volume=31 |pages=970–971 |url=http://books.google.com/books?id=Jqco0ttVn0gC&lpg=PA970&ots=jVb2ir2UK1&dq=%22The%20Cricket%20as%20a%20Thermometer%22&pg=PA970#v=onepage&q=%22The%20Cricket%20as%20a%20Thermometer%22&f=false|accessdate=27 November 2012}}</ref> Dolbear's observations on the relation between chirp rate and temperature were preceded by an 1881 report by Brooks, although this paper went unnoticed until after Dolbear's publication.<ref name=frings62/>

Dolbear did not specify the species of cricket which he observed, although susbsequent researchers assumed it to be the snowy tree cricket, "''Oecanthus niveus''."<ref name=frings57>{{cite journal |last1=Frings |first1=Hubert |last2=Frings |first2=Mable |year=1957 |title=The effects of temperature on chirp-rate of male cone-headed grasshoppers, Neoconocephalus ensiger |journal=Journal of Experimental Zoology |volume=134 |issue=3 |pages=411–425 |doi=10.1002/jez.1401340302 |url=http://onlinelibrary.wiley.com/doi/10.1002/jez.1401340302/abstract |accessdate=27 November 2012}}</ref> <ref name=frings62>{{cite journal |last1=Frings |first1=Hubert |last2=Frings |first2=Mable |year=1962 |title=Effects of temperature on the ordinary song of the common meadow grasshopper, Orchelimum vulgare (Orthoptera: Tettigoniidae) |journal=Journal of Experimental Zoology |volume=151 |issue=1 |pages=33–51 |doi=10.1002/jez.1401510104 |url=http://onlinelibrary.wiley.com/doi/10.1002/jez.1401510104/abstract |accessdate=27 November 2012}}</ref> However, the snowy tree cricket was misidentified as ''O. niveus'' in early reports and the correct scientific name for this species is ''[[Oecanthus fultoni]]''.<ref name=walker62> {{cite journal |last1=Walker |first1=Thomas J. |year=1962 |title=The Taxonomy and Calling Songs of United States Tree Crickets (Orthoptera: Gryllidae: Oecaiithinae). I. The Genus ''Neoxabea'' and the ''niveus'' and ''varicornis'' Groups of the Genus ''Oecanthus'' |journal=Annals of the Entomological Society of America |volume=55 |issue=3 |pages=303–322 |publisher=Entomological Society of America |url=http://entnemdept.ifas.ufl.edu/Walker/buzz/s576lw62.pdf |accessdate=27 November 2012}}</ref>

The chirping of the more common [[field cricket]]s is not as reliably correlated to temperature—their chirping rate varies depending on other factors such as age and mating success. In many cases, though, the Dolbear's formula is a close enough approximation for field crickets, too.

==Equations==
Dolbear expressed the relationship as the following formula which provides a way to estimate the temperature ''T<sub>F</sub>'' in degrees Fahrenheit from the number of chirps per minute ''N<sub>60</sub>'':

<math>T_F = 50 + \left ( \frac{N_{60}-40}{4} \right ).</math>

This formula is accurate to within a degree or so when applied to the chirping of the [[field cricket]].

Counting can be sped up by simplifying the formula and counting the number of chirps produced in 15 seconds (''<math>N_{15}</math>''):

<math>\,T_F = 40 + N_{15}</math>

Reformulated to give the temperature in degrees Celsius(°C), it is:

<math>T_C = 10 + \left ( \frac{N_{60}-40}{7} \right ).</math>

A shortcut method for degrees Celsius is to count the number of chirps in 8 seconds (''<math>N_{8}</math>'') and add 5 (This is fairly accurate between 5 and 30°C):

<math>\,T_C = 5 + N_{8}</math>

The above formulae are expressed in terms of integers to make them easier to remember—they are not intended to be exact.

==In popular culture==
This formula was referenced in an episode (Season 3, Episode 2, "The Jiminy Conjecture") of the American TV sitcom ''[[List of The Big Bang Theory episodes#The Jiminy Conjecture|The Big Bang Theory]]'' (although Sheldon referred to Amos Dolbear as Emile Dolbear).
It is also referenced in an episode (Season J, Episode 10, "Jungles") of the British comedy show [[QI]].
It is also Snapple "Real Fact" CC2#771. <ref>[http://www.snappletop.com/p/601-800.html Snapple Top Collection Services]</ref>

==See also==
*[[Arrhenius equation]]

==References ==
<references/>

[[Category:Zoosemiotics]]
[[Category:Crickets]]

Modular elliptic curve - Revision history

en>Brirush: /* Equivalent formulations */ Added modularity theorem, some references