Dolbear's law

Amos Dolbear about 1880

Dolbear's law applies exclusively to this one type of flower cricket: Oecanthus fultoni

The Dolbearsche Act (Dolbear's Law) describes the relationship between the temperature and the Zirprate one occurring almost everywhere in the US Grille , of the tree cricket belonging oecanthus fultoni (Snowy Tree Cricket), which is also referred to as a thermometer Grille (thermometer Cricket). The “law” was formulated by the physicist and inventor Amos Emerson Dolbear (1837–1910) and published in 1897. In the more precise and simplified form used today, one only has to count for 13 seconds how often the insect chirps. If you add 40 to this number, you get the temperature at the location of the cricket in degrees Fahrenheit .

Dolbear used the following formula to determine the temperature T _F in degrees Fahrenheit from the number N of chirps in 60 seconds:

${\displaystyle T_{F}=50+\left({\frac {N_{60s}-40}{4}}\right)}$

This formula can be simplified by shortening it, which eliminates the division. Then only the chirps have to be counted within 15 seconds, but this is at the expense of accuracy. The temperature in degrees Fahrenheit is obtained simply by adding 40:

${\displaystyle \,T_{F}=40+N_{15s}}$

A conversion of Dolbear's formula for the temperature in degrees Celsius gives exactly:

${\displaystyle \vartheta =10+\left({\frac {N_{60s}-40}{7{,}2}}\right)}$

Usually the denominator is rounded to a whole 7 so that the formula is easier to remember. Shortening this formula does not make sense, since you would then only have to count chirps for 8.3 seconds. The few chirps would lead to unacceptably large errors. In addition, specifying the time is more problematic than with 15 or 60 seconds.

In his original work, Dolbear wrote exclusively of crickets. He does not mention the place or the date. Only a year later do other authors report that his measurements were taken on Oecanthus niveus in Nebraska between August and September . In 1898, Bessey and Bessey published a more precise formula that only yields deviations of one to two degrees between 60 and 80 ° F (16-27 ° C):

${\displaystyle T_{F}=60+\left({\frac {N_{60s}-92}{4{,}7}}\right)}$

In short, this results in exactly:

${\displaystyle \,T_{F}=40,4+N_{12{,}8s}}$

Most of the time, the formula is still given as Dolbear's law, although it differs from the original formulation:

${\displaystyle \,T_{F}=40+N_{13s}}$

A better description of the non-linear relationship, especially at temperatures below 60 ° F (16 ° C), can be obtained by using an Arrhenius equation (T _K is the temperature in Kelvin ):

${\displaystyle N_{13s}=5{,}63\cdot 10^{10}\cdot e^{-{\frac {6290K}{T_{K}}}}}$

The exponent corresponds to an activation energy of around 52 kJ / mol (12 kcal / mol), as is also known from other biological systems. The formula changed according to the temperature, however, contains mathematical operations that make it impossible to calculate in the head (result in Kelvin):

${\displaystyle T_{K}={\frac {6290K}{24{,}8-\ln(N_{13s})}}}$

The dependence of the chirp rate on the temperature is different for each singing cricket or grasshopper species. There are also regional differences. So it depends exactly on the type. Until 1962 the species name O. niveus was often used instead of O. fultoni . The connection found by Dolbear must also be Oecanthus fultoni , because the species Oecanthus niveus in today's sense has a completely different song rhythm that would lead to incorrect results. Another problem is that the cricket west of the Great Plains, which is common across most of the United States (except Hawaii, Alaska, Montana, and Florida), sings faster at the same temperature. Here the simple linear formula has to be changed to:

${\displaystyle \,T_{F}=38+N_{12,5s}}$

More precise results can be achieved if the chirp rates of the cricket chants of the respective area are plotted against the temperature. A curve adapted to the measured values ​​is accurate to one degree Fahrenheit over the entire temperature range in which the animals sing.

Oecoanthus fultoni has the great advantage that the chirping rate does not vary much, the chirping rate depends only to a very small extent on other factors (e.g. age, individual), and the singing can be heard very widely and easily for humans (frequency in a favorable range of 2.7 kHz, relatively high sound intensity), the chirps can be counted well over the entire temperature range due to the species-specific rate and the animal occurs and is common almost everywhere in the USA. Other cricket or grasshopper species are less favorable in one or more of these points, although their chirp rate is also highly dependent on temperature. For this reason there is no other country with a comparably popular “law”.

Web links

Thomas J. Walker, Singing Insects of North America : Snowy Tree Cricket (description, images, sound documents and notes on the temperature dependence of singing)

Individual evidence

1. ↑ Amos Emerson Dolbear (1897): "The Cricket as a Thermometer" in: The American Naturalist 31 (371): pp. 970-971. doi : 10.1086 / 276739
2. ^ Carl A. Bessey and Edward A. Bessey (1898): "Further Notes on Thermometer Crickets" , in: The American Naturalist 32 (376): pp. 263-264. doi : 10.1086 / 276838
3. ↑ Natural Clocks: Cricket Chirps , at: dartmouth.edu, accessed August 12, 2015.
4. ↑ Keith J. Laidler (1972): "Unconventional Applications of the Arrhenius Law", in: Journal of Chemical Education 49 (5): pp. 343-344. (PDF, English)  ( Page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. from: drjez.com, accessed August 12, 2015.  
5. ↑ Thomas J. Walker (1962): "The taxonomy and calling songs of the United States tree crickets (Orthoptera: Gryllidae: Oecanthinae). I. The genus Neoxabea and the niveus and varicornis group of the genus Oecanthus ", in: Annals of the Entomological Society of America 55: pp. 303-322. (PDF, English) at :haben.ifas.ufl.edu, accessed on August 12, 2015.
6. ^ L. Elliott and W. Hershberger, The songs of insects . Houghton Mifflin: Boston, 2007 ISBN 0-618-66397-5 .
7. ↑ Thomas J. Walker, Snowy Tree Cricket at: ungemdept.ufl.edu, accessed on August 12, 2015.