Dolbear's law

The Dolbearsche Act ( Dolbear 's Law ) describes the relationship between the temperature and the Zirprate one occurring almost anywhere in the U.S. Cricket, of the flowers crickets belonging Oecanthus fultoni ( Snowy Tree Cricket ), which therefore also as a thermometer Grille ( thermometer cricket) is called. The "law " was the physicist and inventor Amos Emerson Dolbear (1837-1910) formulated and published in 1897. In the requirements set and simplified form used today, you have to only 13 seconds count how many chirps the insect. If we add to this number 40, then you get the temperature at the location of the cricket in degrees Fahrenheit.

Dolbear was to determine the temperature TF in degrees Fahrenheit of the number N of the chirping sounds in 60 seconds, the following formula:

This formula can be simplified by shortening, which the Division is eliminated. Then only the chirping sounds are to be counted within 15 seconds, but at the expense of precision. The temperature in degrees Fahrenheit is obtained simply by the addition of 40:

A conversion of Dolbearschen formula for the temperature in degrees Celsius results in exactly:

Most of the denominator is rounded to 7, so that the formula can be easier to remember. Shortening is not useful in this formula, because then you would have only 8.3 seconds long are chirping sounds. The few chirping sounds would lead to unacceptably large errors. In addition, the specifying of the time is more difficult than at 15 or 60 seconds.

Dolbear wrote in his original work exclusive of crickets ( crickets ). He mentions neither place nor date. Only a year later, other authors report that his measurements between August and September in Nebraska occurred on Oecanthus niveus. Bessey Bessey and publish in 1898 as more accurate formula ( 16-27 ° C) delivers between 60 and 80 ° F only deviations by one to two degrees:

Abridged gives the exact:

Usually the formula is still rounded as specified Dolbearsches law, although it differs from the original formulation:

A better description of the non-linear relationship, in particular at temperatures below 60 ° F ( 16 ° C), to get when using an Arrhenius Equation ( TK here is the temperature in Kelvin):

The exponent corresponding to an activation energy of about 52 kJ / mol (12 kcal / mole ), as is known from other biological systems. However, the redenominated on the temperature formula contains mathematical operations that make a work out in my head impossible ( result in Kelvin):

The dependence of the Zirprate on temperature is different for each singing crickets or grasshopper. In addition, there are regional differences. It comes here first so precisely to the kind of. By 1962 the species name O. niveus was used instead of O. fultoni often. Also in the context found by Dolbear it must be Oecanthus fultoni act, because the way Oecanthus niveus in the modern sense has a completely different song rhythm that would lead to false results. Another problem is that almost the entire United States ( except Hawaii, Alaska, Montana, and Florida) spread Grille west of the Great Plains sings faster at the same temperature. Here is the simple linear formula must be changed to:

Exact results can be achieved when the Zirpraten the barbecue songs of each area are plotted against the temperature. An adapted to the measured values ​​curve over the entire temperature range in which the animals sing, just one degree Fahrenheit.

Oecoanthus fultoni has the great advantage that the Zirprate little scattered, the Zirprate only to a very limited extent on other factors (eg, age, individual), the song of the people very well and good to hear is (frequency in a favorable range of 2.7 kHz, relatively high sound intensity ), the chirping sounds good can count due to the species-specific rate in the entire temperature range and the animal occurs almost everywhere in the U.S. and is often. Other crickets or grasshoppers species are less favorable in one or more of these points, although their Zirprate strongly dependent on the temperature. For this reason, there is no other country in a comparable popular "law."