Journal of Physics of the Earth

New general differential formulae for the change of the geographical coordinates system are derived under the simple assumptions that the datum point and any other triangulation point are fixed in space and that the small quantities such as products, squares and so on of δa, δe2, δψ0, δλ, δα0 etc. are all negligible. The formulae for δψ, δλ, δh are expressed in terms of geographical longitudes and latitudes, including those given in the text-book of HELMERT and of BONFORD as special cases. With respects to δs, δα12, δα21, the usual formulae are available as they are, provided that δψs', δλs' are previously evaluated by the present formulae.
The astro-geodetic conditions for the azimuth and the zenith distance are derived, and in particular the Laplace condition corresponding to a special case of one of the astro-geodetic conditions is examined from a general view point.

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In order to see whether or not there is a lower limit in the magnitude of earthquakes, in other words whether or not "minimum" earthquakes exist and to investigate the rate of occurrence of microearthquakes, the present writer has designed and constructed Ultra Sensitive Seismometers of short period, which have a magnification of 1.3×10⁷ at 20cps. They were temporarily installed at Mt. Tsukuba, Kanto district. About 400 microearthquakes were recorded in 48 hours in total. This shows that about one hundred thousand microearthquakes are occurring in and near Kanto district every year. These microearthquakes are not aftershocks of a particular large earthquake. Most of them are occurring in the area within 100km from the Tsukuba observatory. Their E are about 10¹⁰ ergs to 10¹³ ergs. Their earthquake-motions have a prevailing frequency of some tens of a cycle per second, and so they can be recorded only by seismometers extraordinarily sensitive for 10cps to 100cps.
Tens of sensible earthquakes are being felt at Mt. Tsukuba every year. Based upon this fact and the number of microearthquakes recorded at the place during 24 hours, it can be concluded that the equation for magnitude frequency relation,
logN(M)=a-bM,
holds for earthquakes of M from less than zero up to about 5 occurring in a certain seismic region. The space distribution of foci of microearthquakes agrees approximately with that of earthquakes of M 4 or 5.

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