Methods of correlation of any number of input functions or signals to be compared are discussed. It is shown that correlation values can be obtained from any one of several arithmetic processes which measure the degree of similarity of the inputs, and that these processes can be mechanized. Included are a simple addition, a sign‐coincidence scheme, and two processes based on analysis of variance. The discussion of analysis of variance procedures as applied to signals shows that the answers can be interpreted in terms of statistical significance, that measurements of coherent signal power can be made, and that the accuracy of such measurements is greatly improved as the number of input signals is increased. Signal‐to‐noise ratio is shown to be uniquely related to statistical significance, and signal detectability is plotted as a function of number of inputs and signal duration. Several means of presentation of data are suggested and illustrated.

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For 35 years the La Coste suspension has been used in gravimeters and vertical component seismometers, yet its precise design and best adjustment have been handicapped by limited knowledge of the forces which combine to produce a stable instrument. The present analysis gives quantitative relations which merit consideration in design, and provides a rational step-by-step basis for obtaining the best possible adjustment of any instrument using the La Coste principle. The magnitude and effect of spurious forces such as may be caused by magnetic impurities or faulty construction is discussed briefly. The special case of the inclined boom seismometer is covered in a discussion of the symmetrical triaxial instrument invented by the author.

The literature on earth noise over the spectrum of periods from 0.1 s to 12 h is reviewed and presented as accelerations which, when expressed as spectral‐noise density, allow all seismographs to be considered on a common basis of sensitivity. Their ultimate sensitivity is limited by thermal agitation of their suspended masses and is calculable by considering the energy flow to and from their lossy elements in accordance with principles elucidated by Nyquist. Practical instruments, including those with feedback loops, are considered as examples. Seismometers and accelerometers are treated here as resonant systems having one degree of freedom. The electrical outputs of their transducers are classified as ‘velocity’ or ‘displacement.’ The dynamic range required to record these outputs depends on the range of accelerations imposed on the instrument and upon the combined filtering effects of the resonant system and transducer. Gravitational variation, tilt, and tidal accelerations are considered as they affect the instrumental problem.