On The Uses Of Harmonic Analysis.

Submitted—The following memorandum by Professor Stokes :

Meteorological elements may be considered and discussed from two points of view. We may either contemplate the progress of the changes at any particular time, as, for example, in tracing the history of a particular storm, or in endeavouring to make out general laws connecting the changes of the various elements, such as Buys Ballot's Law; or we may seek to deduce from large masses of observations regular fluctuations which underlie the total fluctuations presented as the immediate result of observation, of which last a more or less considerable part have no immediate relation to the time, but in contemplating the regular periodic fluctuations are to be regarded as casual.

For the first object great accuracy is not required; what we want is to get a general comprehensive view; and this is afforded in a very available form by the published diagrams. Moreover, for this object means are useless, or very nearly so.

It is for the second object that the publication of hourly results is chiefly, if not exclusively, demanded. Besides the more obvious regular changes which have long been known, investigators may wish to examine whether there may not be other regular periodic changes which may be discovered by discussing a great number of observations.

Suppose now the results for each day were subjected to harmonic analysis, and the numbers read off on the cylinders of the machine alone published, we should have five or seven numbers (according as the analysis was carried to the second or third order) to publish, instead of 24.