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.

S. Kensington,

3rd Nov., 1890.

Dear Sir George,

In the summer you asked me to let you have some quartz fibre. I now leave a box containing one long one wound 18 times up and down the frame. The front and back of the box are of glass so that the fibre may be examined without risk, and black paper is placed at one end in case a dark background may be required.

The glass may be taken out after first removing a screw at the end, and then the frame can be removed.

The fibre is good, in that under the prism test it shows both perfectly uniform pieces and places where the variation in diameter gives rise to small [i.e. short but pronounced and jagged] bends in the dark bands of the spectrum.

To see these spectra to perfection the following is the best way to hold the box and a prism: first see the colours with the naked eye [with light from a slit, the box intervening] and then hold a low-angle prism in front of the eye, not in the natural position of minimum deviation, but inclined so that incident light falls at about the polarising angle. It is only thus that the dark bands appear really dark.

On then moving the box along its own length so as to make successive parts of the fibres occupy the same position, you will see some of the fibres giving a constant spectrum which is the test of uniformity, while some show the irregularities described.

LETTERS TO DR ROMNEY ROBINSON, 1875–1879 AND 1880–1881.

The first group of the following letters have been selected from a series belonging to the period 1875-9, carefully arranged in years evidently by Dr Robinson himself. The remaining part is printed from duplicate typewritten copies preserved among Prof. Stokes’ manuscripts.

A long correspondence on anemometers of the year 1877 is omitted: reference may be made to Dr Robinson's memoir, Phil. Trans. 1878, also to Math, and Phys. Papers, Vol. v. pp. 73–99.

Cambridge, 4th Jan. 1875.

…I heard to-day from Mrs Harcourt. The instrument she referred to is a finely graduated circle, with telescopes for measuring refractive indices, which she gave to me for my life time, leaving the ultimate destination yet to be settled. I was not aware this had been sent to you, and I am not sure that it was. When I was at Nuneham shortly after Mr Harcourt's death, she expressed a wish to give us each some instrument of his. She may have mentioned the refractometer as for you (I cannot now recollect), and I may have suggested that you had an equivalent instrument already, and that it might be very valuable to me as I did not possess one. If she had thought of giving it to you she may have recollected the intention and supposed it had been actually sent. I could not suppose that she meant to offer to me an instrument she had already given to you.

I am not sure whether I mentioned that the Chances have made an experiment on a silico-titanic glass. Hopkinson, Senior Wrangler in 1871, who is their scientific adviser, had the superintendence of it. He sent me a specimen of the glass.