his own way give the formula complete, with its numerical coefficients, as follows:

Q=3·33(L—n2h)h3,

where Q the discharge in cubic feet per second;

L=the length of the notch in feet;

n the number of end contractions;

h=the height from the crest to the still-water surface-level in feet.

Mr. Francis also states that this formula is not applicable to cases in which the height h from the crest to the still-water surface-level exceeds one third of the length, nor to very small depths. In the experiments from which it was determined the depths varied from 7 inches to 19 inches; and he remarks that there seems no reason why it should not be applied with safety to any depths between 6 inches and 24 inches.

Report of the Anthropometric Committee, consisting of Dr. BEDdoe, Lord ABERDARE, Dr. FARR, Mr. FRANCIS GALTON, Sir HENRY RAWLINSON, Colonel LANE Fox, Sir RAWSON RAWSON, Mr. JAMES HEYWOOD, Dr. MOUAT, Professor ROLLESTON, Mr. HALLETT, Mr. FELLOWS, and Professor LEONE LEVI.

The Anthropometric Committee have been engaged during the past year in preparatory work. They have secured the cooperation of gentlemen holding positions under Government as inspectors of the army, of the navy, of factories, and of pauper schools. They have prepared schedules and instructions, and have had them printed; and they have purchased a small outfit of ⚫ instruments to send to places where measurements are to be made in large numbers.

Under these circumstances they are unable to make a report of anthropometric results; neither have they been called upon to expend more than a small portion of the grant of £100 that was made to them in 1875, the larger part of which will be required to pay for the reduction of observations. Consequently they ask that the Anthropometric Committee may be reappointed, with modifications, and that the grant may be carried forward to the year 1876.

* Lowell Hyd. Exp. § 164, page 133.

On Cyclone and Rainfall Periodicities in connexion with the Sun-spot Periodicity. By CHARLES MELDrum.

[Printed in extenso by the authority of the Council.]

IN continuation of the paper on this subject published in the Report for 1874 (pp. 218-240), I beg to submit the following brief discussion of the cyclones of the Indian Ocean, between the equator and 34° S., in the years 1868-75, and of the rainfall in different places from 1854 to 1872.

Cyclones.

The number of cyclones in each year, the positions of their centres at noon on each day, their extent, duration, &c. have been approximately determined in the way already described, and the results are given in Table I.

From that and the similar Table given in 1874 we obtain the following general results for the twenty years 1856-75 :—

It will be seen that, on the whole, the number of cyclones increased from 1857 to 1862, decreased from 1862 to 1867, then increased to 1870, and again decreased to 1875.

The distances traversed had nearly a similar progression, increasing from 1856 to 1861, decreasing from 1861 to 1867, then increasing to 1872, and again decreasing to 1875.

The areas have been determined by finding as nearly as possible the radii

of the spaces (considered more or less circular) over which the wind blew with the force of a "strong gale." They therefore are not the entire areas. But, apart from this, owing to incomplete information, the radii are not known for each day, and hence the areas are only rough approximations. There is no doubt, however, that they increased from 1856 or 1857 to 1860, decreased from 1860 to 1867, increased from 1867 to 1872, and then decreased to 1875.

On the whole, there was a similar progression in the duration of the cyclones, the smallest number of days being in 1856, 1857, 1867, and 1875, and the greatest in 1861 and 1870.

The total areas, i. e. the products of the mean area of each cyclone by the number of days it lasted, increased from 1856 to 1861, decreased from 1861 to 1867, increased from 1867 to 1872, and then decreased to 1875.

It is to be remarked, however, that the total areas for the years 1860–62 were much greater than those for the years 1870-72. This may be owing partly to the radii for the latter years having been underestimated. On the other hand, the number of cyclone-days in the years 1870-72 was somewhat greater than in the years 1859–61.

Rainfall.

A sufficient number of rainfall returns for the years 1873-75 have not yet been obtained; but the annual mean rainfalls at seventy-seven stations from 1854 to 1863, and at seventy-two stations from 1864 to 1872, are given in Table II., in which all the rainfall observations at my disposal have been used, except a few Prussian and Mauritius ones, which would not have affected the general results.

The Table shows that, with hardly an exception, the sun-spots and rainfall were both above or both below their respective averages in the same years.

By taking the longer period 1843-72, and expressing the amounts of rainfall and sun-spots in percentages, we get the following results:—

From 1843 to 1856 there were eighty-four stations, from 1856 to 1867
seventy-seven stations, and from 1867 to 1872 seventy-two stations in various
parts of the globe; and in making the comparisons the same stations have
been used.

Comparing with the sun-spots the depths of water given by Herr Gustav
Wex* for one or more of the rivers Elbe, Rhine, Danube, Oder, and Vistula,
we obtain, for the six sun-spot periods from 1800 to 1867, the following
Table, in which the numbers in the first column represent the years, viz.
No. 1 the years 1800, 1812, 1824, 1833, 1844, and 1856, and so on; AD the
variations of the water-depths; and Ar the variations of the sun-spots:

* Ueber die Wasserabnahme in den Quellen, Flüssen und Strömen. Wien, 1873.

TABLE I.-Showing the duration, extent, &c. of Cyclones experienced in the Indian Ocean from 1867 to 1875.