(b) ST. HELENA, 1840-1847. Long. oh. 22m. 41.9s. W. of Greenwich or Lat. -15° 56° 41.2' S. Height of barometer cistern above mean sea-level 1764-5 feet (by levelling). The observations considered extend from 1840 May to 1847 July, with one interruption. They are published in detail in Sabine's "Observations made at the Mag. and Met. Observatory at St. Helena." Vols. I. and II. London, 1847-1860. The barometer was made by Newman according to a description given by the Royal Society. The internal diameter of the tube is 0.6ins. The scale terminating in an ivory point, is movable. The barometer would thus appear to be of the same type as that which is still in use at the Cape Observatory, but the latter has an internal diameter o.1in. less. Until Sept., 1842, observations were taken at every even hour of Göttingen mean time, after that date until the conclusion of the series, at every hour. Observations were intermitted for 24 hours on Sundays and holidays. The barometer was moved in August, 1840, to a position 19 feet higher. The height given above is that of the barometer after removal. The observations of 1840, May-July, are reduced to 1764-5 feet. Before leaving England, the barometer was compared with the Royal Society's Standard, and found to require a correction of -0.007ins. This correction includes the thermometer error. It was intended to make another comparison with the Standard after the conclusion of the observation, but no record of this having been done, has been found. In 1844, from 22nd April to 3rd May, simultaneous cbservations were made with another barometer near sea-level. The mean difference between the two barometers when corrected for all known errors, was found to be 1.786ins., which must be increased by 0.009 for reduction to sea-level, the lower barometer being 9.3 feet above sea-level. Table 1 gives the mean monthly readings of the barometer at the above station reduced to 32° F. and Lat. 45°. No correction for decrease of gravity due to altitude has been applied,—this has not been necessary, as it is naturally included in the comparison with the barometer near sea-level. The extreme readings of the barometer in each season (reduced as in Table 1) are :— Table 1 shows that in the mean the lowest barometer occurs in March and the highest in July. The means can be represented by a Fourier series. As the calendar months are of varying lengths, we should not assume that the mean of any month is the mean of the corresponding one-twelfth of the year. The introduction of a rational calendar is probably out of the question. Such a one is as follows: The This calendar would coincide with the present one on Jan. 1st, April 1st, June 1st, and from August 1st to the end of the year. quarters and half-years would compare as follows: With this rational calendar, the derivation of the co-efficients of a Fourier series by the assumption that each month is a twelfth of a year would be sufficiently exact for all purposes. In taking monthly means, some meteorologists transfer the last day of January and the first of March to February. But if we keep to the means of the calendar months, we can make use of the formule developed by Mons. A. Angot in the Annales du Bureau Central Meteorologique de France, 1887., Vol. I., pp. B227-B236. This course has not been followed here, as it would be a refinement not warranted by the material at our disposal, and, indeed, we did not know of Angot's formulæ when the computations were made. Where is measured from the middle of January, we find that the expression 28.2210544 cos 0-190 sin 0. + 198 cos 20+ 7 sin 20. 21 COS 30- 47 sin 30. represents the mean monthly height of the barometer at St. Helena as follows: As the average deviation of any given month is about 0.012in. from the mean of a series of years, the above representation is satisfactory. In considering the diurnal variation of the barometer at St. Helena we have confined ourselves to the period during which hourly readings were taken. Allowance has been made for the difference of height in the mercury between the first and last readings in each month, so that the annual variation of the barometer has been eliminated. After the calculations had been completed, it was found that Mons. Angot had also derived the figures. A comparison with Mons. Angot's table (Annales du Bureau, 1889, Vol. I., p. B250) shows that our figures, though in the main following his very closely, sometimes deviate by quantities up to 0.005ins. These differences may arise from two causes, (1) in the published observations a considerable number of errors or misprints were found, and it is probable others have escaped detection by either of us, (2) Mons. Angot probably incorporated the two-hourly series. If we represent the deviation at any hour from mean of day by the series C1 cos h+C2 cos 2h+ C3 cos 3h+etc. +S1 sin h+S2 cos 2h+S3 sin 3h+etc. we find the values given in Table III. The above formula can be transformed to a, sin (h+A)+a, sin (2h+A2)+etc. The co-efficients in this case are furnished in Table IV. Mons. Angot gives the latter co-efficients up to a, and A. reduced to true time. The reduction to true time may amount to 15° in the case of A1. A priori, the introduction of true solar time seems to be correct in principle, but the figures do not show improvement. The angle A, is the most constant; in Table IV. it shows an extreme range of 9°, whereas by reducing to true time, the range will be increased to 13°. It is tempting to find if the co-efficients of Tables III. and IV. can be represented by a Fourier series. The partial results of such an attempt will be found in Table V., in which is measured from the middle of January. The results are not satisfactory. The co-efficients of the different terms vary so irregularly that it is plain that the variations of the barometer are not simple functions of the Sun's longitude. If we attempt to exhibit the equation of time by a simple series in which the variable is the Sun's mean longitude, we come on similar irregular co-efficients. It is, of course, possible to exhibit the equation of time with great exactitude by such a series, but it would throw no light on its causes, which we know reside in the obliquity of the ecliptic, the excentricity of the Earth's orbit and the position of the perihelion. But we do not yet know all the causes of the diurnal variation of the barometer. There is the very great difficulty of finding the true height of the barometer freed from temperature effects. The usual method of correcting a barometer for temperature can only be considered a first approximation. Probably each barometer has its own secondary corrections due to lag, etc. Herein consists the great advantage of the Sprung barograph, which records in effect the varying weight of the mercury. It therefore requires no correction of the first order for temperature, and the correction for terms of the second order is easily made mechanically. It is impossible to say how much of the smaller terms of Table III. are due to the residual temperature effects. |