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which carries the registering paper can be detached by loosening a clampingscre-w which fastens it to the support turned by the clock, so that the sheets can be removed and replaced with speed and facility.
The entire apparatus was constructed by Mr. Spencer, of Aungier Street, Dublin; and he has executed the portion connected with the indication of horizontal movement in such a way, that the addition of a registering apparatus for this part of the instrument will not only bo easy, but will render the entiro combination a complete indicator of the absolute direction of the wind. The results of the instrument in its present state are exhibited on the registering sheets as nearly vertical pencil lines, some above and some below the neutral line, to which each sheet is carefully adjusted.
The anemoscope is at present so placed as not to be overtopped by any building; for it stands on the roof of one of the highest houses in Dublin, in a quarter remarkably open, and close to the south suburbs.
Owing to a variety of delays and obstacles in finishing the apparatus, it was not brought into action until the 31st of August, and thus I am able to report only on the results furnished by little more than the records of a single month. These records appear to indicate that vertical oscillations prevail moro during the mid-day hours than at other periods; for although ten sheets show no definite predominance at any specific period of the day, and two predominance of vertical movements towards midnight, twenty-one show that these movements are most frequent at the hours about noon. From a journal of the weather which was kept at the same time, it appeared that on bright days, when the air had little horizontal motion, gentle upward movements prevailed at mid-day. Such phenomena are distinctly manifested by the sheets for September the 5th, 6th, 7th, 8th, and 9th, and all of these were bright sunny days. Before the 5th, tho weather had been changeable and unsettled: but on comparing the two sheets comprehending from noon of the 3rd to noon of the 5th, I noticed that the amplitude of the oscillations of the anemoscope progressively and regularly diminished; and it occurred to mo that this might indicate a tendency towards convective equilibrium of the atmosphere, and more settled weather. The weather continued fine until the 13th, when there was both high wind and rain, accompanied and preceded by energetic oscillations of the anemoscope. If the general circulation of tho atmosphere takes place, as seems to be now completely established, by a twofold motion, one of translation, whether cyclonic or lineal, and the other undulatory, it follows that the pulsations of the latter movement may be influenced by aerial disturbances. The frequency, regularity, intensity, prevalent direction, and more or less intermittent character of these pulsations must depend on variations of pressure, density, moisture, and temperature, as well as on the rippling motion of the air. It is natural, therefore, to expect, what our limited number of observations soem already to indicate, namely, that the sudden and abrupt commencement of such pulsations is usually a precursor of other disturbances, while their gradual and regular diminution in energy would show a tendency in the air to approach a state of convective equilibrium, and might, thorefore, bo safely relied upon as a forerunner of fine weather. This point is illustrated by the remarks of tho late Professor Daniell relative to the rapid oscillations of tho water-barometer during high winds, and their gradual diminution preceding a return to a calmer state of the air*. Although the atmospheric pulse is undoubtedly compounded of the undulatory movements resulting from tho flow of an elastic fluid over the
* Phil. Trans. 1832, p. 573.
irregularities of the earth's surface, with the effects of convection, in such a way as would render the separation of these effects extremely difficult, yet the careful study of this pulse in connexion with other phenomena may he reasonably expected to add to our power of forming correct conclusions regarding the coming changes of the weather.
Report of a Committee, consisting of the Rev. Dr. Lloyd, General SaBine, Mr. A. Smith, Mr. G. Johnstone Stoney, Mr. G. B. Airy, Professor Donkin, Professor Wm. Thomson, Mr. Cayley, and the Rev. Professor Price, appointed to inquire into the adequacy of existing data for carrying into effect the suggestion of Gauss, to apply his General Theory of Terrestrial Magnetism to the Magnetic Variations.
In order to explain the views of the Committee upon the question submitted to them, it is necessary to refer briefly to the leading points of Gauss's theory.
If dfi denote the quantity of free magnetism in any element of the earth's mass, and p the distance of that element from the point (x, y, z), and if we make
the partial differential coefficients of V with respect to the three coordinates, x, y, z, respectively, are equal to the components of the earth's magnetic force in the direction of the axes of coordinates. V is a function of x, y, and z, or of their equivalents tt, X, and r,—r being the distance of the point from the centre of the earth, and « and X the angles corresponding to the north polar distance, and the longitude, on the sphere whose radius = r. This quantity may be expanded in a series proceeding according to the inverse powers of r, whose coefficients, P,, P2, Pa, &c, are functions of u and X alone; and it is readily seen that, at the surface of the earth, the three components of the magnetic force are
\ du au au J
Z=2P1 + 3P2 + 4P3 + &c,
and are therefore given when P„ P2, P„ &c. are known.
The form of these functions is deduced from the well-known partial differential equation
n(n+l)P.+i^+cotu5? + -ir-^"«»0,
n being the number indicating the order of the function. It is found that the first, P,, contains three unknown coefficients; the second, P2, five; the third, P3, seven, &c. Hence, if the approximation be extended so as to include terms of the fourth order, there will be 24 coefficients to be determined. Each given value of X, Y, or Z, on the earth's surface, furnishes an equation among these unknown coefficients; and for each place at which the three elements are known we have three such equations. Hence to obtain the general expressions of X, Y, Z, to the fourth order inclusive, it is theoretically sufficient to know the three elements at eight points on the earth's surface. But, owing to the errors of observation, and to the influence of the terms neglected in the approximation, the number of determinations must, in practice, be much greater than the number of unknown coefficients.
The foregoing conclusions are based upon the hypotheses that magnetic attraction and repulsion vary according to the inverse square of the distance, and that the magnetic action of the globe is the resultant of the actions of all its parts. It is likewise assumed that there are two magnetic fluids in every magnetizable element, and that magnetization consists in their separation. But for these hypotheses we may substitute that of Ampere, which supposes the magnetic force to be due to electric currents circulating round the molecules of bodies.
This theory may be applied to the changes of terrestrial magnetism, whether regular or irregular, provided only that the causes of these changes act in the same manner as galvanic currents, or as separated magnetic fluids. We have only to consider whether the data which we possess are sufficient for such an application.
It has been already stated that, for the general determination of X, Y, and Z, we must know their values at eight points (at least) on the earth's surface, these points being as widely distributed as possible. Tho same thing holds with respect to the changes oX, IY, SZ; and to apply the formula; so determined, and to compare them with observation, corresponding values must be known for (at least) one more point. In the case of the irregular changes these observations must, of course, be simultaneous. The regular changes must be inferred from observations extending over considerable periods; and there is reason to believe that these periods must be identical, or nearly so, for all the stations, since the changes are known to vary from month to month and from year to year.
The regular variations of the three elements X, Y, Z, or their theoretical equivalents, have been obtained by observation, for nearly the same period, at Greenwich, Dublin, and Makerstoun, in the British Islands; at Brussels and Munich, on the Continent of Europe; at Toronto and Philadelphia, in North America; at Simla, Madras, and Singapore, in India; and at St. Helena, the Cape of Good Hope, and Hobarton, in the southern hemisphere. Of these thirteen stations, however, the three British must be regarded, for the present purpose, as equivalent to one only, on account of their proximity; and the same thing may be said of the two North American stations and of the two stations in Hindostan. This reduces the number of available stations to nine, the minimum number required for the theoretical solution of the problem in the degree of approximation already referred to, and considered by Gauss to be necessary. It is true that we may add to theso the stations at which two only of the three elements have been observed, viz. Prague and St. Petersburg, the three Bussian stations in Siberia, and Bombay. But even with this addition, tho number is probably insufficient for the satisfactory determination of the unknown coefficients; for it is to be remembered that the places, few as they are, are not distributed with any approach to uniformity, and that very large portions of the globe are wholly unrepresented by observations.
For the reason already stated, this defect in the existing data cannot be now repaired by supplemental observations at new stations, unless tho series at all were so far extended as to embrace the whole period of the cyclical changes.
The simultaneous observation of the irregular changes is limited nearly to the same stations. In their case, too, there is the further imperfection, as respects the present problem, that the changes observed on "term-days" are for the most part inconsiderable, while those on days of great magnetic disturbance have seldom been observed continuously for any considerable time at all the stations.
For the foregoing reasons the Committee are of opinion that the data which wo at present possess respecting tho changes of terrestrial magnetism, whether regular or irregular, are not sufficient for the application of Gauss's theory, if, as above assumed, the approximation is to be extended so as to include terms of tho fourth order (P, to P4 inclusive). It is deserving of consideration, however, whether an inferior degree of approximation may not afford some valuable information. The affirmative side of this question has been so earnestly advocated by one of tho members of the Committee, that it has been thought advisable to append his letter on the subject to this Report.
(Signed by order of the Committee) H. Lloyd.
Letter from Professor W. Thomson to Rev. Dr. Lloyd.
"Roshven, Strontian, Sept. 24, 1862.
"My Dear Sir,—I am sorry to have been so long prevented from writing to you on the subject of the Committee's Report on the expression of the Variations of the Terrestrial Magnetic elements in series of Laplace's functions.
"I perfectly agree with the conclusions stated in the draft report of which you sent me a proof, so far as they relate to a complete expression of any class of variations of the elements, or of any individual variation, by means of which its amount in other localities than those of observation could be determined with any considerable approach to accuracy. But, on tho other hand, the amount of knowledge from observation, shown in the report to be available, would, I believe, be sufficient to allow us to estimate, possibly with considerable accuracy, and certainly with a sufficient approach to accuracy for highly important application, the first terms in the harmonic (Laplace's) series. I would therefore advise that some such method as the following should be adopted.
"Choosing any particular variation, for instance the diurnal or the secular, for which tho data from observation are most abundant, find either by trial and error, or any other proper algebraic method, an expression by terms of the first order (three coefficients for each) for the three elements which most nearly represent it. (The method of least squares would give a precise definition of what would be the most near representation, on this principle ; but ruder and quicker methods might suffice in first trials.) Then, judging by the results, try similarly for expressions in series of two terms (3 + 5, or eight coefficients in all, in each expression). After trials of this kind it would be easy to judge within what limits may be the probable errors of the estimated first terms from tho true first terms, and possibly even to arrive at some probable knowledge regarding the true second terms of tho harmonic expressions.
"A very moderate degree of success in such operations as these would allow us to decide whether the origin (magnetic or electrodynamic) of the variation is within the earth's surface or outside.