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showing that the frequent repetition of the process of ethylation had pro^ duced, not the hydriodate of triethylic rosaniline, hut the ethyliodate o< this substance,—a result which appeared particularly welcome, inasmuch as it threw at the same time considerable light upon the degree of substitution which belongs to rosaniline itself.

The facts elicited by the study of the action of iodide of ethjl upon rosaniline open a new field of research, which promises a harvest of results. The question very naturally suggests itself, Whether the substitution for hydrogen in rosaniline of radicals other than methyl, ethyl, and amvl, may not possibly give rise to colours differing from blue; and whether chemistry may not ultimately teach us systematically to build up colouring molecules, the particular tint of which we may predict with the same certainty with which we at present anticipate the boiling-point and other physical properties of the compounds of our theoretical conceptions?

This idea appears to have floated in the mind of M. E. Kopp when, with remarkable sagacity, he concluded his paper on Aniline-red* in the following terms:—" The hydrogen of this substance being replaceable also by methyl, ethyl, and amyl, &c, we may anticipate the existence of a numerous series of compounds, all belonging to the same type, and which might constitute colouring matters either red, or violet, or blue."

Conceptions which only two years ago appeared little more than a scientific dream, are now in the very act of accomplishment.

I propose to continue these researches, and intend in a later communication to submit to the Royal Society the results obtained in the Btudy of two other colouring matters derived from rosaniline, viz. anilinegreen and aniline-violet.

November 26, 1863.

Major-General SABINE, President, in the Chair.

In accordance with the Statutes, notice was given from the Chair of the ensuing Anniversary Meeting, and the list of Officers and Council proposed for election was read as follows :—

President.—Major-General Edward Sabine, R.A., D.C.L., LL.D.
Treasurer.— William Allen Miller, M.D., LL.D.

Secretaries I WiUiam SharPe7> MD> LLD

\ George Gabriel Stokes, Esq., M.A., D.C.L.

Foreign Secretary.—Prof. William Hallows Miller, M.A.

Other Members of the Council.—James Alderson, M.D.; George Busk, Esq.,Sec. L.S.; Col.SirGeorgeEverest,C.B.; Hugh Falconer, M.A.,M.D.;

* Ann. de Chim. et de Phys. [3] lxu. 230.

John Hall Gladstone, Esq., Ph.D.; Joseph Dalton Ilooker, M.D.; Henry Bence Jones, M.A., M.D.; Prof. James Clerk Maxwell, M.A.; Prof. William Pole, C.E.; Archibald Smith, Esq., M.A.; Prof. Henry J. Stephen Smith, M.A.; The Earl Stanhope, P.S.A., D.C.L.; Prof. James Joseph Sylvester, M.A.; Thomas Watson, M.D., D.C.L.; Prof. Charles Wheatstone, D.C.L.; Rev. Prof. Robert Willis, M.A.

The question of Captain Ibbetson's readmission into the Society was put to the ballot, and, the ballot having been taken, Captain Ibbetson was declared to be readmitted.

The, following communications were read:—

I. "Account of Magnetic Observations made between the years 1858

and 1861 inclusive, in British Columbia, Washington Territory, and Vancouver Island." By Captain R. W. Haig, R.A. Communicated by the President. Received November 4, 1863.

(Abstract.)

This paper contains the results of magnetic observations made between the years 1858 and 1861 inclusive, in 'British Columbia, Washington Territory, and Vancouver Island. The results are tabulated; and from them the direction and position of the lines of equal dip, total force, and declination or variation are determined.

Three maps at the end show the position of these lines, the stations of observation, and the observed values of the three magnetic elements at each station.

II. "On Plane Water-Lines." By W. J. Macqtjoen Rankine, C.E.,

LL.D., F.R.SS.L. & E., Assoc. Inst. N.A., &c. Received July 28,

1863.

(Abstract.)

1. By the term " Plane Water-Line" is meant one of those curves which > particle of a liquid describes in flowing past a solid body when such flow takes place in plane layers. Such curves are suitable for the water-lines of a ship; for during the motion of a well-formed ship, the vertical displacements of the particles of water are small, compared with the dimensions of the ship; so that the assumption that the flow takes place in plane layers, though not absolutely true, is sufficiently near the truth for practical pur

2. The author refers to the researches of Professor Stokes (Camb. Trans. ll*42), "On the Steady Motion of an Incompressible Fluid," and of Pro

* Ai water-line curves have at present no single word to designate them in matheamical language, it is proposed to call them Neoidt, from vt)bs, the Ionic genitive of ►aw.

fessor William Thomson (made in 1858, but not yet published), as con taining the demonstration of the general principles of the flow of a liquii past a solid body.

3. Every figure of a solid, past which a liquid is capable of flowing smoothly, generates an endless series of water-lines, which become sharpe: in their forms as they are more distant from the primitive water-line of th< solid. The only exact water-lines whose forms have hitherto been com pletely investigated, are those generated by the cylinder in two dimensions and by the sphere in three dimensions. In addition to what is already known of those lines, the author points out that, when a cylinder moves through still water, the orbit of each particle of water is one loop of an elastic curve.

4. The profiles of waves have been used with success in practice as waterlines for ships, first by Mr. Scott Russell (for the explanation of whose system the author refers to the Transactions of the Institution of Naval Architects for 1860-62), and afterwards by others. As to the frictional resistance of vessels having such lines, the author refers to his own papers —one read to the British Association in 1861, and printed in various engineering journals, and another read to the Royal Society in 1862, and printed in the Philosophical Transactions. Viewed as plane water-lines, however, the profiles of waves arc not exact, but approximate; for the " solitary wave of translation," investigated experimentally by Mr. Scott Russell (Reports of the British Association, 1844), and mathematically by Mr. Earnshaw (Camb. Trans. 1845), is strictly applicable to a channel of limited dimensions only, and the trochoidal form belongs properly to an endless series of waves, whereas a ship is a solitary body.

5. The author proceeds to investigate and explain the properties of a class of water-lines comprising an endless variety of forms and proportions. In each series of such lines, the primitive water-line is a particular sort of oval, characterized by this property, that the ordinate at any point of the oval is proportional to the angle between two lines drawn from that point to two foci. Ovals of this class differ from ellipses in being considerably fuller at the ends and flatter at the sides.

6. The length of the oval may bear any proportion to its breadth, from equality (when the oval becomes a circle) to infinity.

7. Each oval generates an endless series of water-lines, which become sharper in figure as they are further from the oval*. In each of those derived lines, the excess of the ordinate at a given point above a certain minimum value is proportional to the angle between a pair of lines drawn from that point to the two foci.

8. There is thus an endless series of ovals, each generating an endless series of water-lines; and amongst those figures, a continuous or "fair" curve can always be found combining any proportion of length to breadth,

* As a convenient and significant name for these water-lines, the term " Oogenous Neoi'ds" is proposed (from 'Qoyci'i/s, generated from an egg, or oval).

from equality to infinity, with any degree of fullness or fineness of entrance, from absolute bluffness to a knife-edge.

9. The lines thus obtained present striking likenesses to those at which naval architects have arrived through practical experience; and every successful model in existing vessels can be closely imitated by means of them.

10. Any series of water-lines, including the primitive oval, are easily and quickly constructed with the ruler and compasses.

11. The author shows how to construct two algebraic curves traversing certain important points in the water-lines, which are exactly similar for ill water-lines of this class. One is a rectangular hyperbola, having its rertex at the end of the oval. It traverses all the points at which the motion of the particles, in still water, is at right angles to the water-lines. The other is a curve of the fourth order, having two branches, one of which traverses a series of points, at each of which the velocity of gliding of the particles of water along the water-line is less than at any other point on the same water-line; while the other branch traverses a series of points, at each of which the velocity of gliding is greater than at any other point on the same water-line.

12. A certain point in the second branch of that curve divides each series of water-lines into two classes,—those which lie within that point having three points of minimum and two of maximum velocity of gliding, while every water-line which passes through or beyond the same point has only two points of minimum and one of maximum velocity of gliding. Hence the latter class of lines cause less commotion in the water than the former.

13. On the water-line which traverses the point of division itself, the velocity of gliding changes more gradually than on any other water-line having the same proportion of length to breadth. Water-lines possessing this character can be constructed with any proportion of length to breadth, from VZ (which gives an oval) to infinity. The finer of those lines are found to be nearly approximated to by wave-lines, but are less hollow at the bow than wave-lines are.

14. The author shows how horizontal water-lines at the bow, drawn according to thi3 system, may be combined with vertical plane lines of motion for the water at the stern, if desired by the naval architect.

15. In this, as in every system of water-lines, a certain relation (according to a principle first pointed out by Mr. Scott Russell) must be preserved between the form and dimensions of the bow and the maximum speed of the ship, in order that the appreciable resistance may be wholly frictional and proportional to the square of the velocity (as the experimental researches of Air. J. It. Napier and the author have shown it to be in wellformed ships), and may not be augmented by terms increasing as the fourth and higher powers of the velocity, through the action of vertical disturbances of the water.

VOL. XIII.

III. "On the degree of uncertainty which Local Attraction, if no allowed for, occasions in the Map of a Country, and in the meai figure of the Earth as determined by Geodesy: a method of ob taining the mean figure free from ambiguity, from a comparisoi of the Anglo-Gallic, Russian, and Indian Arcs: and speculation: on the Constitution of the Earth's Crust." By the Venerabl< J. H. Phatt, Archdeacon of Calcutta. Communicated by Pro fessor Stokes, Sec. R.S. Received Oct. 5, 1863. (Abstract.) After referring to a former paper in which he had shown that, in th< Great Indian Arc of meridian, deflections of the plumb-line amounting to as much as 20" or 30" would be produced if there were no sources of compensation in variations of density beneath the surface of the earth, and after alluding to a remarkable local deflection which M. Otto Struve had discovered in the neighbourhood of Moscow, the author proceeds to consider, in the first instance, the effect of local attraction in mapping a country according to the method followed by geodesists, in which differences of latitude and longitude are determined by means of the measured lengths of arcs, by substituting these lengths and the observed middle latitudes in the known trigonometrical formulae, using the mean figure of the earth, although the actual level surface may differ from that belonging to the mean figure in consequence of local attraction. He concludes that no sensible error is thus introduced, either in latitude or longitude, if the arc do not exceed 12\° of latitude or 15° of longitude in extent, but that the position of the map thus formed on the terrestrial spheroid will be uncertain to the extent of the deflection due to local attraction at the station used for fixing that position. In the Great Indian Arc this displacement might amount to half a mile if the deflections were as great as those calculated from the attraction of the mountains and the defect of attraction of the ocean, irrespective of subjacent variations of density; but the author shows in the next two sections that some cause of compensation exists which would rarely allow the actual uncertainty to be of any considerable amount, unless the station used for fixing the map were obviously situated in a most disadvantageous position.

The author then proceeds to examine the effect of local attraction on the mean figure of the earth, considering more particularly the eight arcs which have been employed for the purpose in the volume of the British Ordnance Survey. He supposes the reference station of each arc to be affected to an unknown extent by local attraction, and obtains formulae giving the elements of the mean figure obtained by combining the eight arcs, these formulae involving eight unknown constants expressing the deviations due to local attraction at each of the selected stations. By substituting reasonable values for the unknown deflections, he shows that local attraction s competent to affect the deduced mean figure to a very sensible extent.

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