tells us that Wagner, during his stay in England, was amazed at the skill of our vocalists. "Our best singers," he said, "do not sing shakes nor make runs like that." 66 Although I am an English singer," writes Mr. Santley, "I hold that you will find in no country in the world as good and clean execution as you do in England." This superiority he attributes to our practice in singing Handel's oratorios. As to our choral singing in particular, Herr Otto Lessmann, the correspondent of the principal musical paper of Germany at the Leeds Festival of 1887, bears this emphatic testimony "The intonation was as sure as possible; the sound mellow and round, yet abounding in power and brilliancy. The rapid passages which Bach and Handel have written for chorus came out as clearly and flowingly as if from a flute. I repeat dispassionately that I have never heard such first-rate choral performances in any town on the Continent. The performance, as a whole, was without a parallel." : Finally, in the highest department of musical activity-that of composition-the signs are encouraging in no ordinary degree. I can quote no higher authority than that of our countryman, Dr. A. C. Mackenzie, the Principal of the Royal Academy. In an address delivered by him at Manchester five years ago I find the following: -"As regards composers, we may certainly say that England can now hold her own against the Continental nations. I doubt very much whether Italy, France, or Germany has at this time men beside whom, to mention only a few names, our Sullivan, Barry, Cowen, Prout, Corder, Stanford, and Thomas would look small. Nay, I would go further, and say that, excepting Verdi, Gounod, and Brahms, of whom only the last may be said to be in full activity, the Englishmen named by me are the peers, if not more than the peers, of their musical contemporaries in other countries." To the same effect is the witness of the German critic already cited, "If I am not entirely deceived, a new day has dawned for English music with the present musical young England. Although, indeed, educated in Germany, or according to the German masters, and endowed with all the ability which the German school requires of its own adherents, certain young English composers have nevertheless reflected that they owe it to the honour of their country to go their own way." It is true that no composer of transcendent genius has yet appeared. For his advent we must be content to wait; great men come only after a nidus has been formed for their reception. They utter the thoughts of many generations. We cannot conceive of a great musician being born among the savages in the interior of Africa. In the music of the great composers we hear not their own voices only, but the voices of a great multitude who lived before them and around them. It may be that ages of preparation must yet elapse before a great genius like Bach or Beethoven can spring from our race. Every one who loves music may do something to hasten the time. If we try to cultivate in ourselves and others the love of whatever in music is highest and purest and loveliest, then we are preparing a way for our great musician who is to be. April 21, 1891.-JAMES MOIR, M.A., LL.D., President, Mr. WILLIAM SMITH, M. Inst. C.E., Harbour Engineer, read a paper entitled "On the Dynamics of a Cell, and of Muscular Action." On the Dynamics of a Cell, and of Muscular Action. I do not know that the subject of the development of work by the inflation of a cell of flexible material has ever been seriously discussed. It certainly has not hitherto been utilised in the construction and use of artificial motors, nor has it yet been recognised as the primary mechanical principle on which all animal motion is based. The materials for the evolution and illustration of the theory are now copious, much more so than when, in the winter session of 1868, at Glasgow University, I made the first cell of pasteboard and silk to illustrate for myself, by a working model, one of Dr. Carpenter's diagrams of the ultimate cell of muscle. The readiest illustration of the contraction of a cell by inflation is formed by placing the hands together, palm to palm, with the fingers straight. This is a cell extended or flaccid. On opening the hands, by bending the finger joints outwards, keeping the tips of the fingers in close contact, the cell formed by the hands is inflated, and at the same time shortened. Being fixed at the wrists, the finger-tip end is drawn forcibly inwards, and this force is exactly proportioned to the pressure outwards of the fluid supposed to be inflating a cell. Any cell or bag of flexible and inelastic material will contract forcibly lengthwise on being inflated, owing to the deflection of the sides of the cell. Take a straight line, A B (Fig. 1) and deflect it by lateral pressure at the point C, leaving one end, say B free to move towards the other end A. The lateral force applied at the point C, has its counterpart or resultant in the forcible movement of B towards A. If the line A CB (Fig. 2) is rotated on the axis A B, it describes a cell wall; and by applying the lateral force C to every point in the line AB, or cell wall, it becomes the force or pressure of the inflating fluid. The cell wall is both piston and cylinder, and so long as the resistance to contraction F along the line B2 B, is less than the resultant of the inflating pressure P at right angles to it, the movement of the point B towards A will continue. 2 1 Where there is no external resistance on the cell wall, the condition of equilibrium under internal pressure is arrived at on the cell becoming spherical (Fig. 7). The length of stroke of a spherical cell B1 B2, is π r − 2 r = (π − 2) r, where r is the radius of the sphere, and making r unity, the cell contracts to 2/3 of its total extended length, or a little less than; and the stroke or length of contraction is 14 into the radius, or a little more than the radius of the contracted sphere. The cell walls may be considered as consisting of three pairs of pistons forming the sides and ends of a box constantly changing in their relative areas during inflation. Two pairs of pistons, C1, C21 C3, C4 (Fig. 3), are being driven outwards by the inflating fluid in the direction of the equatorial diameter of the cell, while the other pair A, A2, or the ends, are being drawn together along its axial diameter. = 1 1 The two pairs of pistons, C1, C2, C3, C4, are, more correctly speaking, to be regarded as a cylindrical or hexagonal wall, shortening in length as it expands in diameter, while the pistons A, A 2, representing the cylinder ends, increase in area as they approximate. When the area of the cylindrical wall becomes equal to the joint area of the ends, that is, when the length of the cylinder or hexagon the diameter (Fig. 4B), equilibrium of the opposing forces, due to the pressure of the inflating fluid multiplied into the respective areas, is obtained; and the useful work of the expansion of the cell ceases. The volume of the cell increases up to this limit, and any farther expansion of the cylindrical walls, as in Fig. 4C, diminishes the volume of the cell, and expels a portion of the inflating fluid, or otherwise requires a compression of the fluid, which represents negative work, or the storing of potential energy, instead of the development of useful work. The actual representation of an expanding cell under the pressure of an internal fluid, is a series of spheroids, from the initial linear spheroid, or straight line, of the flaccid cell up to the sphere in which last the force of the pressure of the fluid multiplied into the area is equal in all directions (Fig. 5). The useful work done by the expansion (or contraction-the terms being merely relative to the axis considered) of a cell may be computed simply by calculating on the whole range of expansion, or, more elaborately, for any portion of the range. d = Suppose the fluid enters a cylinder having a moveable piston at one end (Fig. 6), then the work done in driving the piston a distance pressure p x area A of piston x the distance d; or, the area of piston x the distance the increase of volume V, that is, the work is proportional to the volume x the pressure, say × p. Taking the case of a cell expanded by an inflating fluid from its initial form of a line, O B, to the final form of a sphere (Fig. 7), 0 B2, then, evidently, the whole work, V × p = πr 3p. Suppose the whole work spent in overcoming a resistance = F, between B1 and B, while the point O is fixed, then the work done in overcoming the average resistance F = F× (π − 2)r; and as F× (π − 2)r = r3p, therefore F 4 π p. That is, the pressure per unit area multiplied by the projected area of the hemisphere is nearly equal to the statical pull of the cell. When the internal pressure per unit area is constant=p [say, so many pounds per square inch], then the whole initial pressure = 0, and the whole final pressure = 4 r 2p. This supposes the whole work to be spent on the resistance F, and thus omits to take into account work done (if any), 1st, in overcoming molecular resistances of the expanding fluid, such as loss by heating, or churning; 2nd, in overcoming resistance of the material of the cell; and 3rd, all work done against external pressures on the surface of the cell. Since the whole work equals the pressure multiplied into the increase of volume, it is evidently indifferent whether the expanding spheroid be a single cell, or is supposed to be divided into any number of cells; provided the initial and final volumes be each the same, the whole work done will be the same, and so also will F, the average resistance. An interesting feature of the cell is the statical advantage it possesses over the resistance near the beginning of the stroke, when slightly inflated. The most powerful method known of applying leverage is that used in the machines for crushing stones and ores, namely, a pair of struts inclined at a low angle to the axial line with a wedge driven down between their upper ends (Fig. 8). |