Music Pens.—There are two kinds of pen used for the purpose of writing music ; the one to rule the lines, and the other to make the dots. The former is a piece of brass with five prongs or points, in each of which is a channel for the ink, which is supplied from a small cup in the solid part of the pen just above the division of the points. The latter is a mere tube with a hole in its side for supplying it with ink, and a small wire or piston fitted within it. The ink flows between tho wire and its case, and the dot is made by placing the pen upon the spot, and pressing the wire down upon the paper.
Geometric Pen. —This is an instrument invented by Suardi, an Italian, for drawing geometric curves. These curves may by combination be made to form an almost infinite variety of patterns. The pen is supported, as shown iu the diagram, by three legs bowed so as to allow room for the instrument to work within them. These legs shut together by the joint at the top for the convenieneb of package. Attached to the joint is a stem or axis x, upon the lower end of which is fixed the toothed wheel A ; this stem, with its wheel, is stationary, and all the other parts of the instrument move round it. Just above the wheel A his small tube or cannon, c, to which is attached an arm carrying two boxes and spindles for supporting the wheels DII; the spindle E is continued downwards, and terminates in a socket s, through which passes an arm carrying the pencil ur tracer, T. The two wheel boxes, D n, on the ono arm, and the socket, 8, on the other, may be fixed at any part of their respective arms by means of screws for that purpose. Fixed to the tube C is a small circular plate of metal with a milled edge, by which the instrument is moved around its axis by the thumb and finger.
The sort of curves produced by this instrument depends upon three circumstances first, the relative size of the wheels A and 13; second, whether the wheel n be employed or not, or in other words, whether the two arms move in directions contrary or similar to each other (this wheel has no effect otherwise, and may be of any convenient size); and third, on the relative distance of the tracer T from the spindle E, and of that spindle from the axis x, which may be expressed as the relative distance of TE and r x. The following diagram gives an idea of a few of the most simple curves. The number of parts or leaves in each figure depends on the first of the three circumstances above mentioned : for fig. 1 the wheels a and n must be equal ; for fiy. 2, as 4 to 1 ; and for the rest, as 3 to 1. On the second circumstance depends whether the loops or points are within the curve, as in figs. 1, 2, and 3 ; or on the outer side, as ih the others ; and lastly, upon the third circum stance depends the shape of the points or loops themselves. For the eight curves given above, TE must be less than Ex; but if this is reversed, the curves assume a most curious, complicated, and some times beautiful arrangement.
Suardi states that 1273 curves may be produced by the changes of twelve wheels, the smallest having eight, the next sixteen, and so on to ninety-six teeth ; and that by the addition of a few pieces, spirals with a circular base, and particularly the spiral of Archimedes, may be produced.
For further information the reader is referred to Suanli's work, entitled ' Nuevo Instrumento per la Descrizione di diverse Curve Antiehi e 'Moderns,' &c.; and to Adam's ' Geometric Essays: