Omittable Planes

In analogy to omittable lines in the plane, we initiate the study of omittable planes in $3$-space. Given a collection of $n$ planes in real projective $3$-space, a plane $\Pi$ is said to be omittable if $\Pi$ is free of ordinary lines of intersection – in other words, if all the lines of intersection of $\Pi$ with other planes from the collection come at the intersection of three or more planes. We provide two infinite families of planes yielding omittable planes in either a pencil or near-pencil, together with examples having between three and seven omittable planes, examples that we call "sporadic," which do not fit into either of the two infinite families.

Drama as Textual Practice

A popular notion in medieval drama study is that plays can be fully accessed only in the moment of performance. This idea has been challenged only recently. This article proposes a somewhat different line of critical enquiry that focuses not on the text’s performative qualities, but on the literate practices set into motion in the text’s articulation and transmission. More specifically, it considers the skills and procedures that are regularly used by trained professionals not only in their ordinary lines of work but also to drama. It looks at the clerk’s job of copying a great London spectacle into the city’s official books while also doing a great deal of creative work, citing a report by John Carpenter about Henry VI’s entry into London as an example. It also examines late medieval English drama in relation to the English liturgy, as exemplified by Resurrection plays. Finally, the article discusses the Terence revival and translation in England.

Collineations of Projective Moulton Planes

In the article "Moulton Planes" (10), I studied F. R. Moulton's construction over any field containing a multiplicative subgroup of index 2. In "Collineations of Affine Moulton Planes" (11), I determined the collineations between two arbitrary affine Moulton planes.The purpose now is to describe the collineations between two projective Moulton planes. Since the affine collineations are known from (11), we are concerned with collineations mapping ideal lines onto ordinary lines. Notations and conventions of (10) and (11) are retained.

On the Number of Ordinary Lines Determined by n Points

More than sixty years ago, Sylvester (13) proposed the following problem: Let n given points have the property that the straight line joining any two of them passes through a third point of the set. Must the n points all lie on one line? An alleged solution (not by Sylvester) advanced at the time proved to be fallacious and the problem remained unsolved until about 1933 when it was revived by Erdös (7) and others.

The theory of the Helmholtz resonator

The ideal form of Helmholtz resonator is a cavernous space, almost enclosed by a thin, immovable wall, in which there is a small perforation establishing a communication between the interior and exterior gas. An approximate theory, based upon the supposition that the perforations is small, and consequently that the wave-length of the aërial vibration is great, is due to Helmholtz who arrived at definite results for perforations whose outline is circular or elliptic. A simplified, and in some respects generalised, treatment was given in my paper on "Resonance." In the extreme case of a wave-length sufficiently great, the kinetic energy of the vibration is that of the gas near the mouth as it moves in and out, much as an incompressible fluid might do, and the potential energy is that of the almost uniform compressions and rarefactions of the gas in the interior. The latter is a question morels of the volume S of the cavity and of the quantity of gas which has passed, but the calculation of the kinetic energy presents difficulties which have been only partially overcome. In the case of simple apertures in the thin wall (regarded as plane), only circular and elliptic forms admit of complete treatment. The mathematical problem is the same as that of finding the electrostatic capacity of a thin conducting plate having the form of the aperture, and supposed to be situated in the open. The project of a stricter treatment of the problem, in the case of a spherical wall and an aperture of circular outline, has been in my mind more than 40 years, partly with the hope of reaching a closer approximation, and partly because some mathematicians have found the former method unsatisfactory, or, at any rate, difficult to follow. The present paper is on ordinary lines, using tire appropriate spherical (Legendre's) functions, much as in a former one, " On the Acoustic shadow of a Sphere.