Volume 21, Issue 1, January 1953
 PAPERS


Graphical Solutions to Optical Problems of Three Different Types
View Description Hide DescriptionThe following problems are considered:
I. Paraxial ray tracing by the focal plane method.—For spherical refracting and reflecting surfaces it is shown that by drawing two secondary axes, one parallel to a ray incident at an arbitrary angle and the other parallel to the path of the same ray after refraction or reflection, the positions of the focal planes are readily established and their necessary properties deduced. The same is done for a lens by a method based on the fact that a focal plane of the first surface is conjugate to a focal plane of the second surface.
II. The variation in the distance L between the conjugate foci of a thin lens (focal length f) with the distance l of one focus from the lens.—A general formula is established, and a simple construction for plotting the graphs between and is described.
III. Refraction by prism combinations and the prismrefractometer.—A graphical method is used to discuss the design of the Amici prism, the direct vision spectroscope, and achromatic prisms giving appreciable deviations. A graphical method is also described for finding the refractive index of a liquid from results obtained with a prismrefractometer.

Computation of the Moment of Inertia of Various Bodies by the Approximate Sum of Numerical Series
View Description Hide DescriptionThe paper presents a simple method of computing moments of inertia of various bodies by approximating the sum of numerical series. The method lends itself to be used in a course of college physics where most students are not familiar with calculus.

Achievement of Physics Students With and Without Laboratory Work
View Description Hide DescriptionTwo general physics laboratory groups were compared in achievement with a group enrolled in the same course without laboratory. The achievement was measured by two pencilpaper examinations and two laboratory performance tests. The analysis of variance and covariance method was used to hold constant three measures of initial differences among students. There were no statistically significant differences between the means of the groups on the mechanics theory test. The laboratory groups were significantly better than the nolaboratory group on all tests dealing with laboratory work.

Determination of Molecular Structure from Microwave Spectroscopic Data
View Description Hide DescriptionA method is described for determining the position of an atom in a molecule from spectroscopicmeasurements on two isotopic species of the molecule. The method is applied to various types of molecules; explicit expressions are derived for linear, symmetric top, planar, and nonplanar asymmetric top molecules. The number of isotopic species on which measurements must be made to complete the structural determination, i.e., determine the position of every atom in the molecule, is discussed for various types of molecules. An application of the method to the determination of mass difference ratios is also considered.

Particle Properties of Radiant Energy in Wave Guides
View Description Hide DescriptionThe mean energy per excitation wavelength of e.m. radiation propagated along a lossless uniform wave guide is found to be , being independent of frequency for a given amplitude of the longitudinal field intensity, mode of the field, and structure of the guide. The frequency and the group velocity of the radiant energy are related by the equation where denotes the frequency at cutoff, and the excitation wavelength at cutoff. This equation permits one to put . The amplitudes of the field intensities are chosen such that equals Planck's constant. Applying the massenergy relation, the term may be interpreted as the “potential” (= rest) energy of the quantum and as the rest mass. The momentum associated with is found to be , being the wavelength along the guide. When radiant energy passes from one guide into another one of different crosssectional structure via a tapered piece of wave guide, a partial conversion of “potential” to “kinetic” energy, and vice versa, occurs along the tapered section. In the case of TEMwaves, which, however, can only be supported in a guide of infinite transverse dimensions, the group velocity becomes and the rest mass zero.

On Fluid Dynamics in Physics Teaching
View Description Hide DescriptionIn the light of private answers suggested for the public questions: What is physics? What is education?, a critical review is made of fluid dynamics in physics teaching. First, general physics is examined for what is being done in teaching fluid dynamics in physics. A critical analysis is made in particular of the important Bernoullitheorem as to what it is, what it says, what it means, and how it is used. Second, theoreticalphysics is examined for what is being done. In this case, the motion of a sphere has been selected as illustrative of present teaching. The typical course in theoreticalphysics is then examined with respect to its material about the motion of a sphere, both in a perfectly inviscid fluid and in a perfectly viscous fluid. This academic material is compared finally with experimental observations, particularly those in wind tunnels and in ballistics ranges. In conclusion, questions are noted on the foundations of fluid dynamics, particularly the role of viscosity,turbulence, the concept of a steady state, and the role of heat. The review ends with a moral question as to the students' stake.

Possible Motions of a Sphere Suspended on a String (The Simple Pendulum)
View Description Hide DescriptionThe possible motions of a sphere suspended on a string are found to consist of combinations of (1) a pendulum type of motion and (2) a rolling motion, in which the ball rolls in angular harmonic motion about an axis very near its center. For (1) it is shown (a) the usual formula for the length of the equivalent simple pendulum should be replaced by , where is the radius of the ball and the distance of point of suspension to center of the sphere, and (b) the best way of starting this motion is to pull the ball aside by a horizontal force through its center. For (2) it is shown that the period of oscillation is very close to .
Photographs are given showing experimental verifications of these effects.

Reproductions of Prints, Drawings, and Paintings of Interest in the History of Physics. 50. Fluents and Fluxions
View Description Hide DescriptionThe frontispiece of John Colson's The Method of Fluxions and Infinite Series together withexplanatory discussion is reproduced. It is an interesting attempt to explain the method of thecalculus pictorially.

An Electronic Differential Analyzer
View Description Hide DescriptionAn electronic differential analyzer designed primarily for classroom teaching is described. The value of building such a device as a project for advanced students is emphasized. The method of setting up differential equations on the differential analyzer is explained, and a few sample solutions are illustrated.
