Mismatching Measures of Output and Prices: Implications for Measuring the Comovement of Prices and Output

price output correlation

A Simple Derivation of the Equation for Mean Free Path

According to simple kinetic theory, in which all the gas molecules but one are considered stationary, the mean free path L is given by L = 1/N π σ2 , where N is the number of molecules per cc. and σ is the molecular diameter. Clausius, considering all molecules to be moving with the mean relative velocity, finds L = 3/4N π σ2. Again, Maxwell, applying his law of velocity distribution, obtains the result L= 1/√2N π σ2. This value found by Maxwell is the one most generally accepted. If we consider it to be correct, then the value from simple kinetic theory is 41% too large, while that found by Clausius is 6% too large. An approximate value of L, much more nearly correct than the first one given, may be derived very simply by considering the gas molecules to be vibrating in sheets. The result obtained is L = 1/ 4 N σ2. This value is 11% higher than that found by Maxwell, as compared to 41% for the first value given above. The mathematical difficulties encountered by Clausius and Maxwell in deriving their formulas are entirely avoided in this development

Correlation of Neatness and Scholarship in Physics

353 reports, written by 33 students in three laboratory sections of junior physics, were graded as to neatness. The average neatness grade and the term laboratory grade for each student were used in a correlation study. For each of the three laboratory sections the correlation coefficient was positive. The coefficient for all 33 students was + 0.27. Although the number of students graded was small, we may conclude that in general we may expect neatness and high grades in physics to be associated. Exceptions to the rule and a low correlation coefficient both definitely indicate that neatness of written reports cannot alone be relied upon as an index of scholarship in physics

Coefficients of Diffusion of Salt Vapors in the Bunsen Flame

The coefficients of diffusion of alkali salts in the Bunsen flame have been determined by a photographic method which is a modification of the method used by H. A. Wilson. The values of the diffusion coefficients obtained for sodium, potassium, and caesium salts are roughly proportional to the reciprocals of the atomic weights of the metals. This is what we should expect from kinetic theory, if we consider the luminosity to be due to free metal atoms in the flame. Lithium salts, however, are found to have a lower coefficient of diffusion than sodium salts, and hence their metal atoms are probably free only a part of the time the vapor is in the flame

The Spectral Distribution of Erythemal Effectiveness of Ultraviolet Radiation

During the last twelve years several determinations of the distribution of erythemal effectiveness of radiation in the spectral region extending from wave-length 2400 or 2500 A. to about 3400 A. have indicated maximal effectiveness at 2967 A. However, all the investigators using monochromatic radiation employed the mercury vapor arc as source, so that their observations necessarily were limited to those wave-lengths represented by fairly intense lines of the mercury arc spectrum. These lines are not close enough together to allow accurate determination of the curve of erythemal effectiveness. Maximal effectiveness was assumed to be at 2967 A., its spectral position being roughly indicated by measurements at that wave-length and at wave-lengths no closer than 2925 and 3024 A

On the Low Energy Decrease in Galactic Cosmic Ray Secondary/Primary Ratios

Galactic cosmic ray (GCR) secondary/primary ratios such as B/C and (Sc+Ti+V)/Fe are commonly used to determine the mean amount of interstellar material through which cosmic rays travel before escaping from the Galaxy (Λ_(esc)). These ratios are observed to be energy-dependent, with a relative maximum at ~1 GeV/nucleon, implying a corresponding peak in Λ_(esc). The decrease in Λ_(esc) at energies above 1 GeV/nucleon is commonly taken to indicate that higher energy cosmic rays escape more easily from the Galaxy. The decrease in Λ_(esc) at energies <1 GeV/nuc is more controversial; suggested possibilities include the effects of a galactic wind or the effects of distributed acceleration of cosmic rays as they pass through the interstellar medium. We consider two possible explanations for the low energy decrease in Λ_(esc) and attempt to fit the combined, high-resolution measurements of secondary/primary ratios from ~0.1 to 35 GeV/nuc made with the CRIS instrument on ACE and the C2 experiment on HEAO-3. The first possibility, which hypothesizes an additional, local component of low-energy cosmic rays that has passed through very little material, is found to have difficulty simultaneously accounting for the abundance of both B and the Fe-secondaries. The second possibility, suggested by Soutoul and Ptuskin, involves a new form for Λ_(esc) motivated by their diffusion-convection model of cosmic rays in the Galaxy. Their suggested form for Λ_(esc)(E) is found to provide an excellent fit to the combined ACE and HEAO data sets