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IN a recent paper, Morris discussed the conditions for steady circular motion of a shaft, allowing for the clearances between the journals of the shaft and the bearings in which it runs. Morris found that a certain degree of unbalance was necessary in order that steady circular motion should be possible, and that the system was very sensitive to small changes of unbalance under certain conditions.

When linear simultaneous equations are ‘ill‐conditioned’, small variations in the (usually measured) quantities on the right‐hand sides of the equations are associated with large variations in the values of some of the unknowns. The basic reason for this is that the matrix of the coefficients has at least one small latent root. Associated with each small latent root λr is a quantity Ur, a linear combination of the quantities on the right‐hand sides of the original equations, and the uncertainty associated with the ‘ill‐condition’ is essentially uncertainty as to the values of the quantities Ur; the original equations can be replaced by another set of equations which is not ill‐conditioned but involves the Ur. General methods are used, but applied to two specific cases; in one of these there are two equal small latent roots of the matrix of coefficients and the necessary adjustments for this case are explained. Two alternative methods for determining the small latent roots of a matrix are discussed.

IF a number n of readings are taken of a dependent variable y for various values of the independent variable x we frequently need to determine a reasonably satisfactory curve to express the relation between the two variables; preferably we should be able to give an equation for this curve. We know that the observations will be subject to random errors due to various causes; we therefore expect the curve not to go through all the points representing the observations, but to lie evenly among these points. If the curve is expected to be a straight line, we may be able to determine it with sufficient accuracy by eye. The ‘least‐squares’ technique for finding the equation of the best‐fitting curve C for which y is a polynomial of degree m in x is well known. If m is small, the curve Cm will be smooth, but may not fit very well; if m=n−1, the fit is perfect, but Cm is likely to have several oscillations which do not correspond to reality. If m has an intermediate value, there will be some oscillations and a fair fit; increasing m rapidly increases the complexity of the equations determining Cm, and the unreliability of Cm from the statistical point of view.

IN the past, the required amount of directional stability was dictated mainly by asymmetric power considerations and by the maximum angles of sideslip in manoeuvres permissible from the structural strength viewpoint. The requirement for satisfactory recovery from steady spin would in certain cases influence both the directional stability and control power in such a fashion as ultimately to be the determining factor. Present indications are that the choice of the required degree of directional stability will be based on supersonic lateral dynamic stability considerations, in particular the stability of the so‐called Dutch roll oscillation, or on considerations of avoiding inertia coupling between the lateral and longitudinal degrees of freedom during rolling. Both of these problems will be discussed in some detail later. It should be emphasized, however, that large values of subsonic directional stability will be required for supersonic aircraft in order to provide satisfactory dynamic characteristics at supersonic speeds at high altitudes.

A conference on noise, dealing particularly with noise in industry, has been organized by the British Occupational Hygiene Society. It will be held in London on Tuesday, April 1, 1958, starting at 11.15 a.m. The conference is open to non‐members of the Society on payment of a registration fee of one guinea. Further details can be obtained from the Hon. Scientific Secretary, Dr D. Turner, The Associated Ethyl Company Limited, Ellesmere Port, Cheshire.

William Baumol famously introduced the “cost disease” according to which the relative price of services vis-á-vis manufactured goods keeps rising because of a negative productivity differential between services and manufacturing industries. Empirical evidence strongly supports the predictions of Baumol’s model of “unbalanced growth” as we show in this article. Baumol was convinced that the cost disease need not have fatal consequences for growing economies as they can afford to earmark ever-higher shares of GDP to pay for services like healthcare and education if the overall “pie” keeps growing. Then, consumption of goods may rise as well even if its share in GDP steadily declines. However, income inequality has surged since the 1980s; and the rising price of vital services means that lower-income strata may be increasingly unable to pay for them. In this article, we develop the nexus between the cost disease and rising income inequality and sketch the ensuing challenges for social policy.

Examines the tenth published year of the ITCRR. Runs the whole gamut of textile innovation, research and testing, some of which investigates hitherto untouched aspects. Subjects discussed include cotton fabric processing, asbestos substitutes, textile adjuncts to cardiovascular surgery, wet textile processes, hand evaluation, nanotechnology, thermoplastic composites, robotic ironing, protective clothing (agricultural and industrial), ecological aspects of fibre properties – to name but a few! There would appear to be no limit to the future potential for textile applications.

Pharmaceutical and personal care products (PPCPs) and phosphorus are pollutants that can cause a wide array of negative environmental impacts. Phosphorus is a regulated pollutant in many industrial countries, while PPCPs are widely unregulated. Many technologies designed to remove phosphorus from wastewater can remove PPCPs, therefore the purpose of this paper is to explore the ability of these technologies to also reduce the emission of unregulated PPCPs.

Through meta-analysis, the authors use the PPCPs’ risk quotient (RQ) to measure and compare the effectiveness of different wastewater treatment technologies. The RQ data are then applied via a case study that uses phosphorus effluent regulations to determine the ability of the recommended technologies to also mitigate PPCPs.

The tertiary membrane bioreactor and nanofiltration processes recommended to remove phosphorus can reduce the median RQ from PPCPs by 71 and 81 percent, respectively. The ultrafiltration technology was estimated to reduce the median RQ from PPCPs by 28 percent with no cost in addition to the costs expected under the current phosphorus effluent regulations. RQ reduction is expected with a membrane bioreactor and the cost of upgrading to this technology was found to be $11.76 per capita/year.

The authors discuss the management implications, including watershed management, alternative PPCPs reduction strategies, and water quality trading.

The evaluation of the co-management of priority and emerging pollutants illuminates how the removal of regulated pollutants from wastewater could significantly reduce the emission of unregulated PPCPs.