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Although the number of traffic accidents in China has been declining year by year, the proportion of major traffic accidents in mountainous areas has continued to rise, reaching 60% in recent years. This shows that a mountain road safety system has not been effectively established. The majority of the methods used in mountain road safety assessments are statistical analysis methods based on accident causation theory. However, these expert methods greatly depend on massive amounts of traffic environmental data, which are very difficult and time-consuming to obtain. This study had the goal of reducing the environmental monitoring data required for this assessment and increasing analysis efficiency. Based on the research of road traffic accident data and traffic flow characteristics in mountainous areas, an attribute reduction algorithm was developed to weigh the significance of the data and construct a systemic analysis mothed. The proposed risk analysis model, which considers the accidents, roadside environment, and traffic safety facilities, is based on Shaanxi province data. The results from the actual implementation of this model indicate that the approach has good operability and holds great promise for mountain road safety assessment.

Particles flow and pack under stress, allowing shaping of the particles into target engineering geometries. Subsequently, in a process termed sintering, the particles are heated to induce bonding that results in a strong solid. Although first practiced 26,000 years ago, sintering was largely unexplained until recent times. Sintering science moved from an empirical and largely qualitative notion into a quantitative theory over a relatively short time period following World War II. That conceptual transition took place just as commercial applications for sintered materials underwent significant growth. This article highlights the key changes in sintering concepts that occurred in the 1945–1955 time period. This time span starts with the first quantitative neck growth model from Frenkel and ends with the quantitative shrinkage model from Kingery and Berg that includes several transport mechanisms.

Karst collapses in Zaozhuang area are the typical karst collapses induced by groundwater over-pumping in north China, which lead to severe economic loss and negative societal influence. Based on the comprehensive analysis of all natural influencing factors and human influencing factors associated with karst collapse in the Zaozhuang Shili Spring Area, China, this paper establishes karst collapse susceptibility evaluation model by means of fuzzy mathematic method, in which the Quantitative theory method was firstly applied in determination of the factor weights. The karst collapse susceptibility evaluation model with 14 evaluation indicators can be effectively used for quantitative evaluation on the karst collapse susceptibility. So, an analysis and evaluation on the karst collapse susceptibility of Zaozhuang Shili Spring Area is completed by means of karst collapse susceptibility evaluation model. The karst collapse area of Zaozhuang region is divided into very high susceptibility area, high susceptibility area, medium susceptibility area and low susceptibility area, which account for about 6.3, 5.2, 10.4 and 78.1 % of the total karst area and the karst collapse susceptibility evaluation map of Zaozhuang Shili Spring Area is completed. The results above will be helpful for the strategic planning and decision-making processes associated with exploitation of karst water resources and with prevention and control of karst collapse hazards of this region.

The amount and intensity of walking to maintain a healthy skeleton is unknown. This study examined the relationship between habitual walking activity and femoral bone mineral density (BMD) in healthy individuals using a quantitative theory for bone maintenance. Our results suggest a gender, weight, and speed sensitivity of walking interventions.Walking has been extensively promoted for the prevention of osteoporosis. The amount and intensity of walking to maintain a healthy skeleton is unknown and evidence to support a specific target of steps per day is lacking. The goal of our study was to examine the relationship between habitual walking activity and femoral bone mineral density (BMD) in healthy individuals using a quantitative theory for bone maintenance.Habitual walking activity and total femur BMD were measured in 105 individuals (49-64 years). An index of cumulative loading (bone density index, BDI) was examined as a predictor of BMD. The BDI-BMD relationship was used to predict the steps per day to maintain healthy BMD values for a range of body weights (BW) and walking speeds.For females but not for males, BDI was correlated with BMD (r (2) = 0.19, p0.001). The total required steps per day to maintain a T-score of -1.0 for a female with the average BW of the study cohort, walking at 1.00 m/s is 4,892 steps/day. Substantially more steps (18,568 steps/day) are required for a female with a BW 20% lighter than the average for our female cohort. For these lighter females, only at a walking speed greater than 1.32 m/s was 10,000 steps/day sufficient to maintain a T-score of -1.0.Our results suggest a gender, weight, and speed sensitivity of walking interventions for osteoporosis. In persons of low BW, the necessary steps per day to maintain BMD can be substantially greater than the often-quoted 10,000 steps.

If prediction of a debris landslide is to be completed, the first problem is how to determine and correlate the dynamic factors. The special composition and complicated geological conditions of debris landslides have many dynamic factors influencing displacement and stability. Correlations are generally very complicated. The relationship and sequence of factors is too complex to be completed by traditional mathematical model. In order to solve the problem above, a systematical study of the quantitative and qualitative dynamic factors using a model of the quantitative theory was performed based on the displacements of Xintan landslide, China. Rainfall was found to be the most important dynamic factor among the six factors controlling displacements. Relative importance sequence and correlation was also established. All prediction results agree with the mechanism and displacement pattern of the Xintan landslide. Optimized measures of prevention and control for debris landslides can be completed with correlation of the dynamic factors by means of the quantitative theory model.

The crisis in the textile industry and light industry and at factories involved with the production and processing of chemical fibers has had serious consequences. To manage production operations and control the quality, structure, and properties of the fabrics that are being made, it is necessary to determine the most important factors that affect the output parameters. Existing methods (factorial experiments, correlation analysis) do not always yield good results because the so-called “ancillary effects” of some input parameters make it necessary to vary the factors within narrow ranges during experiments. Such strict control over the factors is difficult to achieve under factory conditions. Binary information theory has been used in a number of recent studies at MGTU [1-3]. The objective here is to find a method that makes it possible to identify the relevant factors, eliminate ancillary effects, and automate the timeconsuming computational procedure. Study of the given problem entails dealing with a large number of factors, many of which are related to one another. The available empirical data is inadequate, and there are too few reliably substantiated theoretical conclusions on the character and mechanisms of the linkages between the factors. Such information is essential to the construction of a quantitative theory that would make it possible to accurately predict the behavior of a given system in any possible situation. There are two main goals in any cause-and-effect analysis: identify the causes and the effects in the given

Many experiments on animal learning and performance consist of discrete events, such as the onset or termination of a stimulus, the delivery of food, or a response that closes or opens a switch or that breaks a photobeam. Investigators of operant conditioning have made extensive use of the cumulative recorder to record the primary data that consist of times of occurrences of these discrete events (Ferster & Skinner, 1957). These records, although extensive, are not in a convenient form for subsequent analysis. In most cases, only selected examples of performance could be presented. To reduce the random error on individual trials of individual animals, most investigators have presented summary measures of behavior averaged across many trials, and sometimes across many animals. Although the primary data can produce all of the summary measures, the summary measures cannot be used to reconstruct all other summary measures. A good quantitative theory of the processes involved in animal learning and performance should lead to the prediction of the primary data (and thus, all summary measures), not just selected summary measures. The value of archiving primary data will be developed with a case study of an experiment with fixed-interval schedules of reinforcement. In a fixed-interval schedule of reinforcement, a pigeon, a rat, a human, or some other animal receives a reinforcer following a response after a fixed interval following some event, such as food delivery or stimulus onset. Fixed-interval schedules of reinforcement have been used extensively for many years to investigate the ability of animals to adjust to the temporal regularities of their environment.

In intermittent dynamical systems, the distributions of local Lyapunov exponents are markedly non-Gaussian and tend to be asymmetric and fat-tailed. A comparative analysis of the different time-scales in intermittency provides a heuristic explanation for the origin of the exponential tails, for which we also obtain an analytic expression deriving from a more quantitative theory. Application is made to several examples of discrete dynamical systems displaying intermittent dynamics.

A new generalized dimensionless electrochemical factor of corrosive alloy cracking was developed and a quantitative theory of corrosive-mechanical destruction was constructed on its base. The existence of a threshold value of the proposed factor, above which there is no corrosion cracking, was revealed.

Here, the quantitative theory of translation is shown to be of great utility in describing scientific networks. In fact, we deduce a new Zipf's Law for the descriptors of a set of documents, based on the concepts of centres of interest and of irreversible parallel translations. This new law can be generalized to other phenomena, such as the distribution of the sizes of cocitation clusters. Finally, we have established the model, for descriptor presence in a network, which closely fits the values recorded.

We showed previously that ifDictyostelium discoideum cells are sucked up into a small glass capillary with air at one end and plugged with mineral oil at the other, a sharp band of fast moving cells with prestalk characteristics formed within a minute at the air end of the cell mass. We now demonstrate that oxygen inside the capillary is responsible for the initiation and positioning of the sharp division line between prestalk-like and prespore-like cells, and that the length of the prestalk zone is regulated by the oxygen concentration. Our results are compared to a quantitative theory, showing good agreement with the experiments. We also discuss the relevance of these observations to the differentiation of prestalk and prespore zones in normal slugs and the origins of polarity in this organism.

The features of fabrication of metal composites complicates realization of the strength of CF in comparison to carbon-filled plastics. Disordering of the fibres and matrix is possible due to excessive interaction of the components. Three types of structure of metallic carbon materials (MCM) corresponding to insufficient, optimum, and excessive interaction of the components of CM are described. The principles of a quantitative theory of interaction of components in fabrication of MCM are examined and can be used to estimate the optimum parameters of this process.

A few remarks about the early days of the Mossbauer effect will show how much the field has changed in thirty-five years. Some speculations about the future of physics indicate that complex systems will form a major field. Proteins may be the simplest systems that show true complexity; studies of their properties may keep not only biologists and biochemists, but also physicists, occupied for many years to come. The Mossbauer effect has made, and will continue to make, major contributions to structural and dynamic investigations of proteins. The ultimate goal is a quantitative theory of complex systems.

A review is presented of the theory of clathrate compounds, starting with the first quantitative theory suggested by van der Waals and Platteeuw and ending with the current ideas. A brief description is given of the theory of ideal and non-ideal solid clathrate solutions and of the theory allowing us to describe clathrates with an unstable, empty host lattice. The review is composed of results obtained by the different methods based on various approximations.

The temporal contiguity between responses and consequences is an important variable in operant conditioning. This paper examines a selected portion of the empirical literature relevant to the role of contiguity: that of free-operant unsignaled delay of positive reinforcement. Two main issues are addressed: the extent to which this literature supports a role for contiguity, and, comparisons of qualitative and quantitative aspects of contiguity effects across the literature. In contrast to some other literatures, no clearcut exceptions to support for contiguity were found. In addition, quantitative effects were consistent within procedure, offering promise for efforts at a comprehensive quantitative theory.

Professor Nikolai A. Plate tragically passed away on March 16, 2007 at the age of 72. A brilliant representative of a famous Soviet and Russian polymer school founded by Academician Valentin A. Kargin, Plate was a vice-president of the Russian Academy of Sciences (RAS), the director of the A.V. Topchiev Institute of Petrochemical Synthesis in Moscow, Russia, and a professor at Moscow State University (MSU). He was born in Moscow on November 4, 1934, into a family with a rich tradition in chemistry. His father, A.F. Plate, was a Professor and Chair of the Department of Oil Chemistry and Catalysis at MSU. His grandfather, N.D. Zelinsky, was one of the most famous Russian chemists of the 20th century. In 1954, then a student of the MSU Faculty of Chemistry, Plate made his decisive choice in science – chemistry of macromolecular compounds – and joined his mentor, the great V.A. Kargin, with whom he worked for 15 years. In 1960, Plate defended his Ph.D. thesis and subsequently received the degree of Doctor of Chemical Sciences at the early age of 31. In 1974, he was elected as a Corresponding Member of the USSR Academy of Sciences and, in 1987, a Full Member of this academy, the highest recognition for a scientist in Russia. Plate spent his entire scientific career in only two research institutions. First, he advanced through the ranks at MSU from a junior researcher to a full professor, a position he held till his untimely death. Second, he was appointed the head of a scientific group at A.V. Topchiev Institute of Petrochemical Synthesis in 1963, and subsequently became the head of a laboratory and director of the institute in 1985. Plate made outstanding contributions to polymer science. He developed a quantitative theory of polymer-analogous reactions of macromolecules in solution, condensed state, and polymer blends (Kargin Prize of the USSR Academy of Sciences, 1981). He then applied this theory to modifications of polymer materials and was among the first to demonstrate possibilities of a structural–chemical approach to altering properties of numerous materials by polymeranalogous reactions. He was one of the pioneers in the field of thermotropic polymer liquid crystals with mesogenic groups and spacers (State Prize, 1985) and also discovered unusual mesophase structures of linear polymers that do not contain mesogenic groups (Lebedev Prize of the Presidium Colloid Polym Sci (2007) 285:1299–1300 DOI 10.1007/s00396-007-1722-9

The collision efficiency approach to flocculation is analyzed on the basis of a model describing the probability of aggregation by polymer bridging. The model allows for the effect of the randomness of distribution of polymer over particles as well as the effect of simultaneous coagulation and weak flocculation. It is argued that the collision efficiency approach is applicable to a rather limited range of experimental systems and provides a qualitative understanding rather than a quantitative theory of the relationship between flocculation and adsorption.

The resistivity increase of very thin metal films during gas adsorption is stronger than predicted by the commond−1 law. This effect is contributed to surface roughness. A quantitative theory is presented which leads to an additionald−3 term. The theory is checked using literature data obtained for the Ag/O2 system.

A theory of transfection is developed which describes three different types of experiments in transfection: The concentration dependence of transfection, transfection with marker rescue, and the mapping function in transfection crosses. The theory is applicable to transfection systems exhibiting quadratic or higher order dose response (APP1, AP50, SP82). It pictures the essential process in transfection as follows: transfecting DNA molecules, having suffered inactivating events during uptake or intracellularly, have to recombine prior to replication under elimination of these lesions. The probability for recombination, successful in this sense, is calculated as a function of the number of DNA molecules within the competent cell, the mean number of inactivating events per DNA molecule, and the crossover probability per nucleotide. Under the assumption of random distribution of inactivating events over the population of DNA molecules and homogeneous crossover probabilities the theory explains on a quantitative basis a number of experimental observations in transfection, as for instance the relative efficiencies of different helper phage in transfection with marker rescue, the third order concentration dependence in SP50 transfection, and the high recombination frequencies observed in transfection crosses.

This paper aims at a quantitative theory of power absorption in polymeric solids. The theory is based on two principles: the dislocation theory of internal stresses and the fluctuation-dissipation theorem. The latter connects, when applied to shear, the spontaneous shear fluctuations of the body with the relaxation strength of the material. The spontaneous shear fluctuations are caused by fluctuating internal strains which can be attributed to fluctuations in the density of dislocation dipoles. A definition is given of the mechanical dipole moment of a group of atoms, which can shift to and between two equilibrium positions, which is analogous to the definition of dislocation dipoles in the continuum mechanics. The theory is applied to cyclohexyl containing polymers, which have been investigated byHeijboer. The values of the mechanical dipole moment of the cyclohexyl ring found on a large number of cyclohexyl ring-containing polymers, all lie in a narrow range which is in agreement with the hypothetical value.

The rainbow is a bridge between the two cultures: poets and scientists alike have long been challenged to describe it. The scientific description is often supposed to be a simple problem in geometrical optics, a problem that was solved long ago and that holds inter­ est today only as a historical exercise. This is not so: a satisfactory quantitative theory of the rainbow has been devel­ oped only in the past few years. More­ over, that theory involves much more than geometrical optics; it draws on all we know of the nature of light. Allow­ ance must be made for wavelike proper­ ties, such as interference, diffraction and polarization, and for particlelike prop­ erties, such as the momentum carried by a beam of light. Some of the most powerful tools of mathematical physics were devised ex­ plicitly to deal with the problem of the rainbow and with closely related prob­ lems. Indeed, the rainbow has served as a touchstone for testing theories of op­ tics. With the more successful of those theories it is now possible to describe the rainbow mathematically, that is, to pre­ dict the distribution of light in the sky. The same methods can also be applied to related phenomena, such as the bright ring of color called the glory, and even to other kinds of rainbows, such as atomic and nuclear ones. Scientific insight has not always been welcomed without reservations. Goethe wrote that Newton's analysis of the rain­ bow's colors would "cripple Nature's heart. " A similar sentiment was ex­ pressed by Charles Lamb and John Keats; at a dinner party in 1817 they proposed a toast: "Newton's health. and confusion to mathematics. " Yet the sci­ entists who have contributed to the the­ ory of the rainbow are by no means in­ sensitive to the rainbow's beauty. In the words of Descartes: "The rainbow is such a remarkable marvel of Nature . . . that I could hardly choose a more suitable example for the application of my method. " The single bright arc seen after a rain shower or in the spray of a waterfall is

The thicknesses of the layers of a two-phase layered scale depend upon the individual stabilities, rates of growth, and molar volumes of the two compound products at a particular temperature. These factors and the partitioning of cations between the two compounds at their common interface are considered in order to develop a quantitative theory for the growth of double-layered scales on pure metals. Although layer thicknesses have been previously measured for several double-layered scales, all of the data necessary to calculate the relative thicknesses according to the present theory are not available. Thus, the theory cannot be verified at this time. However, the relative thicknesses of FeO and Fe3O4 which should form on Fe for 800⩽T⩽1090°C with $$P_{ O_{_2 } } = 10^{ - 11} atm$$ are calculated. For two-phase layered scale formation in the oxidation of Co, other calculated values are discussed in terms of experimental results of other investigators.

Relative micropsia was measured by a matching technique in patients with unilateral, benign, macular edema. Quantitative assessment of foveolar micropsia appeared to be a sensitive indicator of receptor displacement in this disorder, and may be a useful tool both for diagnosing and for monitoring macular edema. Parallel measurements of grating acuity showed a close proportionality between acuity and micropsia parameters. This result validates a new quantitative theory for the neuro-retinal basis of visual acuity. The theory allows prediction of the proportion of working visual neurons in patients with impaired acuity due to diseases that produce a diffuse loss, or disconnection, of macular cones. Our results indicate that so-called normal visual acuity (1.0, or 20/20) requires no more than 44% of the normal quantity of foveolar, neuro-retinal channels.

The dependence of the positronium decay rate on the gas density is considered. It is known that the positronium can be localized in a dense gas with the formation of a cavity “bubble” around the positronium. It results in a significant delay of the annihilation. The paper containes the quantitative theory of this phenomenon. A comparison is made with the experimental data for He4, He3, Ne.

The suggestion is put forward that radiation-induced recessive lethals, or a large proportion of them, are due to chromosome breaks. About one-third of all the chromosome breaks primarily induced by the radiation are lethals. If the break restitutes, a lethal unaccompanied by chromosomal aberration (type A lethal) results. If the break takes part in chromosome interchange a type C lethal, which is associated with chromosomal structural change, results. Arguments are given against the alternative position-effect explanation of type C lethals. A quantitative theory of dominant lethals is developed on the basis that the dominant lethals are a mixture of single breaks which fail either to restitute or to interchange but instead undergo sister-union, and of non-viable chromosomal structural changes involving two or more breaks. The experimental curve of variation with dose of the yield of dominant lethals is successfully fitted, and also the curve of the yield of viable structural changes. It is shown that the recessive lethal and the dominant lethal theories are consistent in that they require the same postulated number of primarily produced chromosome breaks per unit dose (namely, 0·75 breaks per sperm per 1000 r.). Experiments on the distortion of the sex ratio in the progeny of irradiated males with ring-shaped or rod-shapedX-chromosomes are also shown to be consistent with the theory.

Unstirred layers of solution adjacent to a membrane cause a decrease in the effective driving forces on water (or solutes) during permeability-type experiments. These effects are discussed in relation to transcellular-osmosis studies from which it had been previously deduced that the permeability (strictly hydraulic conductivity) of the membranes of Characean cells to water was greater when water was entering the cell (endosmosis) than when it was leaving the cell (exosmosis). Quantitative theory shows that this polar permeability is not so pronounced as had previously been claimed.

In recent years we have produced new types of age-hardening alloys and new hardening treatments for which the combination of several methods of hardening is typical. We should note first of all the high-nickel and chromium-nickel maraging steels and various methods of thermo-mechanical treatment for age-hardening alloys. In all cases the decomposition processes involve a high density of structural defects. Explanation of the decomposition mechanism in connection with specific types of defects is an urgent problem, the solution of which is already possible with present techniques of electron microscopy (crystallographic analysis of structural defects and new formations is possible with the use of goniometric devices in transmission electron microscopy). Further development of mathematical methods is needed for investigating phase transformations in alloys and refining the quantitative theory of the processes of precipitation and coalescence used for present-day multicomponent alloys and combined treatment. The major problem in this area of metal science is to obtain more complete characteristics of the structure of the material in the state of maximum hardness and establish quantitative relationships between the structural and strength characteristics.

A theory of such neural circuits is developed which provide for formal logical thinking. As a by-product of this study, a neural mechanism is indicated which provides for the conception of ordinal numbers. A quantitative theory of the probability of erroneous reasoning and of the speed of reasoning in its relations to other psychological phenomena is suggested.

When the fluidizing velocity in a liquid fluidized bed of solid particles is suddenly changed, a discontinuity in the porosity is introduced at the bottom of the bed. This discontinuity is propagated upwards through the bed. The boundary between the old and the new porosity broadens or remains sharp depending on whether the porosity is increased or decreased. This behaviour is reflected in the way in which the bed level changes as a function of time. For a few different systems such response curves have been measured by means of a specially designed follow-up system. On the basis of the above mechanism a quantitative theory was developed for the response of the bed level to a step-wise change in the fluidizing velocity. This theory proved to give a satisfactory agreement with the observed facts.

A quantitative theory of the shape of absorption and emission curves for solute molecules dissolved in crystalline solvents based on the Franck-Condon principle is given. The relation between the radiationless transition and absorption or emission is discussed.

We may consider that most of the human behavior is a set of learned responses to certain patterns which recur frequently in the course of human life. Some “abnormal” events or experiences may result in the learning of abnormal responses, and thus in abnormal behavior. The “abnormal” responses may begin to be learned after some of the normal response patterns have been fairly well established. The development of both normal and abnormal behavior may thus be represented by learning curves of the type studied by H. D. Landahl. Applying some of the results of the theory of learning curves and considering that the normal and abnormal reactions may reciprocally inhibit each other, a quantitative theory of some psychoses may be developed. In particular, the effects of shock may be deduced from the assumption that they cause the more recently learned abnormal reactions to be “unlearned” more readily, than the earlier learned “normal” reactions. The effectiveness of shock treatments as a function of the duraction of psychosis is discussed from this point of view.

ALTHOUGH this interesting book bears the copyright date of 1941 at the Stanford Press, it has only recently been available in Great Britain, and will be regarded as an important supplement to Prof. Loeb's treatise “Fundamental Processes of Electrical Discharges in Gases” (1939). The reason for the appearance of a supplement to a very modern book of such comprehensiveness is to be found in the discovery by an Englishman, one of the authors, J. M. Meek, of a simple condition or criterion, which, applied to Prof. Loeb's qualitative streamer theory of spark discharge, converted an interesting speculation into a quantitative theory of great power. Dr. Meek (formerly of the University of Liverpool and the Research Department of the Metropolitan-Vickers Company) studied under Prof. Loeb with a Commonwealth Fund Fellowship, and there developed the conception and mathematical argument which has led to the satisfactory explanation and correlation of many inexplicable, apparently unrelated phenomena of the spark discharge. The Mechanism of the Electric Spark By Prof. Leonard B. Loeb John M. Meek. Pp. xiii + 188. (Stanford University, Calif.: Stanford University Press; London: Oxford University Press, 1941.) 3.50 dollars.

A NUMZZR of quantitative theories of confirmation (or, using Carnap's wellknown terminology, of probability1) contain the following two statements (or equivalents thereof) : 1 (1) For any statements p, q, and r such that r is not logically false and p is logically equivalent to q relative to r (i.e., the statement r ~ (p ~ q) is logically true), c(p, r) = c(q, r). (2) For any statements p, q, and r such that r is not logically false, c(pq, r) ---c(p, r) x c(q, pr).

DR. MARTYN and I have already given a quantitative theory of the phenomenon known as the interaction of radio waves1. This theory has been found to be in good agreement with observation, and has in particular led to conclusions about the acoustic distortion of the impressed modulation which the subsequent observations of van der Pol and van der Mark adequately confirmed. There is, however, in this theory an inaccuracy of which I became aware about a year ago while engaged in a related investigation, and which at first sight appears of no great importance.

DIELECTROPHORESIS is the unidirectional motion of neutral, polarizable material which results from the presence of a non-uniform d.c. or a.c. electric field. It is one of a variety of aligning, rotating and translating effects produced by the action of electrical fields on particles suspended in a fluid1. Dielectrophoresis has been discussed and tested for a variety of uses2–4, but only recently has it been applied to biological investigations5. Because of the universality and potential for research in the life sciences of the dielectrophoretic effect, it is desirable to have a quantitative theory for the dielectrophoretic force in lossy dielectric media.

THE decay of wood blocks by fungi has been described1–4 in terms of a progressive and characteristic decrease of dry weight, and Wilcox5 has correlated these weight losses with the microscopic changes which occur in the decay of sapwood blocks of the hardwood sweetgum (Liquididamber styraciflua L.), and the softwood southern pine (Pinus sp.). Fungi used were Polyporus versicolor L. ex Fr., causing a white rot, and Poria monticola Murr., causing brown rot. Wilcox confirmed that fungi rapidly become established throughout soil blocks6 so that hyphae are numerous in the early stages of decay. During later stages, however, the hyphal concentration decreased considerably and was sparse when 50 per cent of the thin wood samples remained. We have a quantitative theory to describe the relationship between residual wood weight and decay period, which might form the basis of a more general theory which would facilitate widespread attempts to protect wood from decay with preservatives.