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Background: The present study was done to test compare the efcacy of atracurium and cisatracurium regarding onset time, intubating conditions, hemodynamic effects, duration of action, signs histamine release and evaluate whether cisatracurium is more effective than atracurium with regard to the criteria. Materials And Methods: This study was done in the Department of Anaesthesia, Darbhanga Medical College and Hospital, Laheriasarai, Bihar. Study was done for a period from July 2019 to November 2020. An informed consent was taken from all patients. Group A (25 patients) received Atracurium 0.5mg/kg IV and Group B (25 patients) received Cisatracurium 0.3mg/kg IV. Results: Duration of action of Cisatracurium (0.3 mg/kg) is signicantly high compared to Atracurium (0.5mg/kg) with p

In this paper an attempt has been made to study climatological characteristics and forecasting aspects of heavy rainfall over Kolkata for data of 34 years of period from 1974 to 2007. Total 184 events has been found out and the data set has been subjected to various types of analysis along with favourable synoptic system and critical index for occurrence of heavy rainfall over Kolkata. Average occurrence is found as 5.4 events per year. Monthly distribution shows maximum of 26% events in July followed by September 20%, August17% and June as 14%. Seasonal distribution naturally indicates maximum of 77% occurrence during monsoon followed by post-monsoon with 14% and pre-monsoon with 09 %. Synoptic analysis revealed that majority of heavy rainfall events occurred due to low pressure system (LPS). Study of 167 cases (during June to October) suggests that when any one of the favourable synoptic condition prevailed over the region and DPD-Wind-PW-WS index reaches a critical value, heavy to very heavy rain occurred over Kolkata and suburban areas.

In this paper a simple relationship is employed to investigate relative impacts on the movement and landfall of tropical cyclone in the Bay of Bengal region when geopotential height of different troposphere levels is used as an input. Five tropical cyclone during pre-monsoon and post-monsoon season over the Bay of Bengal region has been selected for the study. The RS/RW data of coastal stations namely Kolkata (Dumdum), Dhaka, Agartala, Bhubaneswar, Visakhapatnam, Machlipatnam, Chennai and Karaikal has been collected for the period of the cyclones under study. The geopotential height of different standard levels has been plotted against the time for the stations for every cyclone. The study suggests that the cyclone moves towards and cross near the station having relatively steeper decrease in geopotential height upto mid tropical level followed by increased in geopotential height.

Lifetimes of 18 high spin states of 75Br were measured by Doppler shift attenuation method. The high spin states in the nucleus were populated by the reaction 51V(28Si, 2p2n) at 115 MeV beam energy. The transition quadrupole moments, deduced from the lifetimes, were measured beyond the g9/2 neutron and proton band crossings in the positive and the negative parity bands. The results were discussed in the cranking model with Woods–Saxon potential and Strutinsky shell correction. Change in triaxiality γ due to neutron and proton alignments has been proposed to explain the observed change in transitional quadrupole moments Qt. The experimental results and the cranking calculations suggest that the alignment of a pair of neutrons in the g9/2 orbital tends to drive the shape of the nucleus towards negative value of γ while the proton pair alignment in the g9/2 orbital tends to drive it towards positive γ.

Effect of Triiodothyronine on the Genital Organs and Fertility in Male Rats

Angular distribution of neutron emission from different heavy ion projectiles of energy up to 10A MeV incident on various thick targets have been analyzed with the help of existing models and empirical relations. Owing to the complexity of heavy ion induced reactions, it becomes difficult to obtain any empirical relation for neutron angular distribution involving parameters like projectile energy as well as target and projectile masses. An exponential function of the emission angle has been found to satisfy the relation approximately involving these parameters. The calculated results using our proposed exponential relation are compared with experimental data showing reasonably good agreement. This empirical expression provides an easy, quick and fairly reliable tool to calculate angular distributions of emitted neutrons from heavy ion induced reactions in thick targets, which are required for various applications.

Simple empirical expressions for transmission of flux and dose through concrete are presented for neutrons from proton induced reactions. For this purpose the neutron emission from different targets in proton induced reactions in the energy range 25–200 MeV have been considered. The calculated effective dose outside a concrete shield shows overall good agreement with the effective dose estimated from measured neutron flux in the framework of the Moyer model. The calculated effective attenuation length shows a rising trend with incident proton energy and shield thickness.

An empirical expression has been obtained for double differential neutron yield distributions from proton induced reactions on thick stopping targets. Calculated neutron yield distributions using an exciton (hybrid) nuclear reaction model have been used to generate polynomial expressions relating neutron yield distributions (emission energy and angle) with incident proton energy and target mass. The present expression is obtained by fitting data for 39 elements from 9 Be to 209 Bi and for incident proton energies from 25 to 200 MeV.

An explicitly r 12 dependent wavefunction for the ground state of helium is Fourier transformed and the resulting momentum-space wavefunction is used to study the momentum properties. In particular, results are obtained for the momentum density, moments of momentum density and Compton profile. It is demonstrated that the use of our simple minded wavefunction provides a straightforward analytic method to estimate the effect of electron–electron correlation on the momentum properties of helium atom and gives results which are in good agreement with those obtained by more detailed calculations.

It is assumed that the dynamics of valence electrons of alkali-metal atoms can be well accounted for by a quantum-defect theoretic model while the core electrons may be supposed to move in a self-consistent field. This model is used to study the momentum properties of atoms from3Li to37Rb. The numerical results obtained for the momentum density, moments of momentum density and Compton profile are found to be in good agreement with the results of more detailed configuration-interaction calculations for the atom3Li. Similar results for11Na,19K and37Rb are compared with the corresponding Hartree-Fock-Roothaan values only, for want of data from other realistic calculations

Neutron emission cross section for various elements from9Be to209Bi have been calculated using the hybrid model code ALICE-91 for proton induced reactions in the energy range 25 MeV to 105 Me V. An empirical expression relating neutron emission cross section to target mass number and incident proton energy has been obtained. The simple expression reduces the computation time significantly. The trend in the variation of neutron emission cross sections with respect to the target mass number and incident proton energy has been discussed within the framework of the model used.

The lifetimes of the states of −ve parity 2-qp bands of N=40 nuclei 74Se and 76Kr were measured. The transition strengths and quadrupole moments, obtained from the lifetimes, show a large collectivity of such bands in both the nuclei. The alignment frequencies were calculated from Woods-Saxon cranking model. Previously suggested quasi proton nature of band 5 and 6 of 71Se were argued to be based on quasi neutron excitations. The total Routhian surface calculations suggest triaxial shapes with large +ve and −ve values of triaxiality parameter γ after proton and neutron alignments in these bands respectively.

Emissions of protons and alpha-particles from neutron and alpha-induced reactions have been estimated using two nuclear reaction model codes ALICE91 and PRECO-2000. Calculated results have been compared with available energy differential and double differential emission cross sections from experimental measurements. Analysis of the data based on different nuclear reaction mechanisms revealed the relative importance of these mechanisms as well as predictive capabilities of the codes used. These results are useful in accelerator-driven systems, radioactive ion beam facilities and space dosimetry.

The effect of two initial exciton (particle-hole) configurations, namely 4p0h and 5p1h, on the angular distribution of neutron emission from $\ensuremath{\alpha}$-induced reactions on various thick targets have been analyzed. In the angular distribution of emitted neutrons the relative contribution of the 4p0h configuration is found to vary as the cosine of the angle of emission. Using such dependence, empirical expressions are developed for the total neutron yield, energy spectra, and angular distribution of neutrons in $\ensuremath{\alpha}$-induced reactions in the 25\char21{}200-MeV energy range. These expressions are based on empirical fits to the hybrid model calculations of neutron emission from target elements in the mass range $^{9}\mathrm{Be}$ to $^{209}\mathrm{Bi}$. The results of these calculations are compared with experimental data showing fairly good agreement. The empirical expressions provide a simple, fast, and reliable tool for calculating neutron emission essentially required for radiation shield design and other applications.

Comparisons of calculated neutron yield distributions from $\ensuremath{\alpha}$-particle induced reactions on thick targets are made with measured data to analyze the initial reaction process in the framework of the exciton (hybrid) model code ALICE91 (M. Blann, Lawrence Livermore National Laboratory Report UCID 19614, 1982). We have considered two reaction mechanisms: dissolution of the $\ensuremath{\alpha}$ in the nuclear field, and preequilibrium processes initiated by $\ensuremath{\alpha}$-nucleon collisions. Both these processes seem to contribute to the emitted neutron spectra in varying proportions depending on the incident $\ensuremath{\alpha}$ energy and possibly on the target nucleus. Contributions from other processes appear to be non-negligible.

Energy distributions of neutrons emitted from thick targets of Al and Ti are measured for alpha induced reactions at 30, 40, and 50 MeV projectile energies. Measurements are done at 0°, 30°, and 45° with respect to the projectile direction using the proton recoil scintillation technique. The measured data are compared with results from calculations using three different approaches of the exciton model namely, the master equation, the closed form and the hybrid model ~a variant of the exciton model!. The corresponding nuclear reaction model codes used for the purpose are PEQAG @E. Betak and J. Dobes, Report No. IP EPRC SAS 43/~1983!, Bratislava, 1983#, PRECO-D2, @C. Kalbach, Report No. LA-10248-MS, Los Alamos National Laboratory, Los Alamos, 1985# and ALICE91 @M. Blann, Lawrence Livermore National Laboratory Report No. UCID 19614, 1982#, respectively. Proton induced neutron yield distributions measured by others are also included in the comparison. The calculated results from the hybrid model code ALICE91 give overall close approximations of the measured data compared to the other models.

Expression vectors containing full-length cDNAs for each of the human fibrinogen chains were constructed. COS-1 cells were transfected with single vectors, mixtures of two, or with all three vectors and stable cell lines selected. Cells transfected with single vectors, or with mixtures of any two vectors, expressed the appropriate fibrinogen chains but did not secrete them. COS cells transfected with three vectors expressed all of the chains and secreted fibrinogen. COS cells transfected with three vectors contained, intracellularly, a mixture of fibrinogen-related proteins. The four main intracellular products were nascent fibrinogen, an A alpha.gamma complex, free A alpha chains, and free gamma chains. This is a similar pattern to that noted in Hep G2 cells. The intracellular forms of fibrinogen were sensitive to endoglycosidase H, indicating that they reside in a pre-Golgi compartment. Secreted fibrinogen was endoglycosidase H-insensitive, suggesting that the secreted glycoprotein moieties were processed in the normal manner. When mixed with plasma fibrinogen, radiolabeled recombinant fibrinogen was incorporated into a thrombin-induced clot. These studies demonstrate that COS cells transfected with all three fibrinogen chain cDNAs are capable of assembling and secreting a functional fibrinogen molecule.

The study aim was to determine the demographic profile of female children 0-14 years old living in urban slums in Delhi, India. The sample included 1680 slum dwellers in 386 households, of whom 733 were children 0-14 years old. The sex ratio of the sample population was 900 females per 1000 males, compared to the national ratio of 933 females per 1000 males. The sample population included 796 females and 884 males. The sex ratio among children 0-14 years old in the sample was 960 females per 1000 males. School enrollment of children 5-14 years old numbered 232 (50.4%): 46% males and 27.5% females. The lower enrollment of females in slum areas compared to the national average was attributed to the greater participation of young girls in domestic work. 22% of children 0-14 years old were married. The infant mortality rate was 143.2/1000 live births. The crude death rate was 19.64/1000 population, which was 150% higher than the national rate. Female mortality among those 0-6 years old was higher than male mortality; after 6 years of age, male mortality was higher. The study revealed the needs of female children in urban slum areas of India. Government and voluntary agencies must work together in the areas of social work, nutrition, education, health among the poor urban female population in India.

Previous studies indicated that synthesis of B beta chain may be a rate-limiting factor in the production of human fibrinogen since Hep G2 cells contain surplus pools of A alpha and gamma but not of B beta chains, and fibrinogen assembly commences by the addition of preformed A alpha and gamma chains to nascent B beta chains attached to polysomes. To test whether B beta chain synthesis is rate limiting Hep G2 cells were transfected with B beta cDNA, and its effect on fibrinogen synthesis and secretion was measured. Two sets of stable B beta cDNA-transfected Hep G2 cells were prepared, and both cell lines synthesized 3-fold more B beta chains than control cells. The B beta-transfected cells also synthesized and secreted increased amounts of fibrinogen. Transfection with B beta cDNA not only increased the synthesis of B beta chain but also increased the rate of synthesis of the other two component chains of fibrinogen and maintained surplus intracellular pools of A alpha and gamma chains. Transfection with B beta cDNA did not affect the synthesis of albumin, transferrin, or anti-chymotrypsin and had a small inhibitory effect on the synthesis of C-reactive protein. Taken together these studies demonstrate that increased B beta chain synthesis specifically causes increased production of the other two component chains of fibrinogen and that unequal and surplus amounts of A alpha and gamma chains are maintained intracellularly.

The nucleus 73 Se was studied by the reaction 51 V(28 Si,αpn)73 Se. The level scheme extended upto \(\frac{{41}} {2}\bar h \) in both +ve and −ve parity bands with 10 new transitions placed in the level scheme. Lifetimes of 17 high spin states measured by DSAM. The transitional quadrupole moment is found to drop down after the band crossing suggesting a less deformed configuration. At the band crossing region, Q t increases suddenly in both +ve and −ve parity bands. It is argued that the +ve parity band is a decoupled band.

The mechanism of sintering in chromium oxide in the presence of varying amounts of magnesium oxide in a firing condition that simulates a controlled reducing atmosphere has been investigated. The investigation is based on isothermal shrinkage measurements at different temperatures. The data suggest grain boundary diffusion to be the main process with evidence of vapour transport.

The complete amino acid sequence of rabbit testicular angiotensin-converting enzyme has been deduced from the sequence of the corresponding cDNA clone. A protein of the expected molecular weight of 84,000 was translated in vitro from the mRNA encoded by this cDNA. All of the previously determined sequences of seven tryptic peptides from the enzyme are present in the deduced sequence, thus confirming the identity of the protein. From the deduced sequence it appears that the protein contains a signal peptide at the amino terminus and a hydrophobic anchoring domain near the carboxyl terminus. Northern analysis with oligonucleotide probes, whose sequences represented different regions of the cDNA, revealed not only the regions of extensive homology between the mRNAs encoding the testicular and the pulmonary isozymes but also a stretch of sequence near the 5' end unique to the testicular mRNA.

Green chromium oxide compacts incorporating TiO2 as dopant were sintered at 1400°, 1450° and 1500°C respectively in conditions simulating controlled atmosphere firing having a very low pO2. Studies on the microstructure, density, porosity and hardness revealed that 1.0 wt% of TiO2 caused densification to the extent of 95.59 per cent of theoretical when fired at 1500°C with 0.5 hr soaking. A higher percentage of TiO2, however, resulted in inferior properties.

The mixed model with one factor represented by fixed effects, one factor by random effects, and a normal error, has often stipulated that these random effects be a sample drawn from a normally distributed population. In the case of a single response (or univariate) experiment, the variance of this normal distribution is a natural measure of the dispersion of these random effects, and confidence bounds on the ratio of this variance to the error variance [13], [14], [9] and simultaneous confidence bounds on both variances (in the latter case with a confidence coefficient $\geqq$ a specified value) [9] have already been found for certain classes of experimental designs. But when a distribution is not normal--or not assumed at the outset to be normal--the variance may not reveal as much about the distribution as some other measure such as interquartile range. In the present paper we seek confidence bounds on what, in a sense to be explained presently, might be called representations of the interquartile range and of analogous differences between higher order quantiles of the population from which the random effects are drawn. The method of obtaining these bounds involves an element of approximation comparable to grouping continuous data into $k$ classes, since it replaces the actual random-effects variate by a "substitute variate" having $k$ equally probable discrete values. The main idea is this. Let us assume, for simplicity of discussion, that we have a real valued stochastic variate. One comment here might be helpful. If the stochastic variate is observable, it seems natural to attempt to approximate its unknown distribution by introducing unknown probabilities over a finite set of preassigned class intervals, then trying to estimate these probabilities and then (especially for a continuous distribution) increasing the number of class intervals. On the other hand, if the variate is unobservable, as in the present set-up, it seems natural to try to approximate the distribution by replacing the stochastic variate by a "substitute" variate which is supposed to take, as a first approximation, two (unknown) values with equal probabilities, or as a second approximation, three (unknown) values with equal probabilities, or in general $k$ (unknown) values with equal probabilities. We then try to estimate, in terms of our observations, these unknown values, which may be regarded as approximations to the 1st, 3rd, $\cdots, (2k - 1)$th quantiles of the unknown distribution. The random effects variate postulated in our model may have either a continuous or a discrete distribution, provided in the latter case there are enough distinct values to make these $k$ quantiles meaningful parameters of the distribution. From now on, for brevity, we shall refer to these unknown values as the quantiles of the unknown distribution. It will be seen later that it is the differences between these unknown values rather than the unknown values themselves which we can estimate or make inferences about, and the number, $k - 1,$ of such differences which can be estimated is restricted by the experiment. Turning now to the confidence bounds, we observe that in the derivation of these bounds use is made of the same kind of sums of squares as in the normal variance components analysis. Unlike the more familiar confidence statements where the confidence coefficient may be specified at will, here except for the case of two blocks, only a lower bound on the confidence coefficient is specifiable, and this includes as a factor a decreasing function of $k$, the number of discrete values of the substitute variable. For $k = 2, 3, 4, 5$ the geometric shape of a $(k - 1)$-dimensional confidence region has been found. It is also shown how the usual inference about the fixed effects can be made from this model and then how the above type of confidence bounds can be found for each of several random-effects factors in an experiment with orthogonal design. In the case of a multiresponse--usually called multivariate--experiment, the model frequently stipulates that the random effects be samples from a multivariate normal population. Although the variance matrix of this distribution has a readily available estimator, confidence bounds have presented many difficulties. For the extremely restricted model in which the variance matrix of each random-effects factor is proportional to the variance matrix of the error, Roy and Gnanadesikan [10] obtained simultaneous confidence bounds on the characteristic roots of this latter matrix and on the proportionality constants. In Part II of this paper the authors present (with a confidence coefficient greater than or equal to a preassigned value) confidence bounds on the characteristic roots of the variance-covariance matrix of a random-effects variate without assuming any such relation to the error matrix. The second part will also consider the $p$-variate extension of the univariate substitute variate and the associated confidence bounds for the case where the $p$-dimensional distribution of the random effects is not necessarily normal. This development will be only indicated in principle for $p > 2$ but will be discussed in some detail for the case $p = 2$.

It is clear that a p-variate body of data arranged in a q-way classification will formally look llke a (p+q)-dimensional contingency table, but a distinction can be made between a 'variate' and a ‘way of classification’ in that along the direction of a 'variate' the marginal frequencies are supposed to be stochastic variates while along a 'way of classification' the marginal frequencies are supposed to be fixed. When, along certain directions, the marginals are fixed, an approach based on a conditional probability argument has been used. In the present paper (i) the conditional probability approach is abandoned and we start either from a single multinomial distribution or a product of an appropriate number of different multinomial distributions according as, with multi-way frequency data, all ways are 'variates' or some are 'variates' and some are 'ways of classification'. (ii) Also the hypotheses that are posed are of different kinds altogether according as we have a 'multivariate analysis' situation or an 'analysis of variance' situation. The hypotheses that are meaningful for one situation would not be too meaningful for the other and vice versa. Since the conditional probability approach is altogether abandoned, the mathematical theorems to which appeal is made are the two theorems as stated and proved by Cramer (1946, chapter 30) and a number of other such theorems which have been proved the same way and which, between them, take care of all the hypotheses discussed in this paper. When all ways are 'variates' the hypotheses are analogous to those in the usual multivariate analysis, and when some ways are 'variates' and some are 'ways of classification' the hypotheses are analogous to those in the analysis of variance. The general methods discussed in this paper arose out of an attempt to analyse a large mass of categorical data. The analysis has been carried out, and a few typical cases (together with the numerical analysis) illustrating different parts of the theoretical development will be presented in a subsequent paper. In this paper only the large-sample tests are considered. How 'large' the sample size has to be for the validity of the use of these asymptotic techniques, or in other words, some results on the nature of the approximation involved will also be discussed in a later paper.

The variance-covariance matrices arising in the analysis of variance, response-surface fitting and order statistics have special patterns expediting and facilitating their algebraic manipulation. By appropriate triangulation and partitioning devices, the determinants of these matrices can be evaluated from general formulae. The characteristic equations, and sometimes their roots, can also be obtained in a direct single step.

This paper is a follow-up of a previous paper [1], the full implications of some of the results there being brought out here in terms that are physically more meaningful. Two cases of simultaneous confidence bounds, I and II, are given, in each case with a confidence coefficient which is to be greater than or equal to a preassigned level. Case I relates to the characteristic roots of $\sigma$ and $\sigma_1\sigma^{-1}_2$, where $\sigma$ stands for the dispersion matrix of one $p$-variate and $\sigma_1$ and $\sigma_2$ for the dispersion matrices of two $p$-variate normal populations. Case II relates to a $(p + q)$-variate normal population $(p \leqq q)$, for which the matrix of regression of the $p$-set on the $q$-set is defined in a natural manner. This matrix is denoted by $\beta(p \times q)$ and simultaneous confidence bounds are given on all bilinear compounds of this matrix (with arbitrary coefficient vectors of unit modulus). Confidence bounds on the characteristic roots of $\sigma$ and $\sigma_1\sigma^{-1}_2$ are given respectively by (3.1.3) and (3.2.8). Confidence bounds on the bilinear compounds of the regression matrix $\beta$ are given by (4.7).

In this paper two closely related heuristic principles of test construction (to be explained in Section 3), called Type I and Type II methods, of which Type II is identified with the usual likelihood ratio method, are noticed as underlying most of the classical tests of hypotheses, simple or composite, on means of univariate normal populations, and on total or partial correlations or regressions in the case of multinormal variates. In these situations the two methods are found to lead to identical tests having properties which happen to be very good in certain cases and moderately good in others. For certain types of composite hypotheses an extension is then made of the Type I method which is applied to construct tests of three different classes of hypotheses on multinormal populations (so as to cover, between them, a very large area of multivariate analysis), yielding in each case a test in general different from the corresponding and current likelihood ratio test. In each case, however, the two tests happen to come out identical for some degenerate "degrees of freedom." In contrast to the likelihood ratio test it is found that in these cases, for general "degrees of freedom," the corresponding Type I test is much easier to use on small samples, because of the relatively greater simplicity of the corresponding small sample distribution problem under the null hypothesis. In each case a lower bound of the power function of the Type I test is also given (against all relevant alternatives), anything like which, so far as the author is aware, would be far more difficult to obtain for the Type II tests in these situations. In this paper the general approach to the two methods is entirely of a heuristic nature except that, under fairly wide conditions, a lower bound to the power functions for each of the two types of tests is indicated to be readily available, which, however, is much too crude or wide a bound in general.

The usual MANOVA (multivariate analysis of variance) model (see equation (1)) may be generalized (equation (3)) by allowing for the appending of a post-matrix in the expectation equation. As explained in ? 1, this generalized model (3) is applicable particularly to many kinds of growth curve problems, as well as to other problems. Section 2 is theoretical, and develops techniques of analysis under the generalized model. A numerical example involving growth curves is worked out in ? 3.

The general solution of the equations connecting the motion of the two coupled components in an electromagnetic seismograph has been obtained in another paper and it shows that the magnification of a seismograph depend on seven instrumental constants. Using these results, equations and curves have been derived in the present paper from which the Magnification as well as Phase shifts in the response of a seismograph and their variations with damping and coil inductance can be easily obtained. Based on these curves a number of magnification curves for different combinations, which are in operation at the different seismological stations of the world, have been derived. Suitable equations and curves have also been obtained which can be used for estimating the absolute Magnification of a Seismograph. An experimental method of obtaining the frequency response curves of seismographs in their operating condition has been described and the results obtained by this method has been given. It has been indicated how the results incorporated in the present paper can be used in the proper design of seismographs required for the different purposes.

The development of highly sensitive electromagnetic seismographs and their uses in various problems of seismology and other allied branches have considerably extended the region of their application. The theory of such seismographs was developed earlier under different approximations which are justified as long as it is used only in the study of earthquake waves of frequencies less than one cycle per sec. In the present paper the effect of large inductances in the transducer coils and also of any choke in the galvanometer circuit on the response characteristics has been examined. The response curves for different combinations of seismometers and galvanometers have been obtained, and their variations with the coil inductances have been estimated. It has been shown that considerable errors in the amplitude-period relationship occur if the coil inductances are neglected. This possibly explains the various anomalies which now exist in the interpretations of different results obtained from the analyses of seismograms, obtained with different seismographs. The ‘magnification curve’ for a typical electromagnetic seismograph has been obtained experimentally and this has been compared with the theoretical result derived in the present paper. A number of problems have been indicated, in the study of which precise response curves are required, and it has been suggested that with a proper use of the results derived here a large number of anomalies now existent may disappear.

In a situation in which the observations are frequencies in a multi-way contingency table such that the observations are supposed to be independent and it is only the total number that is supposed to be fixed from sample to sample, a hypothesis on the structure of the probabilities in the different cells or categories is put forward. This hypothesis, by a certain analogy with the customary terminology of analysis of variance, is defined to be the hypothesis of "no interaction" and a large sample test of this hypothesis in terms of $\chi^2$ is offered. Bartlett's results [1] for the case of a $2 \times 2 \times 2$ table and Norton's results [5] for the case of a $2 \times 2 \times t$ table formally turn out to be special cases of the results given here with these differences; (i) Bartlett's and Norton's results refer to "analysis of variance" situations, with marginal frequencies along at least two ways of the table being fixed, while in this paper, for reasons explained elsewhere [7], it is only the total $n$ that is held fixed. (ii) Bartlett's and Norton's papers do not give any indication of the mechanism behind the formulae for the hypothesis of "no interaction," while this paper attempts to give a definite mathematical (and perhaps also physical) mechanism behind the formulae.

In this paper confidence bounds are obtained (i) on the ratio of variances of a (possibly) correlated bivariate normal population, and then, by generalization, (ii) on a set of parametric functions of a (possibly) correlated $p + p$ variate normal population, which plays the same role for a $2p$-variate population as the ratio of variances does for the bivariate case, (iii) on the ratio of means of the population indicated in (i), and, by generalization, (iv) on a set of parametric functions of the population indicated in (ii), which plays the same role for this problem as the ratio of means does for the bivariate case. For (i) and (iii) the confidence coefficient is any preassigned $1 - \alpha$ and the distribution involved is the central $t$-distribution, while for (ii) and (iv), the confidence statement in each case is a simultaneous one with a joint confidence coefficient greater than or equal to a preassigned $1 - \alpha$. For (ii) the distribution involved is that of the central largest canonical correlation coefficient (squared), and for (iv) the distribution involved is that of the central Hotelling's $T^2$. As far as the authors are aware the results on (ii) and (iv) are new and so perhaps that on (i). But the result on (iii) has been in the field for a long time in various superficially different forms. An important point to keep in mind on these problems is that, for such confidence bounds and the associated tests of hypotheses to be physically meaningful, the two variates for the bivariate distribution should be comparable. For example, they might refer to the same characteristic of a set of individuals before and after a feed. Likewise, for a $(p + p)$-variate distribution, the $p$ variates of the first set should be comparable to $p$ variates of the second set. For example, they might refer to several characteristics of a set of individuals before and after a treatment. In each case the confidence bounds are obtained by inverting the test of a certain hypothesis, which is indicated at its proper place. Thus, for the $(p + p)$-variate problem, we assume that there are $p$ pairs of comparable variates and it is the pairwise comparison for these $p$ pairs that seems, in this situation, to be physically more meaningful than anything else. Any general bounds that will be obtained in this paper are to be regarded, in a large measure, as a means to this end, although there could conceivably be physical questions, some of which will be illustrated in a later applied paper to be published elsewhere, to which these more general bounds would be pertinent.