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As a part of our fundamental studies on paper electrophoresis we here present our views regarding selection of the two methods of paper electrophoresis, the Grassmann and the Flynn method. The filter paper used was Whatman No. 1, the stain, Amido Black 10 B.Ten essentially normal human sera were used, and the results from both methods were almost identical, although differing in minor details. It is these minor differences that we wish to consider here.(1) With the electrophoretic time being the same for both methods, the length of the electrophoretic migration was longer for the Grassmann method than for the Flynn method. This may be due to the movement of the buffer toward the center of the paper, as a result of the evaporation from the surface of the paper.(2) The position of γ-globulin with the Flynn method was always on the negative side of the line of origin (electroosmosis), but with the Grassmann method it was consistently on the positive side. This, also, we consider is due to the flow of the buffer to compensate the evaporation loss.(3) The protein adsorbed at the line of origin was more marked for the Flynn method than for the Grassmann method. We are now considering a way to eliminate this defect in the Flynn method. In order to observe the tailing of the albumin, therefore, the Grassmann method is more convenient.(4) The reproducibility of both methods, as compared to free electrophoresis was not very good, owing to the evaporation from the paper and also to the sagging of the paper in the Grassmann method.(5) From the above it is concluded that although the Grassmann method is more popularly used, the Flynn method when properly handled is far from being inferior to the former method.

Among the factors affecting the stiffness of paper, the effects of density, loading and basis weight were studied on the hand-made sheets. A formula and a diagram, by which the effect of basis weight on the stiffness can be calculated independently of pulp variety, beating equipment and pulp freeness, were derived and the concept of stiffness factor was defined as follows.log S =log a+1.832 log WStiffness factor=S(100/W)1.832where S=stiffnessW=basis weight in g/m2 α=α constantAlthough “Koshi”, one of the Japanese traditional methods evaluating paper quality is not a mere stiffness but it depends on the sense of human being, a formula evaluating “Koshi” was derived and it was named “Composed Stiffness”.Composed Stiffness= [S- (1.0-D)× 86.7]× D×T.S.where S= StiffnessD=Density in g/cm3 T.S = Tensile strength in kg

The electromagnetic boundary value problem of two waveguides coupled by an aperture or an aperture in a waveguide radiating into free space may be described by an integral equation. An analytical solution to this integral equation cannot be readily found due to the complexity of the kernel. However, extremely useful results may be obtained if the method of moments is employed to reduce the integral equation to a matrix equation which can be solved by known methods. In this short paper, series and shunt slots in a rectangular waveguide are analyzed using this technique.

IN paper chromatography, the RF value, or ratio of distance travelled by substance to the distance travelled by solvent front, is generally used as the criterion of identity. If two substances have the same RF values in two or more solvent systems, they are assumed to be identical. But although RF values are often quoted with great precision, experience shows that they are, at best, only a rough guide and should not be used as the sole means of identifying a substance.

The advantages of using a newly available square root graph paper for nuclear spectra are illustrated by means of a sample spectrum plotted on linear, logarithmic, and square root scales.

Measuring principle of Bekk's smoothness is analysed and it is clarified that there exists in measuring Bekk's smoothness excessive leakage of air which depends on permeability of paper and the roughness of paper of the opposite side of the tested surface. And so the excessive leakage is measured experimentally to be found out that it can not neglected for determining surface roughness of paper by Bekk's method.A direct reading instrument of smoothness of paper are designed applying a similar principle of air micrometer. Theoretical and experimental analyses show that a flow of air through spaces between a test surface and a flatly finished surface obeys Hagen-Poiseuille's law. From this respect the relation between a value of Bekk's smoothness and pressure drop of the new instrument can be given theoretically.Experimental researches show that the observations of smoothness of paper, which is obtained by the new instrument, coincide with those of Bekk's instrument when they are corrected by estimating the excessive leakage.

Three cases and sources of inaccuracy in finding the value of E in the former paper (Proc. Roy. Soc. vol. xv. p. 429) having been pointed out by Mr. Glaisher, and some other minor errors not noticed by him having since been detected by the author, and these having vitiated the results, but only in a slight degree the inferences drawn from them (for in the former paper the last and leading conclusion as to the value of E, though limited , was certainly correct ), the author has been led, from a deep sense of obligation to the Royal Society, to revise, correct, and extend what he had previously done. And it will be seen, from comparing Mr. Glaisher’s remarks and results with what follows in this paper, that the supplementary matter herein given, including the extension of E &c. to 110 places of decimals, can scarcely be without interest to mathematicians, and especially as regards the summation of the harmonic series in the formula for finding the value of E. Not having seen M. Oettinger’s article in Crelle’s ‘Journal,’ “On Computing the value of E,” the author is unable to state what artifices he used in summing the harmonic series. Mr. Glaisher gives a very simple and obvious one from M. Oettinger, which the author could not but see and employ for calculating the values of the reciprocals of the even numbers.

The method of plotting observations on probability paper becomes clear when the curve on probability paper is regarded as an integral of the histogram. The observations are divided into intervals, which may often conveniently be the natural interval of measurement, and the total frequency of observations up to and including the nth interval is plotted against the upper end of the nth interval. It is shown that in drawing a straight line to fit the observations, less weight should be attributed to deviations from the line towards its ends than in the middle regions.

I have studied the visco-elastic properties of paper by vibrating reed method at super low frequency range and I measured, Youngs modulus internal frictional coefficient (viscosity).Youngs modulus and viscosity varies by direction in hand made paper, but Youngs modulus is independent of frequency in the range of low frequency. It reduces as increasing frequency. This viscosity is so-called apparent viscosity so, I will convert it true viscosity by next method let us shearing stressv2lv : frequency, l : length.rate of shear v2l/η I plot v2l, v2l/η I obtain consistency curve.I will regard consistency curve as two kinds straight line.I think this straight line means the true viscosity. Let us those viscosities ηHF (Viscosity at high frequency) ηLF (Viscosity at low frequency). Reasonable solution of these two kinds viscosity ηHEηLFis the problem of future.Youngs modulusEand ηHF, ηLFincrease as reducing its freeness in hand made paper.but increasing process changes by pulp sorts.

In a recent paper Papadopoulos [1]1 claims to have obtained solutions to the problem of sound propagation from an impulsive point source in a semi-infinite elastic solid which differ in certain respects from solutions previously obtained by Pekeris [2], [3], and by Pekeris and Lifson [4]. The results of Papadopoulos are based on a singular integral source representation developed by him [5]. By tests based on simple special cases we show that, in a number of cases where Papadopoulos claims a result different from that of Pekeris, the results of Papadopoulos are unacceptable whereas the results of Pekeris are acceptable. Reasons for these errors in Papadopoulos's work are suggested. A number of other errors in the paper of Papadopoulos are also noted. 1 Numbers in brackets refer to references at rear.

In a previous paper I investigated the problem of the formation of waves on deep water by wind, and found that the available data were consistent with the hypothesis that the growth of the waves is due principally to a systematic difference between the pressures of the air on the front and rear slopes. Lamb had already discussed the maintenance of waves against viscosity by an approximate method, but without obtaining numerical results. Being under the incorrect impression that Lamb’s approximation would not hold for the short waves I was chiefly considering, I proceeded on more elaborate lines. It now appears, however, that Lamb’s method is not only applicable to the problem of waves on deep water, but is readily extended to cover the case when the water is comparatively shallow, and to allow for surface tension. The fundamental approximations are first, the usual one that squares of the displacements from the steady state can be neglected, and second, that viscosity modifies the motion of the water to only a small extent. The motion of the water can then, to a first approximation, be considered as irrotational. With the previous notation, let ζ be the elevation of the free surface x, y, z the position co-ordinates, t the time, U the undisturbed velocity of the water, h the depth, and φ the velocity potential. Also let σ, p, q , and ϑ denote respectively ∂/∂ t , ∂/∂ x , ∂/∂ y , and ∂/∂ z , and write p 2 + q 2 = - r 2 .

The analogical methods to solve the Laplace or Poisson equation are very useful and important in applied mechanics. In this paper, the author triea to solve the torsion problems with electrical analogies by the conducting sheet with uniform surface resistance. The resistive paper is better than the electrolyte of electrolitic tank method as to handling, but it is difficult to obtain the paper with uniform resistance. For experimental example, the torsion of a square bar with a concentric circular hole is tested and the results are compared with the results given by another investigators.

Summary It is shown that a series of papers by Rikitake and a paper by Rikitake & Yokoyama, concerning electromagnetic induction in a finitely conducting hemispherical shell, contain solutions that require correction. The solutions are compared to those obtained by Hobbs using an alternative method.

1) As regards viscoelastic properties of paper of z-direction (perpendicular to paper surface), it was showed that its properties were able to same treated as other two directions.In compressed case, reciprocal curse for tensile curse was obtained. Apparent Young's modulus of Z-direction was known 109 dyne/cm2 as order, less than x, y direction and from this fact simple consideration about the calendering was made.2) About the smoothness of paper, assuming the strain due to the press N^hich was added to paper surface is proportional to smoothness, straight line relation of compressed stressismoothness was explained, and adaptable region of this straight line relation was derived from the s aloe of apparent Young's modulus and second Young's modulus, fits experimental data considerably.

The flux I 0 reflected at specular angles 45°–45° from the surface of glossy paper and the assumed value of its diffuse component I 2 defined experimentally are measured with a goniophotometer. The ratio of I 0 to I 2 is taken as a measure of gloss, and denoted by G N F according to an earlier paper of E. Fukushima. 1) For a series of machine glazed papers differing considerably in colour, the values of C N F are compared with the visual gradings of 36 Japanese observers, and a linear correlation of the logarithm of G N F with the visual gloss is found with a correlation coefficient +0.986 except for two papers. The method of determining the value of I 2 is also introduced and the voting distributions of the observers for the gloss of the papers are discussed.

K. Brunell has disussed the basic properties and the design characteristics of the constant diameter cam, especially of the cam whose base curve is given as cycloidal displacement function. However it seems that his discussion is questionable in some points, so in this paper, correcting or supplementing his paper, the properties and the design characteristics of the constant diameter cam will be made clear. Let lift h, dwell angle β and cam base curve ν (θ) : 0gθgβ for follower's rise motion be given, then the cam base curve is given by [numerical formula] Let g be radius of the cam base circle, then the governing criterion is to be such a g that satisfies the following conditions for each θ such that 0gθgβ. g+v (θ)+v" (θ)>0, g+h-v (θ)-v" (θ)>0. If the condition v (θ)+v (β-θ)=h : 0gθgβ holds, the governing criterion becomes g+v (θ)+v" (θ)>0 : 0gθgβ. Moreover we studied the constant diameter cam with cycloidal motion follower and we could express its governing criterion graphically.

Discussion of the problem of an elastic half-space with spherical cavity is continued in respect of Rayleigh waves on the plane boundary. Displacements in the initial and first group of higher order Rayleigh waves are derived by using the time-harmonic solution developed in part I of this series with attention confined to the case of time-harmonic normal stress at the cavity. These are employed to find also the response to an exponential shock at the cavity and graphs are presented showing the surface motion due to the initial Rayleigh waves. Finally, in an appendix to the paper, some comments are given on a recent paper by R. D. Gregory on the problem of the half-space with cavity.

The paper considers the pros and cons of spur, single, and double helical gearing. A detailed geometric analysis of the basic load capacities of helical and spur gears, respectively, leads to non-dimensional optimum tooth numbers for each type, having a constant ratio to one another irrespective of size and material. Helical gears are shown to require the same volume as spurs but relatively coarser teeth. Consideration of the possible dynamic effects of characteristic errors leads to the conclusion that spur gears are potentially superior for very high speed applications.

An analogue technique is described giving good approximate solutions of the biharmonic equation. The method uses two plane sheets of conducting paper linked by an array of resistors. The technique is applied to problems involving the slow flow of a viscous fluid past uniformly spaced parallel fibres. Calculated values of the Kozeny constant from the results show much better agreement with the practical and theoretical values than those derived from previous analogue solutions.

A review has been made of the previous attempts to formulate a theory for the elastic modulus of paper in terms of fibre properties. The suggestion is made that, by considering the case of uniaxial stress, previous authors have attempted a problem that is too complex for the present state of knowledge. It is suggested that the case of equal biaxial strain is theoretically simpler and that verification of such a theory can be made more reliably. The biaxial theory is developed and the elastic modulus is written in terms of the moduli of the fibres and the bonded area of the sheet. The biaxial modulus has been measured for three levels of fibre bonded area for one pulp and these admittedly sparse data are in agreement with the theory.

In connexion with Mr Connolly's paper on "New Types of Levelling Instruments with Reversible Levels" it is shown how an accurate test of reversible levels can be carried out in a simple manner. It is also pointed out that levelling instruments with reversible levels have been constructed in Germany since 1875.

The portion of the Courant-Friedrichs-Lwy paper [Math. Ann. 100, 32 (1928)] that was devoted to hyperbolic difference equations is critically reviewed in terms of its basic contribution to the numerical solution of partial differential equations. Some subsequent developments are then discussed, including recent literature related to the von Neumann condition, some irreversible schemes, generalizations of the energy method, some new difference schemes, and mixed initial boundary value problems.

Jacobi, in a posthumous memoir* which has only this year appeared, has developed two remarkable methods (agreeing in their general character, but differing in details) of solving non-linear partial differential equations of the first order, and has applied them in connexion with that theory of the Differential Equations of Dynamics which was esta­blished by Sir W. B. Hamilton in the Philosophical Transactions for 1834‒35. The knowledge, indeed, that the solution of the equations of a dynamical problem is involved in the discovery of a single central function, defined by a single partial differential equation of the first order, does not appear to have been hitherto (perhaps it will never be) very fruitful in practical results. But in the order of those speculative truths which enable us to perceive unity where it was unperceived before, its place is a high and enduring one. Given a system of dynamical equations, it is possible, as Jacobi had shown, to con­struct a partial differential equation such that from any complete primitive of that equation, i. e . from any solution of it involving a number of constants equal to the number of the independent variables, all the integrals of the dynamical equations can be deduced by processes of differentiation. Hitherto, however, the discovery of the com­plete primitive of a partial differential equation has been supposed to require a previous knowledge of the integrals of a certain auxiliary system of ordinary differential equa­tions; and in the case under consideration that auxiliary system consisted of the dynamical equations themselves. Jacobi’s new methods do not require the preliminary integration of the auxiliary system. They require, instead of this, the solution of certain systems of simultaneous linear partial differential equations. To this object therefore the method developed in my recent paper on Simultaneous Differential Equa­tions might be applied. But the systems of equations in question are of a peculiar form. They admit, in consequence of this, of a peculiar analysis. And Jacobi’s methods of solving them are in fact different from the one given by me, though connected with it by remarkable relations. He does indeed refer to the general problem of the solution of simultaneous partial differential equations, and this in language which does not even suppose the condition of linearity. He says, “Non ego hic immorabor qusestioni generali quando et quomodo duabus compluribusve æquationibus differentialibus partialibus una eademque functione Satisfied possit, sed ad casum propositum investigationem restringam. Quippe quo præclaris uti licet artificiis ad integrationem expediendam commodis. ” But he does not, as far as I have been able to discover, discuss any systems of equations more general than those which arise in the immediate problem before him.

This paper considers the problem of determining the inviscid, subsonic compressible (or incompressible) blade-to-blade flow field through a turbomachine blade row, and presents two computer solutions, known as the ‘matrix’ and ‘streamline curvature’ methods, for solving this elliptic problem. In the former method the equations of motion are formulated in terms of a stream function and the numerical solution is based on finite difference approximations; in the latter, the equations of motion are solved in conjunction with the equation of continuity by an iterative process starting from a guess for the streamline pattern. Solutions for several blade profiles, giving flow patterns and blade surface velocity distributions, are included.

Recently Cameron and Storvick introduced and studied an operator valued function space integral related to the Feynman integral. The main theorems of their study establish the existence of the function space integral as a weak operator limit of operators defined at the first stage by finite-dimensional integrals. This paper provides a substantial strengthening of their existence theorem giving the function space integrals as strong operator limits rather than as weak operator limits.

In a previous paper PAYTON [1] (hereafter referred to as WF for wave front) considered the shape of the two dimensional wave front induced in a finitely strained elastic body by an impulsive point body force. This problem was characterized by three parameters ct, fl and ~ which were dependent upon the initial strain and the constitutive relations for the material in question. For certain regions of the (~t, fl, ~) space it was shown that the wave front normal curve possessed inflection points and that the associated wave front curve carried cuspoidal triangles. In WF the wave front shape was classified by the number (and location) of normal curve inflection points. It was remarked (through a note added in proof) that the classification of cases n. 5, n. 8 and n. 13, where n = 1, 2, 3 and 4, was incomplete. In cases 1.8 and 4.8 (where ct =fl) and in cases 2.8 and 3.8 (where ctf l=l) this incompleteness was removed but the remaining eight cases were left open. It is now possible to complete this classification through a unified approach.

The purpose of this short paper is to construct the dissipation and scattering matrices of lossy junctions in terms of the eigenvalues of the dissipation matrix. This removes the need to rely on inequality relations between the scattering parameters of lossy circulators. The eigenvalues of the dissipation, scattering, and admittance matrices are related. The eigenvalues of the dissipation matrix give the dissipation associated with each possible way of exciting the junction. The ones of the scattering matrix give the reflection coefficients associated with these different excitations. The admittance eigenvalues define in each instance the eigennetworks of the junction. This leads to the definition of the entries of the dissipation matrix in terms of the loaded and unloaded Q-factors of the junction eigennetworks. The scattering matrices of a number of lossy 3-port junctions are also constructed directly in terms of the elements of the eigennetworks.

This paper consists of three theorems. The first theorem gives the asymptotic behavior of solutions of the nonlinear delay differential equation. The other theorems give sufficient conditions for oscillatory solutions of variants of that equation.

a) In previous report, it was based on Kane's theory. Kane's theory was different from Corte's theory as regard increment of specific surface and increment of breaking length during beating time. In this report, it was represented that Kane's theory as to increment of specific surfaceduring beating time was exact for Corte's theory at first order approximation, and for breaking length, it was showed that Corte's theory is special case of Kane's theory by simple calculation.b) According to theory of tear factor and burst factor which derived in previous report, the plot lnbreaking length/Tear factor-beating time is to straight line and the plot of beating time-burst factor/breaking length is to almost parallel to beating time axis, if stretch is roughly constant during beating time, and burst factor breaking length ×√ stretch is to straight line. These matter was derived from theary and confirmed by some experimental data. For burst factor-breaking length ×√ stretch, it's trangent of straight line is 0.37 from theory and from experimental data, it is 0.47. It is believed to good agreement, considering that stretch is value of machine direction plus cross direction and the theory is considerably rough approximation.c) For impact strength, it is rough approximation that paper is elastic body, butfrom this assumption substituting Young's modulus from vibrating reed method to next equation, critical velocity was calculatedυ=qσ/Ewhere, q=√E/ρ=velocity of wave propagation, ρ=densityE=Young's modulus σ=tensile strength unit dyne/cm2υ=critical velocity.its values is in the range of 20, -45m/sec which was believed to be exact. The theoretical equation of im pact strength from viewpoint of bonded area. fibre length, stretch was represented. This equation agrees with exprimental data quantitatively and explains well relationship between beating time and impact strength.

A conducting paper analogue has been employed to provide a rapid and inexpensive method for the determination of values of stress in fields of uniaxial tension and of pure torsion, to which the equations of Laplace and Poisson apply. The reliability of the equipment has been verified by comparison of selected experimental results with those of known theories. Applications of the technique to the determination of the stress distributions in thin sheets containing geometric openings are given, and also to the determination of the stress distribution in a circular shaft containing a keyway, in pure torsion. The relevance of of Inglis' theory for equivalent elliptic holes is examined. Results are presented in graphical form.

The general equations for reflection and refraction of plane waves at a plane interface between two semi-infinite elastic solids were given by Zoeppritz (1919). The papers discusses these equations. (Author)

A method of estimating quasi-static discontinuity inductances in microstrip lines is outlined. Numerical results for symmetric right-angle bends are presented and compare well with experimental results.

In terms of scattering parameters, the equation transducer power gain is shown to be capable of representation as a family of circles of constant gain from which the design of load and source terminations to achieve a restricted bandwidth can be obtained. This is an extension of an earlier approach which only allowed either load reflection coefficient or source reflection coefficient to be considered in a given design. Through the use of a specification statement of VSWR, it is shown how a marginal stability factor can be derived. From the study of the interaction between the input and output reflection coefficients, a detuning factor is analytically derived to correlate the interaction between the input and output reflection coefficients. Either of these factors can be chosen and used to select optimum input and output reflection coefficients which provide stable operation for an amplifying stage that is to employ a conditionally stable active element. An example using these factors is given.

It is well known that the fringing capacitances determined for rectangular bars between parallel plates interact with each other when w/(b -t)/spl rarr/0. The limit of this interaction as s/spl rarr/0 for fixed w, b, and t is determined for symmetrical odd-mode fringing capacitances. This limit, together with an exact value known from one rectangular section and the known asymptotic value as s/spl rarr/ 0, permits one to estimate the values for all s. The same is true for the interaction of the symmetrical even-mode fringing capacitances, except that their interaction is readily shown to tend to zero as s/spl rarr/0.

The dynamic response of an infinite, elastic plate to a steadily moving transverse force is studied under the so-called improved plate theory. Analytic solutions for the subsonic and the intersonic cases are obtained using the method of integral transforms. The usual difficulty of the nonuniqueness of the steady-state solutions is circumvented by formulating the problems as initial value problems and then seeking the large time limits of the solutions of such initial value problems. The subsonic and intersonic solutions obtained here are similar to that obtained previously for the supersonic case. However, in contrast with the supersonic solution, which contains two families of Mach lines, the subsonic solution contains no Mach lines and the intersonic solution contains only one family of Mach lines.

A comparison of methods for the numerical solution of the hollow waveguide problem is presented in tabular form. Another table lists waveguide shapes and their cutoff characteristics that have been presented in the literature. These tables and the bibliography afford an aid towards the selection of a method.

A numerical method is given for the determination of the impedance of an infinitely long thin-wire helix. The propagation constant of the current for zero tangential electric field is found and used in a variational expression for impedance. Asymptotic values of resistance versus pitch are compared with resistances of infinitely long straight-wire antennas.

It is shown that, if expansion terms of all the modes appearing in the Green's function for the problem are retained, the singular integral equation method can be made to apply by generating a differential equation for this integral. The solution of the differential equation is straightforward, and the inversion of the resulting integral equation then follows standard methods. The process is applied in detail to the case of the capacitive diaphragm, and the results compared to the quasi-static method with correction terms. The results are close for small guide widths, but the present method should give superior results if the guide width permits some overmoding.

Two lower bounds of Sperb for the first eigenvalue of an elastically attached membrane are proved in an elementary way.

The linear differential equations governing the motion of a ship in a sinusoidal wave disturbance are derived from the principles of rigid body dynamics. Stability criteria are obtained when the linear differential equations have ( a) constant coefficients and ( b) periodic time-dependent coefficients that are needed to describe the ship in a following sinusoidal wave. The frequency of encounter between ship and wave is not necessarily zero.