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Physical calculations and analyses were performed to investigate the load on the TMJ when pressure was applied to (1) the first premolar and (2) the second molar on the same side. The calculations were performed under simplified conditions, considering the pressure side of the mandible only. Measurements were made on 25 cadaver mandibles. The calculations showed that there was a greater load on the TMJ when vertical pressure was applied to the first premolar than to the second molar; the TMJ of the pressure side was always loaded during vertical pressure on the teeth; the load on the other joint was somewhat lower than the assumed resultant force of the muscles of mastication on this side. The analyses gave no information concerning the magnitude of these forces in relation to those of the pressure side. These findings were in accord with those of previous investigations, i.e., that great load on the TMJ may be a factor in its deformation.

A NACA 4412 hydrofoil section was held stationary in an open flume containing streaming water. Pressure distributions were measured at 6 different submergence depths, 4 different speeds and 7 different angles of attack by 30 pressure taps arranged around the center of the hydrofoil span. These pressure distributions were integrated to obtain the lift and drag on the section.In §3, the effect of the submergence depth on the pressure distribution was examined and then discussed the flow characteristics from the standpoints of the gravity effect, inertia effect, boundary layer separation, and ventilation.In §4, two types of stall, ie laminar flow separation and turbulent flow separation were clarified from the standpoint of the resultant force at each submergence depth.In §5, the effect of the submergence depth on the lift and drag was examined and, in particular, the stall characteristics were fully discussed.In §6, the similar law was considered in detail for the shallowly submerged hydrofoil section characteristics and also the scale effect was examined.

The amount of information on the effect of accelerations on human beings is scanty and somewhat rudimentary with the single exception of observations made on aeroplanes. Aircraft in general have to be built to certain factors of safety so as to keep the total flying weight as small as possible, and for this reason accelerometers have been carried to measure the resultant forces experienced in flight. In this way a measure has been obtained of the forces likewise impressed on the human pilot directing the craft. The practice of flying has gradually developed by the careful training of the pilots so that undue stress is not placed on the aircraft structure and as a corollary this has been made possible by the pilot using his physical sensations to limit the violence of any aerobatic manœuvre. But the practice in this respect differs in various countries and so an attempt is here made to collate what information exists on the effect of accelerations on the human body and to consider whether the stresses experienced in flight can be increased with safety. It is, however, realised that the subject is a very open one and that the experimental data are very scanty.

Three subjects were exposed on a human centrifuge to a change in direction of resultant G relative to the body axis. Under the conditions of the experiment the illusion was created wherein a horizontal target line appeared to rotate through an angle corresponding to the change in direction of the resultant force. The subject's task was to keep the line horizontal at all times. Thus, if the line appeared to rotate clockwise, the subject actually rotated the line counterclockwise in order to maintain the line horizontal for himself. A marked discrepancy was noted between the time required to impress the physical force on the subject and the period during which he found it necessary to make adjustments in keeping the line horizontal. This discrepancy was regarded as a measure of the delay in the subject's visual reorientation to a change in direction of resultant G. It is thought that a possible cause of the delay may lie in the characteristic behavior of the otolith organ. This lag phenomenon is of importance to aviation inasmuch as the full disorientating effects of a change in direction of resultant G relative to the body axis will not become manifest if the exposure time is short. (Author)

1. The direction of wear encountered in soft p.t.f.e. sockets used in a now obsolete type of arthroplasty was measured in 37 patients. 2. The direction of wear in the majority of cases lay in a direction inclined 10° to 15° away from the vertical and towards the mid-line of the body. 3. It is presumed that this indicates the direction of the average resultant force. 4. A small but significant number of cases revealed wear in directions which deviated grossly from the average, both qualitatively and quantitatively. No explanation of the deviation could be found from the clinical study of these exceptions. 5. It has to be concluded that in designing an arthroplasty of the hip joint it would be prudent always to consider the resultant force on the hip joint as acting in a vertical direction and not to be over-optimistic in assuming a resultant force inclined in the strongly positive direction which is favourable to the mechanics of an arthroplasty.

SUMMARY Biomechanical analysis of the hand helps provide the basis for designing prosthetic replacements for finger joints. Analysis of the finger as a free body in equilibrium provides information for the forces and moments about each of the joints. The present data suggest that, for design purposes, the interphalangeal and metacarpophalangeal joints may be treated as monaxial joints, although the metacarpophalangeal joint has three degrees of constrained motion. Mathematical analysis of the tendon excursion and joint position relationships allows further understanding of the delicate finger motion. The resultant forces and moments at the joint may be estimated from simple free-body analysis. These resultant forces and moments may then be broken down to obtain the joint surface contact forces and the joint constraint forces by solving a set of simultaneous equations. The joint constraint forces usually consist of various components, depending on the anatomic structures of the joint. These analyses will help in the selection of proper materials for bearing pressures and will allow design of prosthetic constraints sufficient to resist the translatory and rotatory forces in the joint and to provide sufficient range of motion for the joint and tendons so that the normal motion of the finger can be restored. Application of the moment equations further suggests adjustment of the moment arms of various tendons with respect to the joint center and the alignment of the joint center of rotation for improving joint activities.

When a piston subject to an axial pressure drop has to be moved periodically along a bore sticking often occurs owing to hydraulic locking between the piston and the bore. The locking is caused by the hydrostatic pressures acting along the annulus between the two surfaces. The hydraulic instability may be reduced by using a piston tapered to give a converging film shape in the direction of flow, and this paper considers a large number of tapered configurations. The hydraulic pressures are calculated by a solution of Reynolds' two-dimensional equation using a digital computer, and the resultant force and its line of action are obtained. From these results empirical equations for the locking force and its line of action are derived which are valid for a wide range of conditions. The values predicted by the equations agree well with experimental and theoretical results given in the literature.

Infinite and semi-infinite isotropic elastic bodies in finite biaxial extension are in addition subjected to infinitesimal concentrated forces parallel and perpendicular to the extension plane respectively. In the semi-infinite case the forces are on the plane boundary. The problems are analogous to those for transversely isotropic bodies subjected to the infinitesimal concentrated forces only. Solutions to both categories of problems are given with the aid of potential functions. To facilitate the evaluation, expressions for the resultant force on a surface are given in terms of line integrals around the bounding curve. The solutions to the semi-infinite body problems are derived from those to the infinite body problems by adding appropriate potential functions so as to meet the boundary conditions on the plane surface. Computations for the semiinfinite cases of the superposition problems are given.

To determine the forces and moments on movable jet vanes immersed into the exhaust flame of a large solid rocket motor, and to determine the resultant forces and moments upon the motor-missile configuration, two multi-component internal strain-gage floating-frame balances were designed and integrated into the vane actuation systems. These balances provided an accurate, economical, trouble-free multi-component force measurement system which was readily integrated into an existing static motor firing program. The combined average error of the balance data is within ±5.5% for a 99.7% confidence interval. A 1401 computer program based upon equivalent in-place balance calibration results was prepared to reduce the static motor firing data parameters to engineering units. The design and calibration considerations for a specialized balance design and general design considerations for all multi-component force measurement systems are discussed in this paper.

SummaryA theoretical analysis is presented for a two-dimensional air strut with walls consisting of thin membranes which are joined by many inextensible strings. The strut is deflected through large angles so than an appreciable portion of each membrane is buckled and lies along the solid plates which form the ends of the strut. Numerical solutions are obtained for two cases and, in particular, the resultant force on each end plate is determined.

Expressions have been derived for an estimate of the average coefficient of lift, for the variation in bending moment or torque caused by wind forces and by inertia forces, and for the power output during hovering flight on one spot when the wings move according to a horizontal figure-of-eight. In both hummingbirds and Drosophila the flight is consistent with steady-state aerodynamics, the average lift coefficient being 1·8 in the hummingbird and o-8 in Drosophila. The aerodynamic or hydraulic efficiency is 0·5 in the hummingbird and 0·3 in Drosophila, and in both types the aerodynamic power output is 22–24 cal/g body weight/h. The total mechanical power output is 39 cal g−1 h−1 in the hummingbird because of the extra energy needed to accelerate the wing-mass. It is 24 cal g−1 h−1 in Drosophila in which the inertia term is negligible because the wing-stroke frequency is reduced to the lowest possible value for sustained flight. In both animals the mechanical efficiency of the flight muscles is 0·2. It is argued that the tilt of the stroke plane relative to the horizontal is an adaptation to the geometrically unfavourable induced wind and to the relatively large lift/drag ratio seen in many insects. The vertical movements at the extreme ends may serve to reduce the interaction between the shed ‘stopping’ vortex and the new bound vortex of opposite sense which has to be built up during the early part of the return stroke. Two additional non-steady flow situations may exist at either end of the stroke, delayed stall and delayed build-up of circulation (Wagner effect), but since they have opposite effects it is probable that the resultant force is of about the same magnitude as that estimated for a steady-state situation. Most insects have an effective elastic system to counteract the adverse effect of wing-inertia, but small fast-moving vertebrates have not. It is argued that the only material available for this purpose in this group is elastin and that it is unsuited at the rates of deformation required because recent measurements have shown that the damping is relatively high, probably due to molecular factors.

In order to investigate fundamental properties of turning motion of a ship, movements of an elliptic cylinder were dealt theoretically with, when the cylinder in advance was steered suddenly in the perfect fluid.The resultant force on the cylinder in the direction of its long axis is a resistance in a case of stern rudder, while in bow rudder it becomes a negative resistance. But they are small and neglegible.The resultant force on the cylinder in the direction of its short axis is smaller than the lift of the rudder due to steering and acts in the contrary direction. Then the cylinder is on the bodily movement in the direction of the lift of the rudder.The resultant moment due to fluid pressure on the surface of the cylinder is smaller than the turning moment of the rudder and has the contrary sense. Then the turning motion of the cylinder is delayed.These effects is varied in accordance with the shape of the ellipse. The narrow form is effective, that is, it has better directional stability than the broadish one.

A fluid flowing over a loose flat granular bed tends to move the grains forward, and the conditions under which movement begins depend, not only upon the speed, but also upon the nature of the motion in the stream itself: viscous steady motion, steady inviscid motion, and turbulent motion act somewhat differently, and the speed necessary to dislodge grains differs appreciably. Like any solid boundary, the loose granular bed exerts a drag upon the fluid, and the accompanying shear stress is transmitted from bed to fluid almost wholly by the more prominent grains in the uppermost layer. Each such grain transmits a small force, and the manner in which it does so, again depends upon the type of motion, though it is now the local motion which is concerned, rather than that of the main stream. Two extreme cases may be distinguished. At slow speeds and with small grains the pressure at the front of the grain does not appreciably exceed that at its rear, and the force applied is the resultant of viscous stresses acting tangentially as in figure 2. At high speeds and with large grains such tangential drag becomes relatively unimportant compared with the drag due to pressure differences: the pressure distribution is not symmetrical but is less over the downstream half of the grain, so that when integrated it gives rise to a resultant force or form drag whose component resists the motion. Both at low speeds and at high speeds, if the main stream be turbulent, the force applied to the grain fluctuates irregularly. In the low-speed case, if the main stream be steady, the force on the grain is also steady. In the highspeed case, whatever the state of the main stream, eddies are shed from the back of the grains, and grains farther downstream are at least subjected to the cumulative effect of the pulsations from upstream.

When a circular cylinder moves uniformly in an ideal fluid (i.e. frictionless and incompressible) at rest at infinity, the resultant force acting on it is zero, it no external forces act. This is however, only true when the motion is the usual potential motion. Supposing that in addition to the potential stream produced by the motion of the cylinder a circulation around it be considered, the velocity of the fluid is incresased on the one side, an decreased on the other, and this produces a force acting on the cylinder perpendicular to the direction of motion.

Photoelastic tests have been performed to investigate the effect of spin on the contact stresses between rolling bodies. All the tests employed equal spheres, resulting in nominally flat, circular contact areas. The shear-stress distributions on such contact areas have been experimentally determined by the ‘frozen stress’ technique. One set of tests examined the case where no resultant surface force was transmitted between the spheres while they were rolling with spin. Another set of tests allowed a resultant force perpendicular to the rolling direction to be transmitted. The test results are compared with several theories.

Tire shear force data for ten different types of passenger car tires tested on wet surfaces are studied to examine the influence of test surface, velocity, and load on the maximum lateral force, maximum braking force, maximum resultant force, and locked wheel braking force. Tire traction rankings based on these four measures are compared with each other and with rankings obtained from J-turn and diagonal braking tests on a vehicle equipped with the same types of tires using the rank difference correlation method. The findings show that rankings based on a small number of maximum lateral force tests correlate well with rankings based on J-turn tests.

The resultant force of electrostatic attraction between two concentric hemispherical electrodes can be determined rigorously, and it is a suitable arrangement for an absolute electrostatic voltmeter.The curved electrodes have great mechanical rigidity and constancy of form.Stability of balance between the electrostatic and mechanical forces, elimination of the error introduced by the width of separation between the moving electrode and the guard electrode, and other unexpected advantages were obtained by their use.

This paper is concerned with the analysis of stress intensity factors of a strip with a longitudinal crack subject to tension and bending along its edges, and the tension of rectangular plates with a central crack. For both problems three types of boundary conditions, that is, stress conditions, displacement conditions and their combinations are considered. Analysis is based on Laurent expansions of the complex potentials satisfying the stress free relations along the crack. The expansion coefficients are determined from boundary conditions along outer edges, by using a perturbation technique in the first problem and a boundary collocation procedure based on resultant forces and mean displacements in the second problem. Numerical calculations are performed for various plate configurations, and the results are summarized in forms ready for practical use. The accuracy of numerical results are also examined, and they are regarded as correct up to four figures.

A rigid body whose length (2l) is large compared with its breadth (represented by R0) is straight but is otherwise of arbitrary shape. It is immersed in fluid whose undisturbed velocity, at the position of the body and relative to it, may be either uniform, corresponding to translational motion of the body, parallel or perpendicular to the body length, or a linear function of distance along the body length, corresponding to an ambient pure straining motion or to rotational motion of the body. Inertia forces are negligible. It is possible to represent the body approximately by a distribution of Stokeslets over a line enclosed by the body; and then the resultant force required to sustain translational motion, the net stresslet strength in a straining motion, and the resultant couple required to sustain rotational motion, can all be calculated. In the first approximation the Stokeslet strength density F(x) is independent of the body shape and is of order μUε, where U is a measure of the undisturbed velocity and ε = (log 2l/R0)−1. In higher approximations, F(x) depends on both the body cross-section and the way in which it varies along the length. From an investigation of the ‘inner’ flow field near one section of the body, and the condition that it should join smoothly with the ‘outer’ flow which is determined by the body as a whole, it is found that a given shape and size of the local cross-section is equivalent, in all cases of longitudinal relative motion, to a circle of certain radius, and, in all cases of transverse relative motion, to an ellipse of certain dimensions and orientation. The equivalent circle and the equivalent ellipse may be found from certain boundary-value problems for the harmonic and biharmonic equations respectively. The perimeter usually provides a better measure of the magnitude of the effect of a non-circular shape of a cross-section than its area. Explicit expressions for the various integral force parameters correct to the order of ε2 are presented, together with iterative relations which allow their determination to the order of any power of ε. For a body which is ‘longitudinally elliptic’ and has uniform cross-sectional shape, the force parameters are given explicitly to the order of any power of ε, and, for a cylindrical body, to the order of ε3.

A technique has been developed which allows the assessment of the variation with time of the magnitude and direction of the resultant forces transmitted at joints in the human body during normal activity. Tests have been performed on joints in the lower limb and typical patterns of variation of force with time and leg position are shown for normal test subjects walking on level surfaces. The test procedure involves the measurement of external force actions transmitted to the leg and their correlation with photographic records. This information is processed to obtain the resultant force and moment actions at the joint, taking account of the effect of gravity and accelerations. The moment actions are transmitted by the development of tension in muscular or ligamentous connections crossing the joint and the corresponding reaction at the joint. Generally, the number of muscular or ligamentous connections exceeds the number of available equilibrium equations. A guide to the muscles which are acting at any instant is obtained by the myoelectric signals picked up by electrodes secured to the skin over the muscles. Even with this information, an explicit solution is generally not possible and the information is presented as curves of upper and lower limits of joint force corresponding to the use of muscles having the greatest or least moment arm.

To confirm the observations made with the previously described centrifuge-test method (Brandt & Fluur, 1966 b), the following modifications were introduced in these experiments. (1) Only the changes along the Y axis were registered. (2) The resultant force presented was permitted to increase and then decrease without interruption at the same slow rate. (3) The subjects (inexperienced) were seated in the erect position, facing centrifugally or centripetally, and the IR-filmed eye was fixed on the target throughout the trials. (4) The apparent position of the observed indicator was obtained without the interference of any active movement of the eye.

Applying a previously described centrifuge-test method, the changes of position in space along three axes of an observed target in an otherwise dark room were recorded. Ten subjects were positioned heading forwards (HF) with their left sides to the centre of the centrifuge. In order to separate directional and magnitudinal factors inherent in the produced force field, the procedure was repeated with the same subject in three positions of tilt in the frontal plane (erect = HF 0° tilt; tilted 50° inwards = HF 50° inw.; tilted 50° outwards = HF 50° outw.). Using an infrared (IR) technique, one eye was filmed, and its torsional position evaluated concurrently along the same three axes, simultaneously with the subjective data recorded. The increase in the angle formed between resultant force and physical vertical (angle Φ) generally produced an apparent clockwise rotation of the phenomenal horizontal in the two positions HF 50° inw. and HF 0° tilt, in a clear positive relation to the relative direction and als...

As a preliminary step in the study of a system consisting of a flying insect and the air surrounding it, a comparison is made between the system under natural conditions of free flight and under experimental conditions (when the insect is held stationary), in order to ascertain under what conditions conclusions reached with the insect held stationary would hold for free flight. To avoid the difficulty of making this comparison directly in respect of each of the many factors involved, the resultant force which, acting continuously on the body of the insect, would most nearly replace those cyclicly changing forces that normally maintain or modify the state of motion in flight, is taken as an index of what is occurring in the system. When the insect is held stationary in ‘still air’ it is found in most cases that this resultant, though of sufficient magnitude to support the insect in flight, does not act through the centre of gravity: the line of action of the resultant intersects the body axis at some point behind the centre of gravity. The position of this point depends on the amplitude of wing beat. W hen the insect is exposed in a wind tunnel to a stream of air of appropriate speed and direction, however, the resultant acts through the centre of gravity, as in free flight. The forward displacement of the point of intersection between the line of action of the resultant and the body axis, when the insect is exposed to a stream of air, is analysed further, and it is found: (1) that the effect of the stream of air on the body of the insect is negligible in this connexion as compared with the effect on the wings; (2) that changes in amplitude of wing beat do not account for the forward displacement of the resultant; and (3) that when the insect is exposed to a stream of air the path travelled by the wing tip on its downward beat is displaced forwards along the body axis in a direction which would tend to produce the observed displacement of the resultant force. This forward displacement of the path travelled by the wing on its downward beat converts the elliptical course, characteristic of wing movements when the insect is held stationary in ‘still air’, into the figure of ‘8’ course commonly associated with insect flight, and is dependent on the movement or position of the third antennal joint relative to the second, which in turn is determined by the action of the stream of air on the third joint with its arista. The characteristic attitude of the legs in flight, and the continued vibration of the wings when air is blown at the insect from in front also depend on the sensory inflow from the antennae. The maintenance of the figure of ‘8’ path involves the interaction of the sensory inflow both from the antennae and from the halteres.

A theoretical analysis of the buckling problems of heterogeneous aeolotropic cylindrical shells under combined axial, radial, and torsional loads is presented. Four boundary conditions at each end of the cylinder are satisfied for the case of both ends hinged or that of both ends clamped. Classical thin shell theory of small deflection is followed. Because only six elastic coefficients are required out of the usual 21 for a general aeolotropic body, it is possible to solve Flugge's differential equations of equilibrium by assuming suitable functions for the displacements of the middle surface. By the superposition of these solutions, a general solution that satisfies the boundary conditions can be reached. If the thin shell is laminated from layers of different materials, the resultant forces and moments of an element are integrated from layer to layer by considering that the six elastic coefficients are piecewise continuous. Orthotropic and isotropic materials are particular cases of this analysis.

1. The horizontal force on a circular cylinder immersed in a stream is familiar as an example of wave resistance. The following note supplies a similar calculation for the resultant vertical force. The problem was sug­gested in a consideration of the forces on a floating body in motion, the hori­zontal and vertical forces and the turning moment; but the case of a partially immersed body presents great difficulties. It seemed, however, of sufficient interest to compare the resultant horizontal and vertical forces for a simple case of complete immersion for which the calculations can be carried out. The horizontal force, or wave resistance, has usually been obtained indirectly from considerations of energy, but a different method is adopted here for both components of force and the turning moment. In a former paper the method of successive images was applied to the problem of the circular cylinder, taking images alternately in the surface of the cylinder and in the free surface of the stream. Using these results to the required stage of approximation, the com­plete force on the cylinder is now obtained as the resultant of forces between the sources and sinks within the cylinder and those external to it. The same method can be applied to any submerged body for which the image sytems are known, and the resultant force and couple calculated in the same manner. The proposition used in this method is that for a body in a fluid, the motion of which is due to given sources and sinks, the resultant force and couple on the body are the same as if the sources and their images attract in pairs accord­ing to a simple law of force, inverse distance for the two-dimensional case and inverse square of the distance for point sources. This fairly obvious proposition follows directly from a contour integration in the two-dimensional case; and, in view of the application, the extension is given in 2 when the flow is due to a distribution of doublets. In 3 the horizontal and vertical force on a circular cylinder are obtained by this method, the former agreeing with the usual expression for the wave resistance. The different variation of the two components with velocity is of interest, and the expressions are graphed on the same scale. The additional vertical force due to velocity changes direction at a certain speed, and is clearly associated more with the surface elevation immediately over the centre of the cylinder. In 4 reference is made to the couple on the cylinder. This should, of course, be zero for a complete solution; it is verified that the method used here gives zero moment up to the stage of approximation in terms of the ratio of the radius of the cylinder to the depth of its centre.

The purpose of this study has been to clarify the effects of centrifugation on postural equilibrium in relation to labyrinthine function. Twenty normal adults and 32 cases of various labyrinthine disorders were rotated eccentrically in the Still-Werner chair. The position of the unrestrained head relative to the resultant force was measured with an accelerometer attached to the forehead. In the initial stage of eccentric rotation, incomplete postural adaptation of the head was observed not only in cases with labyrinthine disorders but also in normal subjects. The incomplete adaptation was greater in the case of labyrinthine disorder when the hypo-or nonreactive ear was placed outward. During rotation at constant velocity, however, balance was recovered in almost all cases. The labyrinthine contribution for maintaining posture is considered to be most important only when the resultant force is changing direction.

There are two general methods of determining the forces acting on a cylinder due to the two-dimensional motion of a surrounding liquid. One is applicable to the case of a stationary cylinder in a stream, in the form X - Y = 1/2 p ∫( dw / dz ) 2 dz . (1.1) M = -1/2 pR ∫( dw / dz ) 2 z . dz (1.2) where X and Y are the components of the resultant force, parallel to the x and y axes, and M is its moment about tbs origin; p is the density of the fluid, and w is the velocity potential-stream-function for the fluid motion; z is as usual the complex variable x + y . The other is that obtained from the general theory of the "impulse. The first of these is unable to deal with a rotating cylinder, and the second is unable to include "circulation." In the course of an investigation of the effects of rotation upon the circulation round, and the forces acting upon, a Joukowski aerofoil, to which problem neither method applies, since the combined effect of rotation and circulation is needed, a quite general result was obtained, which it is thought worth while to publish separately.

The maximum forces that men and women were capable of applying to emergency exit release handles under various conditions were determined. Experiments were conducted on both port and starboard sides of a cabin mockup simulating the interior of the Convair 240. Approximately 339 determinations of the maximum force that 17 female subjects were capable of applying to emergency exit handles were obtained. This study was extended to include measurement of the resultant force and its direction with 112 tests conducted by eight female subjects, of which three participated in the above series. In addition 162 tests were conducted by nine male subjects, and a few tests on six children. The effects of handle configuration, location, position of the subject, and the duration of the muscular contraction are discussed.

The concept of ``force acting on a dislocation'' (or other imperfection) is intrinsically different from the concept of force as used in newtonian mechanics, and must be defined. A definition is given which preserves the basic property (1) that the direction of the resultant force gives the direction in which the imperfection will actually move if the atomic constraints do not prevent motion. For imperfections in an infinite crystal, and assuming linear elasticity, two further properties are established: (2) the parallelogram law of adding forces is valid, and (3) Newton's law of equal and opposite action and reaction is valid. A critical review of previous work relating to forces between crystal imperfections is given.

As conveying an image of the motion of a rigid body acted on by no forces, Pous7sot’s well-known method of representation, whether by a rolling ellipsoid or a shifting cone, labours under an obvious im perfection; the is not put in evidence by it. Thus when the ellipsoid, with which alone I intend here to deal, is employed, it is true th at the proportional value of the velocity of rotation about the instantaneous axis is geometrically measured by the radius vector drawn from the fixed point to the invariable tangent plane, and so by a process of summation the time of passing from one position to another may be considered as inferentially determ ined; but there is nothing to convey to the senses, or to the m ind’s eye, a notion of the effect of this summation, and thus the relation of the most im portant element— the time— to the position of a free revolving body remains unexpressed. I shall begin with showing how by a slight addition to Poinsot’s ideal kinematical apparatus this defect may be completely removed, and the time between successive positions conceived to register itself mechanically. As the property upon which this depends readily lends itself to a geometrical form of proof, I shall, in the first instance, follow that mode of investigation, as being the more germane to the m atter in hand, reserving to a later point in the memoir the analytical dem onstration; that is to say, assuming P oinsot’s ellipsoid, and the law which connects the velocity with the position of the body, I shall show how the time may be, as it were, mechanically extracted and summed.

A pressure-volume-temperature equation for mixtures of two or more gases has been developed using the “reference substance” technique of comparing the properties of one substance with those of a standard under the same conditions. The compressibility factor is a function of temperature and pressure, with the variation from one substance to another being determined by the forces of attraction and repulsion between molecules. Thus, if the Lennard-Jones 6-12 potential function is used to describe the molecular interaction, the change in the compressiblity function reflects the different force constants, which in turn are functions of the critical constants. A mixture of gases is assumed to have the same thermodynamic properties as some hypothetical or pseudo gas which would have the same force constants existing between each pair of molecules in the mixture. The force constants of the pseudo gas may be evaluated from pseudo critical constants, which may be evaluated from the critical constants of individual components of the mixture. With the resultant force constants, there can be calculated the ratio of the compressibility factors of the gas mixture to those of a pure gas, nitrogen, taken as a reference substance, all values taken at the same reduced temperature and pressure. The compressibility factor of the mixture may be calculated from this ratio and the compressibility factor of the reference substance; and the PVT relations are immediately determinable. A comprehensive survey of the literature for PVT data of gas mixtures was made. More than 1,000 experimental values of PVT data for thirty-four binary systems and four ternary systems have been studied. The proposed method showed an average deviation from experimental data, representing all published work, of 2.3%.

The method is based on the principle that a constrained structure can be considered to be a free body acted upon by multiple forces which include the forces of constraint. By measuring these forces and by exciting the structure so as to develop linearly independent sets of forces, one can compute the response of the free body to one force at a time. Techniques for producing these independent forces are discussed. Computer simulations of tests (including experimental error) are presented. The procedure appears to be a feasible approach to obtaining the in-flight characteristics of aerospace vehicles. Nomenclature / = applied force Tfc = complex force vector F = matrix of forces Fs = matrix of forces due to applied forces at the constraints \?SA = matrix of constraint forces due to excitation at other points M = number of points at which force is applied N = number of points at which responses are measured r,- = reaction force at constraint i yk = vector of measured responses y = matrix of responses Y = mobility matrix relating forces and responses co = frequency of applied sinusoidal forces [ ] = matrix { } = column vector

The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion.The present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach–Kirchhoff program.

This investigation is concerned with the diffusion of an axial load from a bar of arbitrary uniform cross-section that is immersed in, up to a finite depth, and bonded to a semi-infinite solid of distinct elastic properties. The bar is perpendicular to the plane boundary of the embedding medium. The determination of the desired resultant force in the submerged bar-segment is reduced to a Fredholm integral equation by means of an approximative scheme developed and tested earlier in connection with a more elementary three-dimensional load-transfer problem. Extensive numerical results illustrating the decay of the bar-force, appropriate to various choices of the governing geometric and material parameters, are presented for the particular case of a bar of circular cross-section.

Mindlin [1] has formulated a theory of two-dimensional elasticity with couple stresses and obtained invariant relations between stresses and displacements in complex variable form [2]. Here these expressions are extended to include the resultant force and moment around a contour. With these results, the first fundamental problem for a circular hole in an infinite plane has been solved when the radial couple stress on the boundary is zero. The theory has been applied to the problem of a concentrated force in the plane.

(1) It is not so long ago that it was generally believed that the "classical" hydrodynamics, as dealing with perfect fluids, was, by reason of the very limitations implied in the term "perfect," incapable of explaining many of the observed facts of fluid motion. The paradox of d'Alembert, that a solid moving through a liquid with constant velocity experienced no resultant force, was in direct contradiction with the observed facts, and, among other things, made the lift on an aeroplane wing as difficult to explain as the drag. The work of Lanchester and Prandtl, however, showed that lift could be explained if there was "circulation" round the aerofoil. Of course, in a truly perfect fluid, this circulation could not be produced—it does need viscosity to originate it—but once produced, the lift follows from the theory appropriate to perfect fluids. It has thus been found possible to explain and calculate lift by means of the classical theory, viscosity only playing a significant part in the close neighbourhood ("grenzchicht") of the solid. It is proposed to show, in the present paper, how the presence of vortices in the fluid may cause a force to act on the solid, with a component in the line of motion, and so, at least partially, explain drag. It has long been realised that a body moving through a fluid sets up a train of eddies. The formation of these needs a supply of energy, ultimately dissipated by viscosity, which qualitatively explains the resistance experienced by the solid. It will be shown that the effect of these eddies is not confined to the moment of their birth, but that, so long as they exist, the resultant of the pressure on the solid does not vanish. This idea is not absolutely new; it appears in a recent paper by W. Müller. Müller uses some results due to M. Lagally, who calculates the resultant force on an immersed solid for a general fluid motion. The result, as far as it concerns vortices, contains their velocities relative to the solid. Despite this, the term — ½ ρq 2 only was used in the pressure equation, although the other term, ρ ∂Φ / ∂t , must exist on account of the motion. (There is, by Lagally's formulæ, no force without relative motion.) The analysis in the present paper was undertaken partly to supply this omission and partly to check the result of some work upon two-dimensional potential problems in general that it is hoped to publish shortly.

Space and force diagrams are drawn pertaining to some simple two-dimensional, minimum weight frames for particular dispositions of load, which are analogous respectively to slip-line fields and their associated hodographs for certain metal working processes. Displacement diagrams for these frames are drawn, following the well-known method suggested by Williot. 1 It is assumed that the strain in each member of a frame is ± e . A one-to-one mapping between the nodal points of a frame and the corresponding displacement field is observed and certain relevant co-ordinates are given in tabular form. A precise analogy is also established between the displacements of a minimum weight frame and the resultant forces in the corresponding slip-line field. The aim of this paper is to emphasize that the analogy used to define the layout of certain minimum weight frames directly from slip-line fields is valid only for the loaded, i.e. deflected condition of the frame. It is pointed out that for certain classes of frame the unloaded, or constructed form of the frame must be considered.

INTRODUCTION THE general use of screen process printing in the formation of "Printed-and-Fired" or "Thick" films in microcircuitry is described as a new application of the old graphic arts method of printing. As such, this new application requires more understanding of the process. Discussion is limited to the area of off-contact printing of both resistive and pure glazes on ceramic substrates to form hybrid, resistor or resistor-capacitor networks and conductive paths. The assumption is stated that microcircuit applications differ from other forms of screen process printing mainly because resulting components or circuits are extremely sensitive to the thickness of the resultant printed film. Basic areas in process and materials used are pointed out as of primary importance in controlling the printed film thickness. Those areas highlighted in the printing process are (1) the squeegee, (2) the screen or mask and (3) the machine or equipment used. Areas added by the basic materials are (4) the ink or composition to be printed and (5) the substrate. I tem (6), post treatment, is considered the final area of major concern. These six general areas are broken down into forty-seven specific variables which might affect uniformity of results. Since the "squeegee" design and its controlled application can compensate for some of the other variables, this area is assumed of major importance. A theory is stated and discussed in detail as to why a squeegee causes printing to occur. This theory is that: "The resultant force from the speed of squeegee travel and pressure on the squeegee, combined and directed by the angle of attack on the squeegee blade, creates a hydraulic pressure in the composition being printed which causes openings in a screen mesh to be filled with composition under pressure, and as contact occurs, this fill is transferred to the substrate." I t is then concluded that any factor which would affect or vary the hydraulic pressure which causes printing must affect the deposited film thickness. Sketches of various basic designs of squeegees used in screen process printing are shown and discussed and then a new squeegee design is shown and arguments are made as to why it will have superior performance in laying down uniform films. The design basically is a broad 45 ° included angle blade formed by the edge of a ~ in. square cross-section, and mounted so as to hold it as rigid as possible during use.

When the strain-energy function for an elastic body is expressed as a function of the six components of strain, the solution of a given problem for different types of material may assume very different forms. In the present paper, by regarding the strain-energy function as a function of the parameters defining the deformation, results are obtained which are valid for a wide range of materials. The analysis for each problem is performed initially for bodies possessing a suitable type of curvilinear aeolotropy, and results are derived which are independent of symmetries in the elastic material. These results are therefore valid, not only for the general type of material initially considered, but also for isotropic bodies and for materials which are orthotropic or transversely isotropic with respect to the curvilinear co-ordinate system which defines the aeolotropy. Both compressible and incompressible bodies are considered. From this point of view, a general type of cylindrically symmetrical deformation is examined which includes as special cases the problem of flexure, the inflation, extension and torsion of a cylindrical tube, and the shear of a cylindrical annulus. Particular results for these special cases are considered separately, and for the flexure and torsion problems, expressions are found for the resultant forces and couples required to maintain the deformation. A brief analysis is also given for the corresponding types of deformation for a cuboid. In the final section of the paper, a generalized shear problem is considered in which, during deformation, each point of the elastic body moves parallel to a given axis through a distance which is a general function of position in a plane normal to that axis.

(1) An aircraft in steady, straight‐line motion can have no resultant force or couple acting upon it. This condition is never continuously maintained in flight, and the craft proceeds in a series of oscillations or wide, corrected curves. Continuous adjustment takes place in the direction of its flight through either an inherent stability or a judicious use of the controls by the pilot, but the motion may be regarded mostly without error as steady for purposes of design. Calculations carried out on the basis of steady equilibrium have for objects the determination of optimum lay‐out; the selection of most suitable component parts; the provision of adequate and easeful control; the specification of loading for strength design; and the prediction and testing of performance. In practice, such calculations go hand in hand with others concerned with statical and dynamical stability; with accel‐erated motions; with strength and weight; and with a host of purely practical considerations. Deductions drawn from the principles discussed in this Article may not be decisive in a given case till set in proper perspective. In this connection we note, without straying from our subject matter, that many secondary factors are here neglected, whose effect the engineer has, on occasion, to take carefully into account.