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This paper extends the methodology presented in the companion paper to study the effects of non-structural components’ (NSCs) damping ratio and their location in the building on the pseudo-acceleration floor response spectra (PA-FRS) of reinforced concrete buildings, and propose equations to derive floor acceleration design spectra (FDS) directly from the uniform hazard design spectra (UHS) for Montréal, Canada. The buildings used in the study are 27 existing reinforced concrete structures with braced frames and shear walls as their lateral load resisting systems: 12 are low-rise (up to 3 stories above ground), 10 are medium-rise (4 to 7 stories), and 5 are high-rise (10 to 18 stories). Based on statistical and regression analysis of floor acceleration spectra generated from linear dynamic analysis of coupled building–NSC systems, two sets of modification factors are proposed to account for floor elevation and NSC damping, applicable to the experimentally-derived FDS for roof level and 5% NSC damping. Modification factor equations could be derived only for the low-rise and medium-rise building categories, as insufficient correlation in trends could be obtained for high-rises given their low number. The approach is illustrated in detail for two typical buildings of the database, one low-rise (Building #4) and one medium-rise (Building #18), where the proposed FDS/UHS results show agreement with those obtained from detailed dynamic analysis. The work is presented in the context of a more general methodology to show its potential general applicability to other building types and locations.

This paper describes the seismic (shake table) tests conducted on bookcase – partition wall systems. These nonstructural building components can be considered acceleration sensitive (or motion sensitive) rather than drift sensitive. The shake table floor motions used for the seismic testing are described in a companion paper. One bookcase fully loaded with books and two different cantilevered partition wall systems were considered in the shake table tests. Nine different configurations of these free-standing nonstructural building components were tested. For each configuration, three different seismic hazard levels were considered for the motions at the second floor level of a six-storey building designed for two different densely populated Canadian cities (Montréal and Vancouver). A total of 485 shake table tests were conducted in this experimental investigation. The experimental results indicated that pounding between unanchored bookcases and partition walls is very beneficial to the dynamic response of the bookcases, as it prevents resonance from occurring. Also, the seismic performance of bookcases improved dramatically by the proper installation of seismic restraint systems. Experimental fragility curves for overturning of tall bookcases are presented.Key words: bookcases, earthquakes, fragility, interior partition walls, nonstructural, operational and functional components, pounding, seismic restraints, shake table.

Freeway merge maneuvers are complex and may involve a lane change, continuous acceleration, possible deceleration, and finally a gap acceptance. This paper presents a methodology to model ramp vehicle acceleration-deceleration behavior at freeway entrance ramps. Primary data capturing a wide range of information were collected using video tape methods and manually reduced through image processing techniques. Ramp vehicle merging position in conjunction with freeway and ramp flow levels was analyzed for both parallel and taper type entrance ramps. Where vehicle trajectory data were available, merging positions with respect to ramp vehicle speed as well as relative speed and time gap between a ramp vehicle and freeway vehicles were examined. Results show that the merge position has a statistically insignificant effect upon individual traffic parameters. Methodology presented in this paper used the stimulus-response equation as a fundamental rule to model ramp vehicle acceleration=deceleration behavior. The timebase car-following model was modified to a nonlinear distance-base stimulus-response equation to capture the characteristics of the collected traffic data. Calibration of the proposed nonlinear model from a pilot study demonstrated satisfactory results and indicated that a time lag before ramp drivers respond to stimuli does exist. Effects of surrounding freeway vehicles on ramp vehicle acceleration-deceleration behavior were found to be significant. (A)

This paper presents an overview of strong motion records obtained from instrumented structures during the 1994 Northridge earthquake. It describes the behaviour of buildings, bridges, and dams that have been instrumented by the major strong motion instrumentation networks operating in California and highlights important features of the most significant structural motions recorded during the earthquake. The structural damage observed during a reconnaissance visit to the affected areas by the earthquake is correlated with preliminary analyses of the recorded motions. Detailed discussions of the dynamic behaviour of two instrumented reinforced concrete buildings that suffered damage during the earthquake are presented. The behaviour of these buildings during previous earthquakes is also examined. This paper and the companion paper on ground motions provide comprehensive information about instrumental records obtained in the region affected by the earthquake. Key words: earthquake engineering, structural response, strong motion instrumentation, damage evaluation, buildings, bridges, dams, structural dynamics, acceleration, amplification.

Recent studies show that rotational components of earthquakes can amplify the floor acceleration in a base-isolated structure. As a result, the seismic force of nonstructural components could be significantly increased. In this paper, a simple rectangular deck with various geometrical properties mounted on triple concave friction pendulum (TCFP) bearings is examined. At first a set of three translational components from 25 near-fault ground motion records are considered. Then, three rotational components, i.e., torsional and two rocking motions are computed for each earthquake. The results of nonlinear dynamic analysis in a rectangular structure with an aspect ratio in plan equal to 3, demonstrate that the acceleration approximately intensifies 3.4 times in presence of all six ground motion components compared to three translational ones. Finally, a new formula is proposed to determine the maximum acceleration of base-isolated structure without performing the dynamic analysis due to rotational components of ground motions.

The fuzzy weighted input estimation (FWIE) is proposed in this paper to solve the problem of noise disturbance and combined with the three-dimensional motion equation of target trajectory to construct the tracking rule of fire control system. FWIE can estimate effectively the input data of maneuvering target acceleration to obtain the precise target state and solve the problems from the traditional Kalman filter which cannot compute the precise estimation of target state because of the input information in the system. Simulation results show that FWIE can estimate the change of target state rapidly and precisely compared with the extended Kalman filter and the proposed tracking rule can improve the fire control system to figure out the target intercepting points with shorter miss distance.

The load-carrying capacity of manipulators is often considered to be the same throughout their workspace. However, the actual capacity of manipulators largely depends on their posture, their velocity, their acceleration and the limits of their actuators. In this paper, a method is proposed to increase the payload capacity of manipulators through trajectory optimisation. This optimisation is performed on a task basis and therefore, the load-carrying capacity varies from task to task. An extensive analysis of the method is conducted based on its application on a planar RR serial two degree-of-freedom manipulator. This analysis evaluates the ability of the method to find feasible trajectories and compares the results with those obtained using Bang-bang type methods. It is shown that, although the trajectories produced by the proposed method are not time optimal, the method is much more versatile and much simpler to implement than its Bang-bang counterparts.

A dynamically embedded plate anchor (DEPLA) is a rocket-shaped anchor that comprises a removable central shaft and a set of four flukes. The DEPLA penetrates to a target depth in the seabed by the kinetic energy obtained through free-fall in water. After embedment the central shaft is retrieved leaving the anchor flukes vertically embedded in the seabed. The flukes constitute the load-bearing element as a plate anchor. This paper focuses on the dynamic installation of the DEPLA. Net resistance and velocity profiles are derived from acceleration data measured by an inertial measurement unit during DEPLA field tests, which are compared with corresponding theoretical profiles based on strain rate–enhanced shear resistance and fluid mechanics drag resistance. Comparison of the measured net resistance force profiles with the model predictions shows fair agreement at 1:12 scale and good agreement at 1:7.2 and 1:4.5 scales. For all scales the embedment model predicts the final anchor embedment depth to a high degree of accuracy.

This paper presents a kinematic study of a mechanism incorporating a Geneva wheel and a gear train to achieve intermittent motion. The goal of this mechanism is to eliminate the acceleration jump at the beginning and end of the Geneva wheel motion. An epitrochoidal path replaces the circular path for the driving pin in a classical Geneva wheel drive. The epitrochoidal path is generated using a gear train and results in zero velocity, acceleration, and jerk at the beginning and end of the Geneva wheel motion. Presented is a comparison of the position, velocity, acceleration, and jerk between the classical Geneva wheel mechanism and the proposed mechanism. Subsequently, the motion of the Geneva wheel is modified by introducing a non-circular gear pair to adjust the timing of the epitrochoidal path. The motion of the non-circular gear pair is determined by reducing the extreme jerk of the Geneva wheel.

The geomechanical modelling of failure and post-failure stages of rainfall-induced shallow landslides represents a fundamental issue to the proper assessment of failure conditions and recognizes the potential for long travel distances of the failed soil masses. Considering that these phenomena are among the most catastrophic natural hazards, as a contribution to the topic this paper discusses the potential of a hydromechanical coupled finite element model (FEM) to analyze the post-failure stage using an advanced constitutive model. In particular, simple undrained triaxial tests and experimental evidence of centrifuge tests are reproduced first, for both loose and dense soils. Then, two slope scale benchmarks are analyzed in the cases of vertical downward or horizontal water seepage and for both loose and dense soils. Compared with results obtained through standard limit equilibrium analyses, the coupled FEM provides a new comprehensive framework for failure and post-failure scenarios that includes a significant reduction of mean effective stresses, also in the case of a loose soil slope subjected to vertical downward water seepage. The obtained results are particularly encouraging because they outline the possibility to analyse both the failure and post-failure stages in a unique framework. Moreover, the numerical analyses indicate that the post-failure mechanisms are intimately tied to specific predisposing factors and boundary conditions, rather than to a single mechanical or state parameter of soil, such as, for instance, the soil relative density.

This paper presents a novel optimized smooth obstacle avoidance algorithm for robotic manipulators. First, a 3-4-5 interpolating polynomial is used to plan a smooth trajectory between initial and final positions in the joint space without considering any obstacles. Then, a simple harmonic function, which is smooth and continuous in displacement, velocity and acceleration, is applied to generate a new smooth path avoiding collisions between the robot links and an obstacle. The obstacle avoidance portions on the path are optimized such that the length of the path traversed by the end-effector is minimized. Simulation results for a 6 DOF serial manipulator demonstrate the efficiency of the proposed method.

In this paper we study the dynamics of a 5D bulk space-time with our universe as a "test 3-brane" located in the bulk, an idealized model of a topological object whose physical properties is negligible in comparison with that of the bulk. Our universe experiences acceleration and its equation of state parameter crosses the phantom divide line due to the geometry of the bulk space-time., 11 pages, 12 figures; will be published in Can. J. Phys

Earthquake accelerations can cause many problems in sloping ground. One such problem is that accelerations are greatly amplified at the crest of slopes. This topographic amplification can lead to acceleration gradients along the ground surface, which could create tensile forces in long surface structures that extend between areas of different amplifications. This paper uses centrifuge modelling to demonstrate and quantify this as a problem for a particular slope configuration. A special brittle structure has been constructed to undergo damage in the presence of large differential accelerations. The structure is seen to connect the crest to the level ground behind the crest during an earthquake, reducing the amplitude of the crest motion at the expense of structural tension. Topographic amplification is shown to be a clear function of frequency, and is especially serious for loading frequencies above the natural frequency of the soil layer.

Critical static bridge loading scenarios are often expressed in terms of the number of vehicles that are present on the bridge at the time of occurrence of maximum lifetime load effect. For example, 1-truck, 2-truck, 3-truck or 4-truck events usually govern the critical static loading cases in short and medium span bridges. However, the dynamic increment of load effect associated with these maximum static events may be assessed inaccurately if it is calculated in isolation of the rest of the traffic flow. In other words, a heavy vehicle preceding a critical loading case causes the bridge initial conditions of displacement and acceleration to be non zero when the critical combination of traffic arrives on the bridge. Failure to consider these pre-existing vibrations will result in inaccurate estimation of dynamic amplification. This paper explores these dynamic effects and, using statistical analyses outlines the relative importance of pre-existing vibrations in the assessment of total traffic load effects. Irish Research Council for Science, Engineering and Technology Other funder IRCSET The European 6th Framework Project ARCHES (Assessment and Rehabilitation of Central European Highway Structures) ti, ke - AS 04/11/2010

The soil specimen in a centrifuge model is subject to spatial variability depending on the method of sample preparation and the stress field induced by the centrifugal acceleration, even though it is intended to be uniformly prepared. In contrast to extensive measurements for studying the variability of in situ soil properties, soil variability in centrifuge models, especially that which is based on data at very close sampling distances, is less understood. In this paper, the variability of soil density in two centrifuge models is presented. Random field theory is adopted to characterize the spatial soil variability in the two centrifuge models. The importance of taking spatial variability parameters as a model similarity requirement in centrifuge model design is illustrated and discussed. It is demonstrated that, although centrifuge models of different sizes can be designed to simulate the same prototype, the prototypes these models actually represent are not identical in terms of soil spatial variability. To achieve similarity in spatial variability between a centrifuge model and its prototype, one may need to control either the point coefficient of variation or the scale of fluctuation of the model soil so that the coefficients of variation of the spatially averaged soil property in the model and the prototype are the same.

The roller drive is an epicyclic gearing that consists of both the planet gear and the annular sun gear with rollers as its teeth. The roller drive thus has the advantages of easy manufacturing and low cost, and also has attractive attributes including high speed reduction ratio, compact size, and light weight as an epicyclic gearing. In this paper, a mathematical modeling for the kinematic analysis based on the vector loop approach is developed. The position, velocity, and acceleration analyses for the roller drive are performed. Furthermore, an experimental test verifying the analysis results is achieved. The analysis results show that only a single pair of teeth is meshed during gearing. It also shows that the values of gear ratio are inherently fluctuated corresponding with the number of ring gear rollers. This undesirable fluctuation can be minimized if the selected values of the design parameters satisfy a specific four-linkage constraint.

The main objective of this paper is to establish floor accelerations to be used for shake table testing of operational and functional components that are sensitive mainly to horizontal accelerations. For this purpose, two different ensembles of floor accelerations were generated from nonlinear time–history dynamic analyses of three- and six-storey building models incorporating ductile reinforced concrete cantilevered walls. The first ensemble was generated based on synthetic ground motions representative of the intraplate regions of eastern Canada, and the second ensemble was generated from synthetic ground motions representative of the crustal and subcrustal earthquakes of western Canada. The ground motions were selected based on the deaggregations of the seismic hazard for each region in terms of most likely magnitude – epicentral distance scenarios. The building models were designed in accordance with the current seismic provisions of the National Building Code of Canada applicable for each region. Application of the resulting floor accelerations in shake table testing of free-standing bookcases and interior partition walls is reported in a companion paper.Key words: floor accelerations, ground motions, nonlinear dynamic analyses, nonstructural, operational and functional components.

The paper compares the MOBILE5a, MOBILE6, Virginia Tech microscopic energy and emission model (VT-Micro), and comprehensive modal emissions model (CMEM) models for estimating hot-stabilized, light-duty vehicle emissions. Specifically, Oak Ridge National Laboratory (ORNL) and Environmental Protection Agency (EPA) laboratory fuel consumption and emission databases are used for model comparisons. The comparisons demonstrate that CMEM exhibits some abnormal behaviors when compared with the ORNL data, EPA data, and the VT-Micro model estimates. Specifically, carbon monoxide (CO) emissions exhibit abrupt changes at low speeds and high acceleration levels and constant emissions at negative acceleration levels. Furthermore, oxides of nitrogen (NOx) emissions exhibit abrupt drops at high engine loads. In addition, the study demonstrates that MOBILE5a emission estimates compare poorly with EPA field data, while MOBILE6 model estimates show consistency with EPA field data and VT-Micro model estimates over various driving cycles. The VT-Micro model appears to be accurate in estimating hot-stabilized, light-duty, normal vehicle tailpipe emissions. Specifically, the emission estimates of the VT-Micro and MOBILE6 models are consistent in trends with laboratory measurements. Furthermore, the VT-Micro and MOBILE6 models accurately capture emission increases for aggressive acceleration drive cycles in comparison with other drive cycles.Key words: transportation energy, transportation environmental impacts, VT-Micro Model, CMEM, MOBILE5, MOBILE6, fuel consumption models, emission models.

This paper describes a convenient simulation model, based on the compound binomial-gamma distribution, to assist the planning and design of groundfish trawl surveys. The analysis uses swept-area density measurements from stratified tows to give a simple nonparametric biomass estimate. A parametric simulation model requires only three input parameters for each stratum, which can be estimated initially from past surveys or commercial fishery data. Analytical results provide intuitive algorithms for estimating variances, investigating tow allocation strategies, and exploring potential survey results. Simulations make it possible to compare the estimated biomass with its true value and to assess coverage properties of confidence intervals obtained from bootstraps. Bias correction and acceleration both improve the results, but small samples taken from populations with highly variable densities tend to produce underestimates of available biomass. The simulation framework allows easy adaptation to address broader issues, such as the design of a multispecies survey.

The planning of foundations for equipment that is sensitive to vibrations requires a thorough dynamic investigation of the proposed location of the foundation with regard to the effect of already existing or additional vibration sources. This paper discusses the analyses performed for a number of foundations supporting vibration-sensitive equipment that has been subjected to ground-transmitted excitations. These analyses considered the dynamic response of the foundations resulting from the normal operation of the supported equipment or the ground-transmitted excitations. In one case, the foundation of the Canadian Light Source, a third generation synchrotron that will be capable of generating electromagnetic radiation used in the study of the atomic and subatomic structure of materials, is examined. Another case involves the vibration analysis of a magnetic resonance imaging unit affected by traffic excitation. In the third case, a power plant facility that is subjected to blast-induced vibration from an adjacent quarry is investigated. The last case involves the response analysis of a compressor foundation affected by the ground-transmitted vibration from another compressor situated on a different foundation within the same facility. To assess the level of seismic excitation at the site due to traffic on an adjacent roadway in the first two cases and to blasting activity in the third case, extensive "green field" ground vibration-monitoring programs were carried out. The ground accelerations due to traffic and blasting were measured and recorded for three directions simultaneously: a vertical and two orthogonal horizontal directions. The measurements with the most intense ground accelerations taken at the ground surface in the location of the future equipment foundation were selected as the final design acceleration time-history. A Fourier analysis approach was used to predict the response of the foundation to the ground-induced vibrations in the first three cases, and a frequency domain analysis was used in the last case.Key words: machine foundations, vibration, blasting, kinematic, soil-structure interaction.

In this paper we introduce the kinematic analysts of two circular-arc cams with profile design and experimental validation. In particular, an algorithm is proposed in terms of geometrical parameters and the cam profile, mainly for design purposes. Numerical examples are reported to prove the soundness of the proposed algorithm. Displacement, velocity and acceleration diagrams are obtained for the synthesized cam profile by means of equivalent slider-crank mechanisms, in order to derive a simple procedure for testing cam profiles with a low-cost test-bed. An experimental test-bed has been set up at the Laboratory of Robotics and Mechatronics in Cassino in order to validate the kinematic characteristics of the two circular-arc profiles so that the experimental results can be used also to test the profile quality.

The Statnamic (STN) load test is characterized by a relatively long duration and low pile velocity and acceleration compared with the dynamic load test. The estimation of the static capacity of piles and their static performance characteristics from dynamic loading tests usually requires a signal matching process. In this process, the soil parameters are varied until an acceptable match between the computed and measured responses is achieved. The soil properties obtained are then used to characterize the static behaviour of the pile. In this paper, an approach is presented to analyze the response of flexible and rigid piles during the STN load test. In this approach, a one-dimensional model is used to represent the pile-soil system accounting for nonlinear soil behaviour, slippage at the pile-soil interface, and energy dissipation through wave propagation and different types of damping. The postpeak resistance of certain types of soils is also considered in the analysis. An automatic matching technique (AMT) was developed to facilitate the signal matching process for the analysis of pile response during the STN load test. The proposed AMT has several advantages, including reducing the bias in the results due to the initial selection of the soil parameters; increasing the accuracy and reliability of computed pile capacity; and reducing computational time, thus allowing for the analysis of the test results in the field. It is then possible to compute the pile capacity and make a timely decision on its suitability. The proposed approach was used to analyze the results of six STN load tests, and the comparison between the measured and computed results was good.Key words: piles, Statnamic, pile load test, signal matching, transient load, capacity.

In this paper, a general and efficient procedure for the dynamic analysis of road bridges is presented, that takes into account bridge-vehicle interaction and the road profile in a realistic way. With this approach, the bridge structure can be modeled with a tridimensional finite element method using shell and beam elements. The vehicle model is represented using a discrete method based on Lagrange equations. This method uses the modal superposition technique for the bridge components, with a correction for the displacement based on the method of modal acceleration. The Newmark- beta method is used to solve the movement equations of each bridge and vehicles system and the solution is obtained through an iterative process of the interactive forces between the bridge and the vehicles. A simple academic example is presented to show the validity of the proposed algorithm.Key words: shell, dynamics, finite elements, interaction, bridge, roughness, vehicle.[Journal translation]

This paper proposes general expressions describing the instanteous kinematics of spatial cam mechanisms, such as transformation matrices, relative velocity matrices, and relative acceleration matri...

The seismic loading provisions included in the 1985 edition of the National Building Code of Canada simulate the dynamic response of structures using a seismic response factor, which has three branches depending upon the relationship between the velocity-related seismic zone Zv and the acceleration-related zone Za. This paper utilizes three ensembles of actual seismic strong motion records to evaluate the seismic response factor; each ensemble has acceleration/velocity ratios corresponding to one of the three branches of the seismic response factor. These strong motion time histories are used as input to relatively simple elastic models of frame and wall structures in order to obtain dynamic seismic response factors. The comparison of these dynamic factors with those specified in the NBCC 1985 indicates that the code factors are generally quite satisfactory, with the exception of the case of frame structures with low fundamental periods located such that Za is two zones higher than Zv. The paper reference...

The paper presents a microcomputer program designed for the evaluation of wind-induced forces, displacements, and accelerations of rectangular buildings in accordance with the stipulations and the methodology of the National Building Code of Canada. Meteorological data for Canadian cities have been included in a database file, so it is sufficient to provide information about the geometric, dynamic, and exposure characteristics of the building along with the name of the city of its location for a complete analysis by using either the detailed procedure or both the simple and detailed procedures. The program has been used in a parametric study to provide data of maximum displacements and accelerations of buildings. These data have been organized in charts useful to the professional engineer for preliminary design purposes. Key words: acceleration, building, code, design, displacement, pressure, wind, vibration.

Summary We have been using the Jerie Analogue computer for the horizontal adjustment of blocks of sections for cadastral purposes. The operations were speeded up by using an electronic computer for all computations associated with the Jerie Analogue giving satisfactory results. The section block adjustment was adopted for future projects and it was decided that a numerical solution would be the best approach to use. The following are some of the characteristics that are most important for numerical adjustments: — it must of course give satisfactory results — it must be economical: this should include computer hours and man hours both for development and for normal production — it should have the minimum possible restrictions concerning the geometry of the sections and the positions of the ground control points and tie points — it should require tittle data handling; this is to prevent blunders and reduce the number of man-hours — it should be integrated with existing production schemes. The paper gives the formulation and shows how it is implemented in a working computer programme. We were more concerned with the organization than with the solution itself. An iterative solution was chosen because it permits us to solve more equations without using demping procedures, thus giving us more freedom. The solution used has a very interesting behaviour. The system does not converge asymptotically but oscillates about the path of convergence. The oscillations decay as the iterations proceed. During these oscillations it is not possible to compute and apply acceleration factors. After some experimenting it was found that these oscillations could be damped externally by applying “undercorrections” during the initial steps of the solution. Once the oscillations are damped out it is possible to compute the acceleration factor. During one adjustment the system was iterated 600 times. Even with this large number of iterations the solution costs only $ 120. including man-hours. We are therefore satisfied with the programme as it stands. It seems worthwhile to pursue the study of the system as it might have some use where other methods fail; more work is necessary to determine the “dynamic” properties of the system. At the present time it is relatively easy to accelerate the convergence by a factor of 3 with the use of damping factors and accelerators. The results of our tests will soon be published in full.

Michelson (1973) has suggested modifications to the classical equilibrium tide theory, and his paper has received an enthusiastic review (Anon. 1974). I feel, however, that it is his modifications that are in error rather than the original equilibrium theory. Michelson claims that proponents of the classical theory, 'Newton, Bernoulli, Laplace, Darwin, Bassett, and Lamb, among others,' do not properly treat the rotation of the earth and the acceleration of its centre. In fact, the classical development of the equilibrium tide theory correctly allows for acceleration of the earth's centre by requiring it to be exactly that acceleration demanded by the gravitational attraction of sun and moon acting at the centre of the earth. Since the coordinate system being employed is fixed in the rigid body of the earth, this acceleration of the centre must enter the equation of motion as a component of the acceleration of the coordinate system. Thus far there seems to be no difference of opinion between Michelson and the earlier workers. The difference arises in consideration of the acceleration component due to the rotation of the coordinate system, that is, the rotation of the rigid body of the earth about its axis. The term expressing this component of acceleration does not commonly appear explicitly in the equilibrium theory because it is simply the centripetal acceleration term usually incorporated as part of the earth's 'gravity.' This development is fairly accurately described by Michelson in his Case I, but it does not require the earth's motion to be irrotational as he implies. In his Case 11, Michelson derives an expression that would be appropriate for an earth on which tidal friction had constrained the rotation to one revolution per lunar month about an axis normal to the lunar orbit; however, until such a condition is achieved this seems to have little pertinence to the real situation. In his Case 111, Michelson attempts to derive the acceleration terms appropriate to the orbiting and rotating coordinate system fixed to the rigid body of the earth. He does this by a rather indirect route which should, however, arrive at the same result as the classical equilibrium theory. That it does not is due to an error in the tortuous path of logic. This error seems to enter when Michelson considers rotation of the earth about an instantaneous axis of rotation displaced from but parallel to the polar axis. He states that "acceleration of any point of the Earth is then directed toward the new displaced axis" (p. 1756) and seems to overlook the fact that the instantaneous axis of rotation has an acceleration which must be considered. Correction for this error will bring Michelson's equation [lo] and what follows into agreement with the classical theory. I fear, however, that Michelson's readers may have been made unduly mistrustful of tidal predictions as a result of the article. It needs to be emphasized that the equilibrium tide theory is used primarily to describe the character of the tide-raising forces, particularly their frequencies and relative magnitudes. Predictions are made by harmonically analysing actual records of water level at the frequencies prescribed by the theory and by projecting the contributions of these harmonic constituents into the future. It is well realized that such a theory as the equilibrium theory that denies the presence of continental barriers, irregular bottom topography, and friction, and that neglects the response times of the system cannot be expected to predict to any accuracy the actual heights or times of local tides. Tidal predictions based on harmonic analysis at the frequencies indicated by the equilibrium tide theory, however, have been eminently successful.