If A is the major axis of an ellipsoid and B and C are the other two axes, the radius of curvature in the ab plane at the end of the axis Af, and the difference in pressure along the A and B axes is Af.

If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O ' 1 there is a circular disk of confusion of radius O ' 1R, and in a parallel plane at O ' 2 another one of radius O ' 2R2 ; between these two is situated the disk of least confusion.

If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture — there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e. g. in photography.

If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.

If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.

If is an outward pointing in-plane normal, whereas is the unit vector perpendicular to the plane ( see caption at right ), then the orientation of C is chosen so that a tangent vector to C is positively oriented if and only if forms a positively oriented basis for R < sup > 3 </ sup > ( right-hand rule ).

If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).

If these three ligands and the metal ion are in one plane, the isomer is said to be meridional, or mer.

If the axes are named x, y, and z, then the x coordinate is the distance from the plane defined by the y and z axes.

If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.

Many results about plane figures are proved, e. g., If a triangle has two equal angles, then the sides subtended by the angles are equal.

If any part of the ball reaches any part of the imaginary vertical plane transected by this line while in-bounds and in possession of a player whose team is striving toward that end of the field, this is considered a touchdown and scores six points for the team whose player has advanced the ball to, or recovered the ball in, this position.

If friction arises from a weight being drawn up the inclined plane of successive asperities, why isn't it balanced then through descending the opposite slope?

# If two straight lines in a plane are crossed by another straight line ( called the transversal ), and the interior angles between the two lines and the transversal lying on one side of the transversal add up to less than two right angles, then on that side of the transversal, the two lines extended will intersect ( also called the parallel postulate ).

If the angle between the plane and the axis is less than the angle between the line on the cone and the axis, or if the plane is parallel to the axis, then the conic is a hyperbola.

If the Earth were perfectly spherical and homogeneous, then longitude at a point would just be the angle between a vertical north-south plane through that point and the plane of the Greenwich meridian.

If the pump beams E < sub > 1 </ sub > and E < sub > 2 </ sub > are plane ( counterpropagating ) waves, then:

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

If any part of either wrestler is in contact with the ropes or has otherwise broken the plane of ropes all grappling contact between the wrestlers must be broken within a five count or else the attacking wrestler may be subject to disqualification.

If a fault has lineations formed by movement on the plane, e. g. ; slickensides, this is recorded as a lineation, with a rake, and annotated as to the indication of throw on the fault.

If the tip is moved across the sample in the x-y plane, the changes in surface height and density of states cause changes in current.

If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results.

If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained.

If we take the simple valence bond structure and mix in all possible covalent and ionic structures arising from a particular set of atomic orbitals, we reach what is called the full configuration interaction wave function.

If a ray tracing is then made as if a light wave ( as understood in classical physics ) is wide enough to take both paths, then that ray tracing will accurately predict the appearance of maxima and minima on the detector screen when many particles pass through the apparatus and gradually " paint " the expected interference pattern.

If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the magnitude of the displacement is the sum of the individual magnitudes – this is constructive interference.

If a crest of one wave meets a trough of another wave then the magnitude of the displacements is equal to the difference in the individual magnitudes – this is known as destructive interference.

* If the molecule has some symmetry, the degenerate atomic orbitals ( with the same atomic energy ) are grouped in linear combinations ( called symmetry-adapted atomic orbitals ( SO )), which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations ( SALC ).

* If a storm or wave capsizes a small monohull, it may recover when the weight of the ballast in the keel rights the boat, if it does not broach and sink before it recovers.

If the pump waves and the signal wave are superimposed in a medium with a non-zero χ < sup >( 3 )</ sup >, this produces a nonlinear polarization field:

If two waves of the same wavelength and frequency are in phase, both the wave crests and wave troughs align.

If E < sub > i </ sub > is a sine wave, triangular wave, or wave of any other shape that is symmetrical around zero, the zero-crossing detector's output will be square.

If one knows the corresponding wave function at the instant before the measurement, one will be able to compute the probability of the wavefunction collapsing into each of the possible eigenstates.

If the wavelength is much shorter than the target's size, the wave will bounce off in a way similar to the way light is reflected by a mirror.

If an electron of energy E is incident upon an energy barrier of height U ( z ), the electron wave function is a traveling wave solution,

If the first part of a tsunami to reach land is a trough — called a drawback — rather than a wave crest, the water along the shoreline recedes dramatically, exposing normally submerged areas.

If a traveling wave has a fixed shape that repeats in space or in time, it is a periodic wave.

If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion.

If the impermeable area overlies the aquifer pressure could cause it to become a confined aquifer.

If the distinction between confined and unconfined is not clear geologically ( i. e., if it is not known if a clear confining layer exists, or if the geology is more complex, e. g., a fractured bedrock aquifer ), the value of storativity returned from an aquifer test can be used to determine it ( although aquifer tests in unconfined aquifers should be interpreted differently than confined ones ).

If the aquifer is confined by low-permeability layers, the reduced water pressure in the sand and gravel causes slow drainage of water from the adjoining confining layers.

If the flow of a fluid is confined by a surface, it is referred to as an internal flow.

If the material is a poor thermal conductor, the heat is confined to the surface of the material.

If a confined aquifer follows a downward grade from its recharge zone, groundwater can become pressurized as it flows.

If the wireline exits that confined area under pressure, the pressure will force the steel ball up towards the hole where the wireline had been.

If we imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone.

If the ship needed to sail before some of the passengers ’ indentures had been sold, an agent in the American port kept them confined until a buyer presented himself.

If a piece of paper can be easily ignited, it is probably not a true flameless lighter and certainly not safe in hazardous environments where smoking is confined to specific safe areas.

If the players do not know which one of them is which, then the mixed Nash is an evolutionarily stable strategy ( ESS ), as play is confined to the bottom left to top right diagonal line.

If p spatial dimensions satisfy the Neumann boundary condition, then the string endpoint is confined to move within a p-dimensional hyperplane.

If there is action, it is generally confined to isolated minigames.

If a threat arose, it could quickly wipe out their population because their breeding grounds are confined to a small island group.

If the oscillations are confined to a plane the radiation will be linearly polarized.

If the nonzebra parent was patterned ( such as a roan, Appaloosa, Pinto horse / paint, piebald, or skewbald ), this pattern might be passed down to the zebroid, in which case the stripes are usually confined to nonwhite areas.

If the players do not know which one of them is which, then the mixed Nash is an evolutionarily stable strategy ( ESS ), as play is confined to the bottom left to top right diagonal line.

If any cardinal elector is by reason of infirmity confined to his room, the Infirmarii go to their rooms with ballot papers and a box.

If we have an experience, we are confined not just in our communication of it, but also in our knowledge of it, by the words we possess.

If a steam explosion occurs in a confined tank of water due to rapid heating of the water, the pressure wave and rapidly expanding steam can cause severe water hammer.

In 1964 the UK Prime Minister, Sir Alec Douglas-Home, met with the American Attorney General, Robert Kennedy to explain why international intervention is required stating that " If they had not done so, there would probably have been a massacre of Turkish Cypriots " which were confined in enclaves totalling little more than 3 % of the island.

If the criteria are not met by the lesion during the initial examination by the kohen, the individual is confined in his home for seven days, pending a follow-up examination ( Leviticus 13: 4, 21, 26, 31 ) If the criteria for tzaraath are again not met and the lesion has not spread, there is a difference in protocol depending of the type of lesion.