Then the curvature form is the-valued 2-form on P defined by

Then the curvature form is defined by

Then the formulas for the signed curvature k ( t ), the normal unit vector N ( t ), the radius of curvature R ( t ), and the center Q ( t ) of the osculating cicle are

Then a final scholium points out how problems 6 and 7 apply to the horizontal and vertical components of the motion of projectiles in the atmosphere ( in this case neglecting earth curvature ).

Then our covariant differential constraint on shows how variations in the trace of the stress-energy tensor in our spacetime model can generate a nonzero trace-free Ricci tensor, and thus nonzero semi-traceless curvature, which can propagate into a vacuum region.

Then pour water or light oil from a graduated beaker into the chamber to fill the chamber to its gasket surface.

Then we imagine the rays are parallel ( and given by two angles ), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point.

Then it reacts with the surface or simply desorbs after enough energy and time.

Then, using his fingers, he takes some of the blessed oil floating on the surface of the baptismal water and anoints the catechumen on the forehead, breast, shoulders, ears, hands and feet.

If he occupies himself with dthikr, He ( God ) will unveil to the secrets of the vegetable world, then the secrets of the animal world, then the infusion of the world of life-force into lives, then the " surface sign " ( the light of the Divine Names, according to Abdul-Karim al-Jeeli, the book's translator ), then the degrees of speculative sciences, then the world of formation and adornment and beauty, then the degrees of the qutb ( the soul or pivot of the universe-see # 16 ) ( 59 ) Then he will be given the divine wisdom and the power of symbols and authority over the veil and the unveiling.

Then, a further specific antibody is applied over the surface so it can bind to the antigen.

Then Surveyor 1 fell freely to the surface from this height, and it landed on the lunar surface on June 2, 1966, on the Oceanus Procellarum.

Then we can apply Gauss – Bonnet to the surface T formed by the inside of that triangle and the piecewise boundary given by the triangle itself.

Then the Phong reflection model provides an equation for computing the illumination of each surface point:

Then during the direct illumination calculation, instead of sending out a ray from the surface to the light that tests collisions with objects, the photon map is queried for shadow photons.

By Pauli's exclusion principle, both the particles after scattering have to lie above the Fermi surface, with energies Now, suppose the initial electron has energy very close to the Fermi surface Then, we have that also have to be very close to the Fermi surface.

Then, a sudden collapse of the land surface can occur.

Then it is possible to associate this clue with surface observations and numerical models prediction to produce output such as the ones seen on television weather programs that divide radar echoes into rain, mixed and snow precipitations.

Then came a series of state-sponsored " systematic " renovations in the Konbaung period ( 1752 – 1885 ), which by and large were not true to the original designs — some finished with " a rude plastered surface, scratched without taste, art or result ".

Then the circuit board ignitor relay is energized which sends 120 volts to the hot surface ignitor and makes it glow bright and get extremely hot.

Then replace the ( r, φ ) plane with a surface dimpled in the w direction according to the equation ( Flamm's paraboloid )

Then, Rarey would gently but firmly cause the horse to lie down on a comfortable surface.

Then the surface of the columns was sculpted with scenes celebrating a ruler named 13 Rabbit, who probably had this structure built.

Then, either the surface or thin layer is exposed to the laser beam along a predetermined pattern to ablate desired portions.

Then, according to the motion equation of the contour, one can easily derive a similar flow for the implicit surface that when applied to the zero-level will reflect the propagation of the contour.

Then at last the darkness began to dissolve.

Then he was on his way at a gallop.

Then, helpfully, as she merely stared at him in weary silence, `` Maybe you could write it down for me, huh??

Then, on July 2, there occurred another incident which set tongues to wagging at a furious clip.

Then the boy straight-armed himself up, twisting at the last moment so he landed sitting.

`` Then I return to the United States for engagements at the Hollywood Bowl and in Philadelphia '', he added.

Then I spent the next two days at the baseball park and at Jack Doyle's pool parlors.

Then I spoke at the ninetieth birthday party of W. E. Burghardt Du Bois, who embarked on a fictional trilogy at eighty-nine and who, with The Crisis, had created a Negro intelligentsia that had never existed in America before him.

Then, all but blind, he said there was nothing in Back to Methuselah --, -- `` G.B.S. ought to have known that '', -- and `` I look at my bookshelves despairingly, knowing that I can have nothing more to do with them ''.

Then we have surviving at least one instance of a poem prepared for another, in Naturam non Pati Senium, and perhaps also the De Idea Platonica.

Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.

Then see what a boom in all trades, as well as slum clearance at no cost to taxpayers, will happen.

Then the audience saw a small, dim figure appear at the edge of the Presidential box.

Then she looked at the old woman again, her eyes calm.

Then, when he had it pointed down the hill, he stopped to gaze at her through the window.

Then he stood back to look at Mr. Jack, who was pulling on his pigskin gloves.

Then he looked at his finger, at the wrinkled, heavy knuckle and the thick nail he used like a knife to pry up, slit, and open.

Then you can do the finishing touches at your leisure.

Then, for the above parasites, feed continuously at these levels: Feeder cattle -- 2-5 grams of phenothiazine daily ; ;

Then, at last, his day would fall into an ordered pattern and he would be free to read, or garden or just wander through the woods in the late afternoon, accompanied by his dogs.

Then at least he would have a place to hang his tools and something to work on.

Then, my mother blushed at this small lie ; ;