* If the metric space X is compact and an open cover of X is given, then there exists a number such that every subset of X of diameter < δ is contained in some member of the cover.

If we think of the atoms as impenetrable steel discs and the impinging particle as a bullet of negligible diameter, this ratio is the probability that the bullet will strike a steel disc, i. e., that the atomic projectile will be stopped by the foil.

If a second hanging tom is used, it is 10 " diameter and 8 " deep for fusion, or 13 " diameter and one inch deeper than the 12 " diameter tom otherwise, or very occasionally a 14 " diameter hanging tom is added to the 12 ", both being 8 " deep.

If we draw an ellipse twice as long as it is wide, and draw the circle centered at the ellipse's center with diameter equal to the ellipse's longer axis, then on any line parallel to the shorter axis the length within the circle is twice the length within the ellipse.

If Rømer had known the diameter of the Earth's orbit, he would have calculated a speed of 227, 000, 000 m / s.

If you are a " perfectionist ", multiply the bore diameter by 0. 82 and subtract this value from the tube length.

If ( D ) is the wheel diameter, the torque on the runner is: T = F ( D / 2 ) = ρQD ( V < sub > i </ sub > − u ).

If viewed from a distance of 1 astronomical unit, it would span an angular diameter of 35 ° and shine at magnitude − 38.

If a modern ' flügelhorn ' bell has a flare similar to the one shown on the larger saxhorn pictured here, then it may indeed be a soprano saxhorn, but if the conical bell is nearly the diameter of the bell rim until just before a small final flare, then it is a true flügelhorn.

If the beam has been collimated using a lens or other focusing element, the divergence expected can be calculated from two parameters: the diameter,, of the narrowest point on the beam before the lens, and the focal length of the lens,.

If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the " string " is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid ( i. e. twice the diameter of the generating circle ), the bob of the pendulum also traces a cycloid path.

It occurs because of inter-molecular attractive forces between the liquid and solid surrounding surfaces ; If the diameter of the tube is sufficiently small, then the combination of surface tension and forces of adhesion between the liquid and container act to lift the liquid.

If the polar vertex is " pulled down " 90 °, so that the vertex is on the equator, or transverse diameter, then it becomes the transverse graticule, upon which all spherical trigonometry is ultimately based ( if the longitudinal vertex is between the poles and equator, then it is considered an oblique graticule ).

If done properly, when the tape is removed, the fused end will be about 1 / 8 " to 1 / 4 " thick, and slightly narrower than the unladen diameter of the rope.

If the area available for the windings is filled up, more turns require going to a smaller diameter of wire, which has higher resistance, which cancels the advantage of using more turns.

If we know the angular diameter and the Distance, then we can solve for d < sub > R </ sub > as follows:

If the fiber density is known you also have a fiber diameter, otherwise it is simpler to measure diameters in micrometers.

If an electrode is small enough ( micrometers ) in diameter, then the electro-physiologist may choose to insert the tip into a single cell.

If a typical mammalian cell ( diameter ~ 10 micrometre ) were magnified to the size of a watermelon (~ 1 ft / 30 cm ), the lipid bilayer making up the plasma membrane would be about as thick as a piece of office paper.

If pollination occurs, the plant will produce a bright red to blue-black spherical berry fruit about 5 – 10 mm in diameter that matures in the fall.

If these 32 lenses could be replaced with only two, the high explosive sphere could become an ellipsoid ( prolate spheroid ) with a much smaller diameter.

Formulae connecting a tangential angle, the angle anchored at the ellipse's center ( called also the polar angle from the ellipse center ), and the parametric angle t < ref > If the ellipse is illustrated as a meridional one for the earth, the tangential angle is equal to geodetic latitude, the angle is the geocentric latitude, and parametric angle t is a parametric ( or reduced ) latitude of auxiliary circle </ ref > are:

The report to the European Parliament of 2001 states: " If UKUSA states operate listening stations in the relevant regions of the earth, in principle they can intercept all telephone, fax and data traffic transmitted via such satellites.

If buried on hot coals or ashes, the heat can kill pathogens, the dry ash can desiccate, and the earth can block oxygen and further contamination.

If buried where the earth is very cold, the earth acts like a refrigerator.

If international finance Jewry in and outside Europe should succeed in thrusting the nations once again into a world war, then the result will not be the Bolshevisation of the earth and with it the victory of Jewry, but the destruction of the Jewish race in Europe.

The inscription on his tomb contains Persian words penned which state: اگرفردوس روی زمین است همین است و همین است و همین است ( If there is a paradise on earth, it is this, it is this, it is this!

McVeigh argued that " imminent " does not mean " immediate ": " If a comet is hurtling toward the earth, and it's out past the orbit of Pluto, it's not an immediate threat to Earth, but it is an imminent threat.

If they both used the Attic stadion of about 185 meters, then the older estimate is 1 / 6 too large, and Ptolemy's value is 1 / 6 too small, a difference explained as due to ancient scientists ' use of simple methods of measuring the earth, which were corrupted either high or low by a factor of 5 / 6, due to air's bending of horizontal light rays by 1 / 6 of the Earth's curvature.

If found, these features can be compared with known features in the spectrum of various chemical compounds found in experiments where that compound is located on earth.

If a supercontinent covers a portion of the earth ’ s surface where heat from the mantle accumulates under the crust, it causes the land mass to dome upward.

If a photon rocket begins its journey in low earth orbit, then one year of thrusting may be required to achieve an earth escape velocity of 11. 2 km / s if the vehicle is already in orbit at a velocity of 9, 100 m / s, and 400 m / s additional velocity is obtained from the east to west rotation of the earth.

If the observer is close to the surface of the earth, then it is valid to disregard h in the term, and the formula becomes

If the latter is too hard, the roots will not penetrate it readily and, as a result, the plant will be pushed up and out of the earth during the process of growth.

If the masters and disciples obey the divine teaching of Moses, " our rabbi ," then their society, the school, replicates on earth the heavenly academy, just as the disciple incarnates the heavenly model of Moses, " our rabbi.

Tiberius received the diadem on his knees ; and Justin, who in his abdication appeared most worthy to reign, addressed the new monarch in the following words: " If you consent, I live ; if you command, I die: may the God of heaven and earth infuse into your heart whatever I have neglected or forgotten.

If they conceive of the circle casting as cutting a line in the air with the tool of air, then they may choose to purify the circle with the remaining three elements of fire, water, and earth ; this would involve using a candle to purify the circle, and omitting the incense, since the circle has already been imbued with the element of air.

" If I do that, I must be paid with the lives of the people of the earth, all the human beings, the animals which have four legs, the birds and insects of the air, the fishes and all the people under the water.

If the position of the earth in its orbit around the sun is reckoned with respect to the equinox, the point at which the orbit crosses the celestial equator, then its dates accurately indicate the seasons, that is, they are synchronized with the declination of the sun.

If the position of the earth ( see above ) is reckoned with respect to the fixed stars, then the dates indicate the zodiacal constellation near which the sun can be found.

" Concerning the author, the critic said, " If ever on earth there lived a man who kept the law of Christ, and could give proof of it, and be absolutely unconscious that he was giving it to them, it is this man whom the Mongols called ' our Gilmour.

If the receiver was also moving relative to the earth, such as aboard a ship or airplane, this would cause mismatches with the idealized Doppler curves, and degrade position accuracy.