If the Union conceded this to them, the same right must be conceded to each remaining state whenever it saw fit to secede: This would destroy the federal balance between it and the states, and in the end sacrifice to the sovereignty of the states all the liberty the citizens had gained by their Union.

If the railroads, for example, regularly slaughtered 25,000 passengers each year, the high priests of the cult would have cause to tremble for their personal safety, for such a holocaust would excite demands for the hanging of every railroad president in the United States.

If a branch extended out too far, each man held it back for the next, and if they met a low overhang, each warned the other.

If coffee is sold at the cafeteria, let a few workers in each department get it for the whole group.

If no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

If each text form is marked when matched with a dictionary form, the text forms not contained in the dictionary can be identified when all dictionary forms have been read.

If cell Af is an information cell, it and any information cells in the Y-region that have been linked to Af each contain an address in the W-region where a potentially matching form is stored.

If the bottom name in each column did not have a responsible executive identified, the next name above which identified such a responsible executive was substituted.

If the wedding party lasted late, and the travel schedule means there are only a few hours before resuming the trip or making an early start, the husband may forestall tensions and uncertainties by confiding to his bride that lying in each other's arms will be bliss enough for these few hours.

If he is not told which of four or five readings was meant for him, he can more readily assess each item in a larger frame: `` Does that statement really sound as if it were for me, significant in my particular life??

If laborers are merely commodities competing against each other in a market place like so many bags of wheat and corn ( unsupported, by the way, by any agricultural subsidy ), then they may be pardoned for reacting with complete antagonism to a system that imposes such status upon them.

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.

If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles.

If the square mile is divided into quarters, each quarter has a side length of mile ( 880 yards ) and is square mile in area, or 160 acres.

If each node additionally records the size of its subtree ( including itself and its descendants ), then the nodes can be retrieved by index in O ( log n ) time as well.

If the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.

If a water absorbing swale for each yard is combined with permeable concrete streets, storm drains can be omitted from the neighbourhood.

If the candidate relies on sponsors, the celebrant asks them if they will raise the child in " the Christian faith and life " ( ECUSA BCP ), and will raise the child through " prayers and witness to grow into the full stature of Christ " to which the parents will state to each, " I will, with God's help.

If the dealer does not bust, each remaining bet wins if its hand is higher than the dealer's, and loses if it is lower.

If all four players pass in the first round, the deal is not played ; in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair and returned to the board.

If the line passes through the leftmost portion of the pixel, only the red subpixel is lit ; if it passes through the rightmost portion of the pixel, only the blue subpixel is lit.

If we already created such a " mark ", then we preserve our previous mark and move to the next pixel following the right-hand rule.

If both are empty, then the current pixel can be painted and the painter can move following the right-hand rule.

If a mesh covers more pixels in screen space than it has vertices, interpolating colour values from samples of expensive lighting calculations at vertices is less processor intensive than performing the lighting calculation for each pixel as in Phong shading.

If a mode greater than 24 bits per pixel is desired, the least significant bits are sent on the second link.

If there are 4 bits per pixel ( 16 colors ), each frame buffer byte defines two pixels, one in each nibble.

If another object of the scene must be rendered in the same pixel, the method compares the two depths and chooses the one closer to the observer.

If a pixel has a value of 0 % in its alpha channel, it is fully transparent ( and, thus, invisible ), whereas a value of 100 % in the alpha channel gives a fully opaque pixel ( traditional digital images ).

If the texture has a basic size of 256 by 256 pixels, then the associated mipmap set may contain a series of 8 images, each one-fourth the total area of the previous one: 128 × 128 pixels, 64 × 64, 32 × 32, 16 × 16, 8 × 8, 4 × 4, 2 × 2, 1 × 1 ( a single pixel ).

If each pixel in the original image is split randomly into two shares as described above, the shares are correlated together and reveal the original image.

If one of these displays is examined with a sufficiently strong magnifier, it will be seen that each pixel is actually composed of red, green and blue sub-pixels which blend together at normal viewing distances, reproducing a wide range of colors as well as white and shades of gray.

If the current pixel is behind the pixel in the Z-buffer, the pixel is rejected, otherwise it is shaded and its depth value replaces the one in the Z-buffer.

If not, then the pixel is considered significantly different from all current regions and a new region is created with this pixel.

If the test statistic is sufficiently small, the pixel is added to the region, and the region ’ s mean and scatter are recomputed.

If a diagonal line were only one pixel wide, it would appear alternately purple and green as it meandered down the screen between even and odd horizontal coordinates.

If the bleached spot is effectively a single pixel then the bleaching as a function of position will typically be diffraction limited and determined by the optics of the confocal laser scanning microscope used.

If the pixel would take up 1 / 100 of the texture in one direction, trilinear filtering would interpolate between the result of filtering the 128 * 128 mipmap as y < sub > 1 </ sub > with x < sub > 1 </ sub > as 128, and the result of filtering on the 64 * 64 mipmap as y < sub > 2 </ sub > with x < sub > 2 </ sub > as 64, and then interpolate to x = 100.

If just one pixel in an 8 × 8 block was recolored because a moving part of the display touched it, the entire block would change color.

He said: `` If it's all right with you, Mr. Morgan, I'll sleep out here on the couch.

If she sensed any unusual preoccupation on the part of her mother, she did not comment upon it.

If he spun out now, he would join his opponent on the ground.

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

`` If you want to see something, he's back on the other side by the trunk of the car ''.

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If `` Jack the Courtier '' is really to be taken as Swift, the following remark is obviously Steele's comment on Swift's change of parties and its effect on their friendship: `` I assure you, dear Jack, when I first found out such an Allay in you, as makes you of so malleable a Constitution, that you may be worked into any Form an Artificer pleases, I foresaw I should not enjoy your Favour much longer ''.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If it proclaims that the best is yet to be, it always arouses, at least in the young, either a suspicious question or perhaps the exclamation of the Negro youth who saw on a tombstone the inscription, `` I am not dead but sleeping ''.

If the would-be joiner asks these questions he is not likely to be duped by extremists who are seeking to capitalize on the confusions and the patriotic apprehensions of Americans in a troubled time.

If the decision goes wrong, it may be -- as Mr. Stevenson fears -- `` the first step on the slippery path downhill '' to a U.N. without operational responsibilities and without effective meaning.

If you're lyin' out in the hammock at night, and it gets kinda cool -- you know -- you just take these sides with the fringe on -- see -- and wrap 'em right over you.

If the record buyer's tastes are somewhat eclectic or even the slightest bit esoteric, he will find them satisfied on educational records.

If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.

Mr. Richard Preston, executive director of the New Hampshire State Planning and Development Commission, in his remarks to the Governors Conference on Industrial Development at Providence on October 8, 1960, warned against the fallacy of attempting to attract industry solely to reduce the tax rate or to underwrite municipal services such as schools when he said: `` If this is the fundamental reason for a community's interest or if this is the basic approach, success if any will be difficult to obtain ''.

`` If the day should ever come that foreign invaders swarm ashore along the Gulf Coast '', the account reads, `` they can count on heavy opposition from a group of commando-trained telephone employees -- all girls.

If we make it established custom that whenever butchery on the highways grows excessive, say beyond 25,000 per annum, then somebody is going to hang, it follows that the more eminent the victim, the more impressive the lesson.

If it comes down too hard on the potential dangers of fallout, it will box the President on resuming atmospheric tests.

`` If William agrees, we should insist on a public debate '', he said at length.

If you want to fight, go down on the sidewalk ''.

If there is anything which we can do in the executive branch of the Government to speed up the processes by which we come to decisions on matters on which we must act promptly, that in itself would be a major contribution to the conduct of our affairs.