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 a circle passing through two of the input points doesn't contain any other of them in its interior, then the segment connecting the two points is an edge of a Delaunay triangulation of the given points.

If two triangles do not meet the Delaunay condition, switching the common edge BD for the common edge AC produces two triangles that do meet the Delaunay condition:

If there is an edge from a vertex x to a vertex y, then the element is 1 ( or in general the number of xy edges ), otherwise it is 0.

If heaven is a state of supernatural happiness and union with God, and hell is understood as a state of torture and separation from God then, in this view, the Limbo of Infants, although technically part of hell ( the outermost part, " limbo " meaning " outer edge " or " hem ") is seen as a sort of intermediate state.

If the user has built up a substantial charge, the discharge can jump around the door's edge or pass through the door itself ( dielectric breakdown ).

If the edge length of a regular octahedron is a, the radius of a circumscribed sphere ( one that touches the octahedron at all vertices ) is

( If the graph has no weights, 1 indicates an edge, 0 indicates no edge.

If the original rhombicuboctahedron has unit edge length, its dual strombic icositetrahedron has edge lengths

If a pushwall exits the boundaries of the level, the game quits with the error message " PushWall Attempting to escape off the edge of the map ".

If no path exists between two cities, adding an arbitrarily long edge will complete the graph without affecting the optimal tour.

If a feature was intended to be located from the center of the part, the operator needs to locate it from the center of the model, not, perhaps, from a more convenient edge or an arbitrary point, as he could when using " dumb " solids.

If an ant were to crawl along the length of this strip, it would return to its starting point having traversed the entire length of the strip ( on both sides of the original paper ) without ever crossing an edge.

If the strip is cut along about a third of the way in from the edge, it creates two strips: One is a thinner Möbius strip — it is the center third of the original strip, comprising 1 / 3 of the width and the same length as the original strip.

If this theory is correct, then the transition to a conductive state could be explained by a rearrangement at the pore edge, in which the lipid heads fold over to create a hydrophilic interface.

If the edge weights are not unique, only the ( multi -) set of weights in minimum spanning trees is unique, that is the same for all minimum spanning trees.

If the cross-section of the circular object deviates slightly from its circular shape ( but it still has a sharp edge on a smaller scale ) the shape of the point-source Arago spot changes.

If Halley was once a long-period comet, it is likely to have originated in the Oort Cloud, a sphere of cometary bodies that has an inner edge of 20, 000 – 50, 000 AU.

If its leading edge is raked back enough, it will escape the shock wave formed at the nose of the aircraft as transonic speeds are reached, reducing drag considerably, and the center of lift moves less than on conventionally configured aircraft, reducing trim drag.

If the point is outside the edge, the point is removed.

If they want to score they will have to try and risk an edge to a wide ball and hit through the packed off side, or trying and drag the ball from far outside the stumps to the sparsely-populated leg side.

If the gust front, or leading edge of the outflow boundary, races ahead of the thunderstorm, its motion will accelerate in tandem.