
356 F.Supp. 675 (1973)
Roy MOSS, Jr., By and Through his mother and next friend Linda D. Moss, et al.
v.
STAMFORD BOARD OF EDUCATION et al.
Civ. No. B-586.
United States District Court, D. Connecticut.
March 26, 1973.
*676 Steven P. Hershey, Stamford, Conn., for plaintiffs.
Theodore I. Koskoff, Bridgeport, Conn., for defendants.

MEMORANDUM OF DECISION
NEWMAN, District Judge.
This is a civil rights suit brought pursuant to 42 U.S.C. § 1983 challenging the elementary school integration[1] plan presently used by the Stamford, Connecticut, Board of Education, on the grounds that it places a disproportionate share of the burden of achieving racial balance on Black and Spanish-surnamed[2] children and therefore stigmatizes them on account of their race in violation of the equal protection clause of the Fourteenth Amendment. Plaintiffs are Black and Spanish-surnamed children attending Stamford elementary schools. Defendants are the Stamford Board of Education, its members, and the Superintendent of the Stamford public schools. Jurisdiction is conferred by 28 U.S.C. § 1343(3).
On November 14, 1972, this Court denied defendants' motion to dismiss the complaint, Moss v. Stamford Board of Education, 350 F.Supp. 879 (D.Conn. 1972). That decision held that plaintiffs' claims of discrimination resulting from the implementation of a plan to achieve racial balance stated a cause of action under § 1983. It also ordered a bifurcated trial to consider first the issue of whether there was a constitutionally significant discrimination, which, if established, would thereafter require consideration of whether such discrimination was justified. See Chance v. Board of Examiners, 458 F.2d 1167 (2d Cir. 1972). A hearing on the first issue was held November 30, 1972. Testimony and detailed documentary evidence, including maps and statistics on attendance and bussing, were presented.

I
The city of Stamford is roughly rectangular in shape, extending north from Long Island Sound approximately ten miles to the New York State border. The southern border of the city is about four miles long and the northern border, five miles. Census data indicate that virtually all Black residents of Stamford live in the urbanized, southernmost third *677 of the city, with the heaviest concentrations in the western half of this zone. No figures have been presented as to the residential pattern of Spanish-surnamed individuals, but school attendance statistics suggest that their pattern is generally similar to that of Blacks.
In September, 1970, the Stamford Board of Education began a two-phased plan to improve the racial balance within the several elementary schools of its school system. The goal was a White to minority ratio of seventy to thirty per cent, plus or minus ten per cent in each school.[3] In broad terms, the plan called for the closing, over a two-year period, of two schools (Rice and Stevens) and grades 4, 5, and 6 of another (Ryle). These were the schools most heavily enrolled with minority students and were located in census areas with the highest percentage of minority residents. During the same period, 1970-1972, three new schools were opened (Toquam, Davenport, and Stillmeadow), each located in virtually all-White residential areas. The school districts for Rice, Stevens, and Ryle (grades 4-6) were divided into a series of satellite attendance zones, each affiliated with a principal school district in the system, invariably in a predominantly White area. The satellite zones were entirely separated from their principal school districts. All students formerly attending the closed schools or grades were bussed to the school in the district with which their satellite district was affiliated. These students from the closed schools had to cross other school districts, and frequently to pass other schools, before arriving at the schools to which they were assigned. This cross-district bussing continues today and forms the substance of the burden alleged by plaintiffs.
The precise nature of the burden challenged by plaintiffs has been clarified from that alleged in the original complaint. Initially plaintiffs attacked both the school closings and defendants' bussing plan. However, the amended complaint abandoned the attack on school closings and focused entirely on a consequence of those closingsthe bussing of the minority children who attended those schools to non-contiguous school districts. Plaintiffs have further refined their claim to focus only on cross-district bussing that results from the Board's integration plan, although since all of the cross-district bussing in Stamford is undertaken for the purpose of achieving racial balance, this last refinement *678 is irrelevant.[4] Plaintiffs' precise claim is that the bussing of elementary school children to non-contiguous districts as a result of the Board's integration plan is required of a disproportionately larger percentage of minority children than of White children.
Plaintiffs do not claim that the minority children travel a significantly longer distance or time than other children in the school system, nor that the bus rides impair the educational process. Nor are plaintiffs really complaining about the crossing of artificial lines on a map. Anyone familiar with political districting knows the artificiality of meeting a requirement of contiguity of districts. Plaintiffs would scarcely consider themselves less burdened if the defendants had connected each satellite zone to its principal zone with a narrow strip, thereby eliminating bussing to a noncontiguous district without shortening the trip at all.
What plaintiffs are really complaining about is the stigma imposed upon them by being regarded as "foreigners" by the "natives" attending the schools to which the bussed children are assigned. Brice v. Landis, 314 F.Supp. 974, 978 (N.D.Cal.1969). This stigma probably does not arise in every instance where a child is required to attend school in a non-contiguous district. But it may well arise in those instances where the bussing pattern removes the child from his own neighborhood and requires him to attend school in an entirely different neighborhood. The essence of plaintiffs' complaint is the social dislocation of assignment out of their home neighborhoods.
The difficulty in assessing plaintiffs' claim is that there is no ready definition of "neighborhood," so that bussing to a non-neighborhood school cannot always be identified. Plaintiffs' comparison of the percentages of minority children and White children bussed to non-contiguous districts is at best an approximation of the disparity between the groups with respect to neighborhood dislocation.
Defendants contend that the more pertinent comparison is among children bussed to schools other than the schools closest to their homes (hereafter "not-nearest school"), rather than among children bussed to non-contiguous districts. This comparison, they argue, more adequately identifies the dislocation of which plaintiffs complain and, at the same time, gives proper weight to the burden suffered by White students, few of whom attend schools in non-contiguous districts, but many of whom attend schools that are not closest to their homes. In addition, defendants prefer to compare pupil assignments for the entire school system, grades kindergarten through 12 (hereafter grades K-12).
Each of the comparisons urged by the parties is somewhat unsatisfactory. Bussing to non-contiguous districts and bussing to not-nearest schools are both, at best, approximations of the true extent of neighborhood dislocation suffered by the bussed students. Neither formulation expresses a burden that is inherently more onerous than the other. A bus trip to a non-contiguous district may be longer or shorter than a trip to a not-nearest school depending on the circumstances.[5]
*679 More significant to analysis of the equal protection claim, each comparison is somewhat unfair to either the White students or the minority students. While the amount of cross-district bussing may fairly indicate the degree of dislocation of the minority children, since their cross-district trips take most, if not all, of them away from their neighborhoods, this measure does not indicate the dislocation of White students because, as a result of the Board's plan, many White children are bussed away from their neighborhoods (usually to not-nearest schools), even though few of them are bussed to non-contiguous districts. Thus comparison of the percentages of White and minority students bussed to non-contiguous districts skews the relative burden in favor of plaintiffs' claim. On the other hand, examination of bussing to not-nearest schools leads to a comparison of relative burden that is skewed in favor of defendants' position. Since Stamford's elementary schools are concentrated in White neighborhoods, many of the White students who attend not-nearest schools are still attending schools reasonably close to their homes, in effect, neighborhood schools. Yet probably all minority children who attend not-nearest schools are bussed to schools away from their neighborhoods.
The statistical expression of the relative bussing burden suffered by minority elementary school students compared to White students thus eludes precise formulation. It is fair to say, however, that the comparisons proposed by the parties bracket the range within which the comparative burden of actual neighborhood dislocation is to be found. Moreover, it may not be necessary to decide (1) whether comparison should be made between groups of children bussed to noncontiguous districts or to not-nearest schools, and (2) whether comparison should be made among only elementary school children or those attending grades K-12, for no matter which figures are used as approximations for the comparative neighborhood dislocation suffered by plaintiffs, the percentage of minority students affected is more than double the percentage of White students. If cross-district bussing of elementary students is examined, the evidence shows that 56% of all Black and Spanish-surnamed students are bussed to non-contiguous districts, while the corresponding figure for Whites is only 4.5%.[6] If bussing to schools other than those closest to students' homes is compared for these grades, the evidence shows that 50.9% of minority students are bussed to not-nearest schools, while the corresponding figure for Whites is 16.7%. Finally, for grades K-12, the comparative percentages of minority and White children bussed to not-nearest schools are, respectively, 52.7% and 23.3%. The difficult question is whether, in the circumstances of this case, these comparisons, regardless of which is chosen, establish a constitutionally significant burden.


*680 II
If the approach in cases like Chance v. Board of Examiners, supra, is appropriate here, then any of the comparisons developed by the parties appears sufficient to require justification by the defendants. But Chance arose in a different context, which makes its approach not precisely applicable. The issue there was whether an employment exam discriminated against racial groups, and a prima facie showing of a constitutionally significant burden was established by a comparison of widely different passing rates for different racial groups. Chance drew significance from this disparity in passing rates because when a racially neutral exam is given to members of different racial groups, there is a theoretical expectation that the percentage of each group that passes the exam will be equal, regardless of the number of applicants in each group. If, instead of such a racially neutral result, the exam produces a disparity in passing rates among racial groups, this disparity creates a prima facie showing that the exam is not racially neutral, requiring the employer to justify use of the exam despite its racially disparate result.
Two factors distinguish the school integration context from the employment exam context. First, for reasons to be developed, a racially neutral integration plan, unlike a racially neutral exam, can be expected to produce a racially unequal result: the percentage of each racial group adversely affected will be different. Thus, a prima facie case of discrimination in this context is established not simply by the existence of a disparity between the percentages of each group affected, but only by a disparity significantly greater than the one to be expected from use of a racially neutral plan. But the actual disparity cannot be compared to the expected disparity unless each can be determined with some precision. These determinations encounter the second factor distinguishing a bussing case from an employment exam case: the absence of precise measurements of the actual disparity between the bussing burdens of each racial group and of the expected disparity under a plan of racial neutrality. Both factors require some explanation. Analysis of the first factor, the expectation of inequality, is assisted by considering first the percentage of groups of students who must be reassigned, under an integration plan, to different schools before considering the comparative burden of the bus trips required to carry out the reassignment.
When an integration plan is carried out in a community with a racial minority, the expectation is that the percentage of each group of students who must be reassigned to achieve integration will not be equal, even if the plan is designed with scrupulous regard for racial fairness. This results from the obvious difference between comparing numbers of students and comparing percentages of students. If total enrollment at each school remains constant before and after integration, however many minority students are reassigned from schools with heavy minority enrollment to reach a targeted percentage of uniform minority enrollment in all schools must be replaced with an equal number of White students. Since by definition there are fewer minority students than White students in the school system as a whole, this number will always be a larger percentage of all minority students than of all White students. In fact, as long as total enrollment at each school remains constant before and after integration, a significant mathematical relationship emerges that always expresses exactly how much larger the percentage of reassigned minority students is compared to the percentage of reassigned majority students. The ratio of the percentage of reassigned minority students to the percentage of reassigned majority students is the reciprocal of the ratio of all minority students to all majority students (whether expressed in numbers of students or as percentages of the student population). As the example in the *681 margin illustrates,[7] if 20% of all the students are Black and 80% are White, producing a one to four ratio of Blacks to Whites, the percentage of Blacks who must be reassigned to achieve racial balance will always be four times the percentage of Whites reassigned, producing a ratio of four to one. This ratio remains constant for any given number of minority and majority students in the school system, regardless of the degree of segregation before the integration plan,[8] and regardless of differences in enrollment among the various schools.[9] What this "reciprocal ratio" principle means is that the smaller one group is *682 in the school population, the larger is the percentage of that group that must be reassigned to achieve racial balance.[10]
If before integration, some schools are not filled to capacity and total enrollment at each school changes after integration, then the ratio between percentages of groups of students that must be reassigned to achieve racial balance can be varied. The percentage of Blacks reassigned can be increased by moving more of them to the predominantly White schools with previously unused excess capacity, or the percentage of Whites reassigned can be increased by moving more of them to predominantly Black schools with previously unused excess capacity.[11] In either case the total enrollments at the schools selected for extra reassignment will be greater after integration than before. For purposes of this opinion, a racially neutral reassignment plan will be considered to be one where school enrollments remain the same before and after integration, thereby eliminating the opportunity for the variations that can be accomplished by using excess capacity to the disadvantage of either group. Under the Stamford bussing plan, it should be noted, there has been a net decrease in total enrollment at schools that, prior to integration, were more than 70% White. Thus there has been no attempt to use whatever excess capacity may have existed at these schools as a means to increase the percentage of minority pupils reassigned.[12]
In the context of the Stamford elementary school integration plan, the inevitable *683 disparity between percentages of groups of students reassigned can be expected to be augmented because of the fact that some schools were closed and new schools were constructed. At two predominantly minority-enrolled schools and at three grades of another, all minority students had to be reassigned when these facilities were closed. These closings increased the number and hence the percentage of minority students to be reassigned above what would have been required had all schools remained open.[13]
It is relatively easy to compute a prediction of the inevitable disparity between percentages of each group of students that would have to be reassigned in Stamford under a racially neutral reassignment plan to achieve the targeted racial balance in each school. From the computation in the margin,[14] it appears that 71% of the minority students and 18% of the White students in the elementary schools would have to be reassigned to achieve 70-30 racial balance in each school, given the pre-integration enrollments at each school and the school closings that occurred.
While this expected disparity reflects only percentages of students to be reassigned, without regard to the neighborhood dislocation of bussing, it is of interest that the expected reassignment disparity approximates the disparity of the bussing percentages claimed to be burdensome by the plaintiffs. In fact, plaintiffs' minority cross-district bussing percentage of 56% is less than the predicted minority reassignment percentage of 71%. This results because at three schools (Franklin, Hart, and Westover) the percentage of minority enrollment has remained well above the target of 30%. However, plaintiffs' White cross-district bussing percentage of 4.5% is considerably less than the predicted White reassignment percentage of 18%. This results because many of the reassigned White students did not have to travel across a district, but instead were reassigned to schools in newly drawn districts in which they resided. Since for most of these White students their reassigned schools were not the ones closest to their homes, defendants' not-nearest bussing percentage for Whites of 16.7% closely approximates the predicted White reassignment percentage of 18%
The fact that the predicted disparity in reassignment rates falls generally within the range of the actual disparity in bussing rates, established by the figures proposed by each side, indicates at most, however, that minority students have not been disproportionately reassigned under the Stamford integration plan. This fact does not preclude the possibility that the bussing pattern (i.e. the pattern of reassignment) has burdened minority students with unnecessary *684 dislocation from their neighborhoods. Moreover, the disparity (expressed as a ratio) between groups of elementary school students bussed to non-contiguous districts (56% to 4.5%) is greater than the expected reassignment disparity (71% to 18%).
Theoretically, it might be possible to calculate for any school system the unavoidable disparity in percentages of out-of-neighborhood reassignments for each racial group required to achieve racial balance and then to consider a prima facie discrimination established whenever the actual disparity is significantly above the predicted disparity. However, the predicted and actual disparity in neighborhood dislocation for each racial group cannot be calculated without determining the boundaries of each "neighborhood"an inherently amorphous concept. Since precise neighborhood dimensions are invariably lacking and are not apparent from the evidence here, the necessary measurements cannot be made.
This case thus differs from Chance, where the adverse consequence, exam failure, could be readily measured, the disparity between the percentages of each group that passed the exam could be readily calculated, and this disparity could be compared to an expected result, namely, equality of passing rates. Here, the adverse consequence, neighborhood dislocation, cannot be readily measured, the disparity between groups bussed out of their neighborhoods can at best be only approximated, and there is not available for comparison, even with plaintiffs' approximation of disparity, an expected result, namely, the unavoidable disparity between groups bussed out of their neighborhoods under a plan of racial neutrality. The essential point is that the simple mathematical comparisons of the type made in Chance cannot be made here.[15] What is required is a pragmatic assessment of the salient facts.

III
Plaintiffs challenge the bussing pattern that results from the Board's plan to achieve racial balance. That plan closed all or part of three schools. The children attending those schools had to be bussed somewhere. Since plaintiffs do not challenge the selection of schools to be closed nor the location of new schools, it is apparent that the students who had attended the closed schools had to be bussed out of what were formerly their school districts. Whatever happened to them, whether benefit or burden, would happen to a disproportionate percentage of minority children for the obvious reason that the children attending the closed schools were 91% Black and Spanish-surnamed. This case does not present the question of whether the school closings and new school locations could have been challenged at an earlier time on the basis of their likely effect.
In this context, the relevant inquiry is whether the bussing of these children from the closed schools is done in such a way as to burden unnecessarily the Black and Spanish-surnamed members of that group. There is no evidence that this is occurring, and the evidence presented makes clear why this is so. Once the three schools were closed, the schools nearest to the homes of the displaced children became Westover, Hart, Franklin, and Rogers. These are also the school districts contiguous to the districts of the closed schools. Of these four nearby schools, the first three already have minority enrollments above the 30% average percentage the Board is trying to achieve.[16] To bus more minority children to these schools would *685 only increase the minority percentages, and to bus them while maintaining the existing percentages would require bussing out a minority child for every one bussed in, scarcely a way of reducing the bussing burden upon minority children. Rogers, with current minority enrollment at 28%, could accommodate about seven more minority students. Thus, for seven minority students, bussing beyond Rogers is unnecessary, but this number, when compared to the approximately 2,000 students who had to be reassigned from the closed schools, is not constitutionally significant.
Some students from the closed schools are bussed beyond four other schools, Belltown, Stillmeadow, Newfield, and Murphy, which are near but not contiguous to the districts of the closed schools and all of which have minority enrollment slightly below 30%, sufficient to accommodate about 143 more minority students. But none of these districts is contiguous to the districts of the closed schools. If minority children were assigned to these schools, their bus trip would be slightly shortened, but they would still be bussed to noncontiguous districts. Hence for them the burden plaintiffs complain of would not be reduced at all. It is also true that total enrollment is below state-rated capacity at some of the schools with minority enrollment above 30%, those located near the center of Stamford, north of the closed schools. Plaintiffs correctly point out that if White students were bussed from schools in the northernmost districts of Stamford to fill these vacancies, the percentage of Whites bussed across district lines would rise and, as a result, the disparity between the percentages of Whites and minority students bussed would drop. But such a change would not shorten the bus trip of a single minority student. The absence of more cross-district bussing of Whites does not create a constitutionally significant burden upon the minority students unless it is shown that such absence has resulted in some unnecessary cross-district bussing of Blacks and Spanish-surnames. There is no such evidence here.
In the absence of any evidence to show that the burden of bussing has been imposed unnecessarily on minority students, the mere fact that the unchallenged closing of heavily minority-enrolled schools required a large percentage of minority students to be bussed out of their former districts to schools with low minority enrollments does not establish a violation of the equal protection clause. See Hart v. County School Board of Arlington County, 459 F.2d 981 (4th Cir. 1972); Gordon v. Jefferson Davis Parish School Board, 446 F.2d 266 (5th Cir. 1971), reh'g denied, 460 F.2d 1062 (1972); Norwalk Core v. Norwalk Board of Education, 423 F.2d 121 (2d Cir. 1970); Felder v. Harnett County Board of Education, 409 F.2d 1070 (4th Cir.1969); Mims v. Duval County School Board, 447 F.2d 1330 (5th Cir. 1971); Brice v. Landis, Civ. No. 51805 (N.D.Cal. filed July 9, 1971); see also Swann v. Charlotte-Mecklenburg School District, 306 F.Supp. 1291 (D.C. N.C.1969), aff'd, 402 U.S. 1, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971).
Integration planning must necessarily be "color conscious"[17] and it is constitutionally proper for it to be so. Where, as in this case, there are few schools near minority neighborhoods and *686 many near White neighborhoods, it follows that to obtain racial balance throughout the school system, minority pupils are likely to be dispersed across district lines, while Whites remain close to homethis is where the schools are.[18] Such cross-district assignment of pupils is, moreover, a legitimate device of school desegregation. Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 27, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971); Davis v. School Commissioners of Mobile, 402 U.S. 33, 91 S.Ct. 1289, 28 L.Ed.2d 577 (1971). Plaintiffs have offered no proof that the disproportionate burden they bear is anything other than the inevitable result of the present location of Stamford's elementary schoolswhich plaintiffs do not challenge and the legitimate and commendable desire of Stamford's school officials to integrate their school system.
The cases[19] upon which plaintiffs rely do not find constitutionally significant discrimination on facts similar to those established here. In each, the unequal allocation of the burden of integration was not based solely on the disproportionate bussing of minority students; rather, additional acts by school officials, such as the closing of usable minority schools or racial gerrymandering, contributed significantly to the inequality. Because these acts were obviously detrimental to the interests of minority students and at the same time appeared on their face to serve no legitimate school board interest, the acts were suspect as racially discriminatory, and the defendant school boards were called upon to justify them, which they were unable to do. As a result, modifications in the challenged desegregation plans were ordered. The same approach has been used, at least implicity, in suits where challenged desegregation plans have been upheld.[20]
This is not to suggest that a bussing plan involving the same numbers of White and minority students as in the Stamford plan precludes the possibility of suspect acts by school officials. If, for example, minority students were bussed in disproportionate numbers to the most distant or least desirable schools in the system, or if they were not bussed, except in token numbers, to some previously all-White schools, a question might arise as to whether racial considerations had improperly impinged on the integration process. There is no evidence of such actions here nor of the type of suspect actions found significant in the cases relied on by the plaintiffs.
Since the evidence presented at the trial on the severed issue fails to establish *687 a prima facie case of a constitutionally significant discrimination, judgment will enter for the defendants, denying the relief sought by the plaintiffs.
NOTES
[1]  It seems more appropriate to call Stamford's plan one for "integration" rather than "desegregation" since the plan was undertaken at the initiative of the School Board to promote racial balance, rather than in response to a determination that either de jure or de facto segregation existed. However, plaintiffs suggest that the Board may have been anticipating a finding that would otherwise have been made.
[2]  Plaintiffs use the phrase "of Hispanic origin" to describe this class of persons, and defendants refer to them as "Spanish speaking." However, "Spanish-surnamed" appears to be a more accurate designation than either and will be used herein. "Minority" is used to denote the combined class of Black and Spanish-surnamed individuals.
[3]  The progress Stamford has made toward this goal is evident from the following table, comparing the White and minority percentages in each school in 1969 and 1972.



                                Per Cent White             Per Cent Minority
                              1969          1972           1969         1972
Belltown ....................  95           74.2             5          25.8
Davenport (new) .............   -           74.1             -          25.9
Franklin ....................  68           56.6            32          43.4
Hart ........................  50           56.3            50          43.7
Murphy ......................  97           78.2             3          21.8
Newfield ....................  97           78.8             3          21.2
Northeast ...................  97           75.1             3          24.9
Rice (closed) ...............   9            -              91           -
Riverbank ...................  98           74.3             2          25.7
Rogers ......................  69           71.8            31          28.2
Roxbury .....................  97           69.6             3          30.4
Ryle (4-6) (closed) .........  20            -              80           -
Springdale ..................  99           69.5             1          30.5
Stark .......................  88           70              12          30
Stevens (closed) ............  19            -              81           -
Stillmeadow (new) ...........   -           72               -          28
Toquam (new) ................   -           67.4             -          32.6
Westover ....................  59           43.2            41          56.8
Willard .....................  94           79.2             6          20.8

[4]  If racial comparisons were attempted with respect to all bussing, rather than cross-district bussing, it would be understandable why plaintiffs would prefer limiting the inquiry to bussing to achieve racial balance. Before the integration plan, many students rode buses because they lived some distance from the nearest school, and plaintiffs would want to distinguish these students from those burdened by the integration plan itself. Stamford now provides in-district bussing for 2862 Whites and 60 minority students. This is apparently undertaken wherever pupils live more than one mile from the schools they attend or where the absence of sidewalks or other safety reasons so require.
[5]  A cross-district bus trip may be a long ride across the city, or a very short trip starting at a home in District A, cutting across the corner of District B, and ending up within District C at a school that is actually closer to the student's home than the school in District A. Similarly, a trip to a not-nearest school might also be a cross-town ride, or a very short trip if the student lives close to two or more schools.
[6]  This percentage reflects the White students previously attending Rice, Stevens, and grades 4-6 of Ryle, who comprised approximately 9%, 14%, and 15%, of those student bodies, respectively, at the time these facilities were closed. In addition, 110 students, all of them White, are bussed from a satellite zonethe Dogwood sectionto the Davenport School. When the Davenport district was established under Phase II, population patterns and the geographic proximity of several other elementary schools to the Davenport School made it necessary to attach the Dogwood section, a White residential area, to the district. The Dogwood area, as charted for school attendance purposes, touches the principal Davenport district at only one point. While technically this one common point makes it contiguous to the Davenport district, the children living in the Dogwood section must, in fact, pass through the Willard district to reach their school, and thus are properly viewed as attending a school in a non-contiguous district.
[7]  In Example 1 in this footnote and all of the examples that follow in footnotes 8, 9, 11, and 13, a school population of 1,000 students is assumed, divided into 800 Whites and 200 Blacks, who, before any reassignment, are attending ten schools. Unless otherwise specified, enrollment capacity of each school is 100.

Example 1: Each school is totally segregated with 100 Whites in eight schools and 100 Blacks in two schools. To achieve racial balance each school must enroll 80 Whites and 20 Blacks. This requires reassigning 20 Whites from each of the eight all-White schools and 80 Blacks from each of the two all-Black schools, or a total of 160 Whites and 160 Blacks. This 160 is 20% of the 800 Whites and 80% of the 200 Blacks. The ratio of the percentage of reassigned Blacks to the percentage of reassigned Whites is four to one, the reciprocal of the ratio between their percentages in the school population, which is one to four.
The constancy of this ratio of reassignment percentages is explained by the fact that, as long as enrollment at each school remains unchanged before and after reassignment, an equal number of Whites and Blacks will always have to be reassigned. The reassignment percentage of each group is obtained by dividing the number of reassigned students of that group by the total number of the group. Since the divisor for the White percentage is four times the divisor for the Black percentage, the quotient or White reassignment percentage will be one-fourth of the Black reassignment percentage, regardless of the number of students reassigned in any example.
[8]  The following example illustrates the constancy of the four to one ratio in reassignment percentages when the degree of segregation before the integration plan is reduced from the total segregation of Example 1 in footnote 7.

Example 2: Each school is substantially segregated. One school has 92 Blacks and 8 Whites, and nine schools have 88 Whites and 12 Blacks. To achieve racial balance each school must enroll 80 Whites and 20 Blacks. This requires reassigning 8 Whites from each of the nine predominantly White schools and 72 Blacks from the one predominantly Black school. The total of Whites and Blacks reassigned is 72 for each group. This 72 is 36% of the 200 Blacks and 9% of the 800 Whites. The ratio of the percentage of reassigned Blacks to the percentage of reassigned Whites is still four to one.
It should be noted, however, that the total number of children to be reassigned is reduced when less than complete segregation exists prior to integration.
[9]  The following example illustrates the constancy of the four to one ratio in reassignment percentages when the enrollment at each of the schools is not the same, as it was in Example 1 in footnote 7. Enrollment at each school is still assumed to remain unchanged before and after integration.

Example 3: The enrollment at one school is 160, at another school, 120, and at each of the eight other schools, 90. The 160-pupil school has 152 Whites and 8 Blacks, the 120-pupil school has 112 Whites and 8 Blacks, six of the 90-pupil schools have 82 Whites and 8 Blacks, and two of the 90-pupil schools have 22 Whites and 68 Blacks. To achieve racial balance the 160-pupil school must enroll 128 Whites and 32 Blacks, the 120-pupil school must enroll 96 Whites and 24 Blacks, and each of the 90-pupil schools must enroll 72 Whites and 18 Blacks. This requires reassigning 24 Whites from the 160-pupil school, 16 Whites from the 120-pupil school, and 10 Whites from each of the six predominantly White 90-pupil schools, or a total of 100 Whites. Racial balance also requires reassigning 50 Blacks from each of the two predominantly Black 90-pupil schools, or a total of 100 Blacks. This 100 is 50% of the 200 Blacks and 12½% of the 800 Whites. The ratio of the percentage of reassigned Blacks to the percentage of reassigned Whites is still four to one.
[10]  This analysis assumes that each student who must be reassigned to achieve racial balance is transferred directly to a school where that student's racial group was formerly underrepresented. The number of students reassigned can be increased if students of one racial group are reassigned from one school to a second school nearby where their racial group is overrepresented, requiring a further reassignment of students at the second school to a third school where that group is underrepresented.
[11]  The following example illustrates how the ratio of the Black reassignment percentage to the White reassignment percentage exceeds four to one when previously unused excess enrollment capacity at predominantly White schools is used.

Example 4: As in Example 1, each school has 100 students enrolled, and each school is totally segregated before reassignment. After reassignment the enrollment at four of the eight previously all-White schools is increased to 120, and enrollment at each of the two previously all-Black schools is decreased to 60. To achieve racial balance each of the four 120-pupil schools must enroll 96 Whites and 24 Blacks, each of the four 100-pupil schools must enroll 80 Whites and 20 Blacks, and each of the two 60-pupil schools must enroll 48 Whites and 12 Blacks. This requires reassigning 48 Whites to each of the two previously all-Black 60-pupil schools, 20 Blacks to each of the four previously all-White 100-pupil schools, and 24 Blacks to each of the four 120-pupil schools, or a total of 96 Whites and 176 Blacks to be reassigned. The 96 reassigned Whites are 12% of the 800 Whites, and the 176 reassigned Blacks are 88% of the 200 Blacks. The ratio of the percentage of reassigned Blacks to the percentage of reassigned Whites is now 7 1/3 to one.
Conversely, use of previously unused excess capacity at predominantly Black schools will reduce the ratio to less than four to one.
[12]  Any enrollment at Stamford's three new elementary schools in excess of the enrollments at the closed schools, it should be noted, would have the same impact on minority student reassignments as the use of previously unused excess capacity at the formerly over-70% White schools. Thus, while the new school openings are not themselves challenged here, the capacities of the new schools might place an unnecessary burden on plaintiffs. In fact, the enrollment at the new schools, 2,519, exceeds the enrollment at the closed schools and grades, 2,181, by 338 students. However, enrollment at the schools that were more than 70% White before integration dropped, after integration, by 336 students. Thus, even if the new school enrollment in excess of that needed to replace the capacity lost in the school and grade closings is considered in the same light as "previously unused capacity" at other schools, on balance, there has been no attempt to increase the minority reassignment percentage by enlarging the enrollments at the schools to which minority students must be bussed.
[13]  The following example illustrates how the disparity between the percentages of groups of reassigned students increases when a predominantly minority-enrolled school is closed.

Example 5. As in Example 2, each school is substantially segregated. One school has 92 Blacks and 8 Whites, and nine schools have 88 Whites and 12 Blacks. The predominantly Black school is closed, and a new school is opened (with the same enrollment as the closed school). Now the number of Blacks to be reassigned increases from 72 to 92, or 46% of the 200 Black students, and the number of Whites to be reassigned increases from 72 to 80, or 10% of the 800 White students. The ratio of the percentage of reassigned Blacks to the percentage of reassigned Whites increases to 4.6 to one.
[14]  Examining school enrollments as of September, 1971, prior to the implementation of Phase II, all the minority students from the closed schools, 2,071, plus the minority students at the other schools in excess of the targeted minority enrollment of 30%, 380, are a total of 2,451 minority students to be reassigned, which represented 71% of all minority students in the elementary school population (3,482) at the time. All the White students from the closed schools, 288, plus the White students at the other schools above the targeted White enrollment of 70%, 1,176, are a total of 1,464 White students to be reassigned, which represented 18% of all White students in the elementary school population (8,147) at the time.
[15]  To the extent this Court's opinion denying the motion to dismiss indicated otherwise, it was unduly optimistic.
[16]  The present minority enrollment percentages for the schools are:



               9/72
              ------
   Westover   56.8%
   Hart       43.7%
   Franklin   43.4%
   Rogers     28.2%

[17]  Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 28, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971); McDaniel v. Barresi, 402 U.S. 39, 41, 91 S.Ct. 1287, 28 L.Ed.2d 582 (1971); cf. United States v. Jefferson County Board of Education, 372 F.2d 836, 876 (5th Cir. 1966):

The Constitution is both color blind and color conscious. To avoid conflict with the equal protection clause, a classification that denies a benefit, causes harm, or imposes a burden must not be based on race. In that sense, the Constitution is color blind. But the Constitution is color conscious to prevent discrimination being perpetuated and to undo the effects of past discrimination.
[18]  Cf. Green v. School Board of City of Roanoke, 316 F.Supp. 6, 10 (W.D.Va., Roanoke Div., 1970), modified 444 F.2d 99 (4th Cir.), cert. denied, Winston-Salem v. Scott, 404 U.S. 912, 92 S.Ct. 230, 30 L.Ed.2d 186 (1971):

The plaintiffs' objection that the black community should not be required to shoulder the largest part of the burden involved in the desegregation process has merit, although the realities of the actual physical facts [closing two predominantly Black schools] makes such imposition difficult to avoid.
[19]  Lee v. Macon County Board of Education, 448 F.2d 746 (5th Cir. 1971); Bell v. West Point Municipal Separate School District, 446 F.2d 1362 (5th Cir. 1971); Spangler v. Pasadena City Board of Education, 311 F.Supp. 501 (C.D.Cal. 1970); Green v. School Board of the City of Roanoke, supra; Brice v. Landis, 314 F.Supp. 974 (N.D.Cal.1969); see also, Cisneros v. Corpus Christi Independent School District, 467 F.2d 142 (5th Cir. 1972).
[20]  Hart v. County School Board of Arlington County, supra; Gordon v. Jefferson Davis Parish School Board, supra; Allen v. City of Asheville Board of Education, 434 F.2d 902 (4th Cir. 1970); Wright v. Board of Public Instruction of Alachua County, 431 F.2d 1200 (5th Cir. 1970); Carr v. Montgomery County Board of Education, 429 F.2d 382 (5th Cir. 1970); Norwalk Core v. Norwalk Board of Education, supra; Felder v. Harnett County Board of Education, supra; Mims v. Duval County School Board, supra; see also, Haney v. County Board of Education of Sevier County, 429 F.2d 364 (8th Cir. 1970).
