What follows is based on section 5.2 of the Ph.D. thesis “The Alignment and Clustering of Quasars”, by Glyn George (1983).
N points are distributed randomly over a field
of area A. Around any given point, one
would expect to find, on average, in the distance range


The pivotal quasar forms one end of a candidate alignment. Each of these other quasars, in turn, will form the other end of a candidate alignment of length x. If an intermediate quasar falls within a distance p_{max} of the line joining the first two quasars, then it is in the acceptance zone shown here and the candidate alignment will be accepted. 
Having taken one point as the pivot and another as the far
end of the alignment, there are
We expect the number of alignments of “tolerance”
p < p_{max} and of span
Integrating over all values of the alignment span d
up to d_{max}, we obtain the number of
alignments expected around each point to be
Now we take each quasar in turn as the pivotal quasar and sum the expectations. However, each distinct alignment will be counted twice: once with the quasar at one end as the pivot, then again with the quasar at the other end as the pivot. We must therefore divide this sum by 2 in order to give the total number of alignments of distinct triples of points expected, E[n_{P}], in a field with periodic boundaries:
Let us now determine the boundary correction for the
L×L square, for which we assume
The square divides into three obvious regions, (centre, edges and corners), whose extent varies with the alignment span x. Elementary search annuli whose centres fall in
region (1) will lie entirely within the square
and will be unaffected by edge effects.
That is, C_{i} = the edgeeffects correction factor for region (i). 
In region (2), one of the four edges will cause some
of the search area to be lost, as shown here.
s is the distance from the centre of the
search annulus to the nearest edge of the square and
x is the inner radius of the annulus.
Let A(s) be the proportion of the search
area remaining inside the field. Then, using the
notation in this figure, Recalling that the search area is an elementary annulus, we have The probability of finding a randomly placed point in
the range 
For a given span x, the mean proportion of area
remaining in a search area placed at random in region (2)
is
Therefore, in region (2),
In region (3), part of the elementary search area will be
lost over two of the four edges.
s is the distance from the centre of the
search annulus to the nearer vertical edge of the square,
t is the distance from the centre of the
search annulus to the nearer horizontal edge of the square and
x is the inner radius of the annulus.
Let A(s, t) be the proportion
of the search area remaining inside the field.
Then, using the notation in this figure, 
The probability of finding a randomly placed point in the
range
For a given span x, the mean proportion of area
remaining in a search area placed at random in region (3)
is
Therefore, in region (3),
Bringing the correction factors for the three regions together, we arrive at the overall correction factor C(x) for edge effects on an alignment of span x:
ThereforeAt the start of the derivation of E[n_{P}],
we replace
by
With this amendment, we proceed as before, to obtain
For the standard 5°×5° field in the thesis, with L = 5°, d_{max} = 1° and p_{max} = 30" , we have
and
E[n_{F}] = 0.8156 × E[n_{P}] = 2.2775×10^{–5} N (N – 1) (N – 2)
In the thesis, these expressions were verified by MonteCarlo simulations and by comparison with the few published works available at that time.