### Mean Separation Distance

This is a measure of how dispersed your name is.

The clearest way that I can think of to understand how to apply the formula is through the following example.

Consider 4 places (parishes, registration districts) A,B,C,D each with holders of your surname numbering 100, 50, 20, 10 repectively. Enter these numbers into the following grid, as well as entering a measurement of the distance of all the other places from each other (noted here as dBA,dCA ,dDA = distance of B,C, and D from A). This is represented in this case by the third, fourth anf fifth columns below.

Numbers | distA | distB | distC | |
---|---|---|---|---|

A | 100 | – | ||

B | 50 | 15 | – | |

C | 20 | 25 | 10 | – |

D | 10 | 30 | 7 | 5 |

######
Formula 1: The enumerator

(B x dBA) + (C x dCA) + (D x dDA) + (C x dCB) + (D x dDB) + (D x dDC) To enter the relevant numbers simply start at the red number 15 in the grid, and work down each column in turn (B x 15) + (C x 25) + (D x 30) + (C x 10) + (D x 7) + (D x 5)
By substitution of the nameholders in each place this completes to = 1870 |

This is known as the Total Separation Distance. This figure must now be divided by the Total of Separated Persons cited in the demoninator to result in a Mean Separation Distance of the name. The citiations will for every time the placenumber has been used in the first formula, but this time also including the surname number in place A.

Formula 2: The denominator = Total of Separated Persons

(A + B + C + D) + C + (D +D) = 100 + 50 + 20 + 10 + 20 + 10 + 10= 220 |

The Mean Separation Distance in this case is 1870/220 = **8.5 km**.

You might like to copy the grid and formulae into a spreadsheet and experiment with the numbers.

For example, if the distances remain the same , but the numbers in place A were much higher , say a concentration of 1000 (and not 100), the MSD would drop to 0.18.

If the numbers were equal (say 10) in each place, then the MSD= 13.14

If the numbers remain unaltered, but the distances from A are increased by 100km each, then the resulting MSD =106.22

And if the number of nameholders are the same, and the distance increased by 100 km, then the MSD=98.85

The above formula and example is after SchÃ¼rer (2004), but the exposition is mine.

I also would sort places first by highest surname density, and then take the raw numbers from that rank order.

It may be that one would need then only to input a relatively small selection to obtain a fairly good idea of the MSD .

A problem will be how to measure accurately (and in a consistent fashion) the distances between places, when those place are areal units, like parishes and registration districts. How does one determine what is the centroid of each is?

GenMap UJ has a tool to measure straightline distances between registration districts (but you will still have to guesstimate where the centroid is).

Historic Parishes of England and Wales Gazetteer [link no longer available] has the 6 figure OS grid reference of each parish. There may be freeware to measure distances between OS grid references? Otherwise the OS has a page on how to manually calculate distances between grid references. Or use a piece of string :-))

### Mean Separation Distance of the Place

The above allows you to compare the dispersion of 1 surname with another, but does not give one a national perspective of the relative dispersion of all names by place. To do so, one would have to feed all the MSD’s back into the original locations.

For example, in Parish A, has a total population of 90 people, comprising just 3 surnames (p,q,r) with occurrences of 16, 8, 3 and associated Mean Separation Distances (19, 16 and 6).

The MSD of the whole parish would then be calculated as:

p19 + q16 + r12/ total parish population

by substitution

(16 x 19) + (8 x 16) + (3 x 6)/90 = 304 + 128 +18/90 = 450/90= MSD of the parish = 5

This is a daunting exercise for anyone without access to large computing power, but it has been done by the University of Essex for each parish of England and Wales in the 1881 census, and the output plotted onto a map, and published in Local Population Studies no 72 (2004).

This map reveals certain broad belts of low separation distances.

- South Lancashire and West Riding of Yorkshire
- Cheshire, north Staffordshire and North-east Derbyshire
- Much of Sussex and south-west Kent

Surname density seems to cut across these areas: except that a core area of the South Lancashire seems to fit within the 1st belt. This seems to be an area of low surname density, in which the holders ramified greatly within the same region, as opposed say to North Wales, where the high migration to England co-existed with low surname density.