Annex D

Estimated Net Out-Migration from Ayr, Angus, Fife, Lanarkshire, 1755–1790s

The level of migration into or out of any given area over a specific time period can only be accurately calculated if four vital statistics are known: the population levels at the start and end of the period, and the numbers of both births and deaths. The difference between the latter two reveals the natural rate of increase, while the difference between the two successive censuses give the actual change in population level. By subtracting the natural increase from the actual population change a crude measure of the level of net in- or out-migration becomes apparent. However, variations in both nuptiality and fertility ratios can mean that gains and losses may imply other consequences than simply rates of human mobility.

Demographic data for the eighteenth century are sparse by comparison with later periods. On a national scale and prior to the first national census of 1801, only the Webster enumeration of 1755 and that of the OSA in the 1790s are of any use to the historian in this context. Unfortunately, however, there are no data on fertility and mortality rates for later-eighteenth-century Scotland comparable to those of enumeration. Thus, to even approximately measure the scale of migration, it becomes necessary to estimate the rate of natural increase. This has been done here by using the crude national average rate of population increase of 6 per cent per decade or 0.6 per cent per annum.

Table 1 below together with Tables A–D provide population counts for the four counties at the two periods followed by the actual change in numbers. The estimated percentage multipliers on the county sheets are arrived at for each parish by multiplying the assumed national percentage yearly rise of population (i.e. 0.6 per cent) of the appropriate number of years between the two population counts. For example, a parish which gave 1790 as the date of its OSA report would have an estimated multiplier of 35 × 0.6 per cent or 21.0 per cent. Thus, with this estimated natural increase, the estimated level of net in- or out-migration is deduced as described above and the figure can then be expressed as a percentage of the original population level of 1755. The estimated mean percentage multiplier for each county, as indicated in Table 1, is simply the average figure calculated from the total of those multipliers of each parish as shown on the tables for each county in Tables A–D. It should be borne in mind, however, that local variation in both nuptiality and fertility could affect these figures.

Table 1 Estimated net out-migration from the four counties, 1755–1790s

To move beyond the generalized picture, a migration factor analysis was conducted. From the OSA reports, four independent factors were examined which might have influenced migration at the parish level. These were: reduction of cottar numbers, industrial presence, farm consolidation and the presence of villages or towns. This exercise deals in the numbers and percentages of parishes in the four counties examined, not those of population as such. In other words, the importance of a specific factor, and its impact on population movements, is not gauged here by the actual size of the estimated migration flows but by the number of cases of parishes demonstrating this coincidence of presumed cause and effect. For example, the absence of some kind of industrial presence was associated with out-migration in 33.3 per cent of the forty-five Ayrshire parishes analysed, but this does not imply that the lack of some kind of industry accounted for one third of out-migration from Ayrshire parishes.

Tables 2 and 3 lay out the numerical and percentage results of the single (and in some cases) combined factor analysis for the three counties. As can be seen, it is divided into two main sections: those parishes demonstrating net out-migration and those demonstrating net in-migration. These two groups were isolated in turn from the database and then checked against the individual factors laid out in the left-hand column. For each of the two groups in each county the actual number of parishes with the particular factor present is given in the first column and this figure is then expressed as a percentage of the total number of parishes.

It should be noted that in all four counties the denominator used to calculate percentages is slightly less than the actual total number of parishes because, in a few cases, there were no usable data given in the OSA. Note also that only where a particular factor, such as industrial presence, was indicated in the parish account can the result be relied upon, since it is possible that in some cases other factors – assumed here to be absent – were simply not mentioned in the OSA reports.

These results shown in Tables 2 and 3 give some indication of the explanatory power of the various factors vis-à-vis the in- or out-flows of population since they outline the percentage of parishes in which the specific and presumed causes and effects were associated with each other.

Table 2 Estimated migration in the shires of Ayr, Angus and Fife, 1755–1790s: factor analysis

Tables 4 and 5 attempt to extend this analysis further by combining the results of both sides of a particular hypothesis. If it is assumed that in this period the absence of an ‘industrial presence’ from a parish would have acted as a ‘push’ factor and that, conversely, the existence of some kind of industry would have functioned as a ‘pull’, then in Ayrshire, for instance, this total hypothesis is supported by the results from 66.6 per cent of parishes, and so on. However, given the caveat entered above on the reliability of presumed ‘negative’ evidence, the hypotheses built into the ‘migration’ figures, the results of this exercise must be treated with caution. Nevertheless, both the factor and combined-factor analysis indicate a broadly similar result. The existence or reduction of the cottar class was not associated in more than about one fifth of Ayr, Angus and Fife parishes with a static or increasing population on the one hand or a decreasing population on the other. Only the Lanarkshire figures marginally rise above this average. On the other hand, the industrial village/town and consolidation variables ranked very much higher as factors associated with mobility. This short statistical exercise suggests that the results of cottar displacement were far from simple.

Table 3 Estimated migration in the shire of Lanark, 1755–1790s: factor analysis

Table 4 Estimated migration in the shires of Ayr, Angus and Fife, 1755–1790s: combined factor analysis

Table 5 Estimated migration in the shire of Lanark, 1755–1790s: combined factor analysis

Table A Estimated net out-migration from Lanarkshire parishes, 1755–1790s

Table B Estimated net out-migration from Angus parishes, 1755–1790s

Table C Estimated net out-migration from Fife parishes, 1755–1790s

Table D Estimated net out-migration from Ayrshire parishes, 1755–1790s