208 On the Numerical Changes of the 



To give a more perfect idea of the great fluctuations which the 

 three established divisions of the English population have under- 

 o-one during the period under consideration, is the object of 

 plate VII. The lines ab, a'b', a"b", may be regarded as lines 

 passing through zero, or a common origin, and to which all the 

 changes indicated in the preceding tables are referred. Those 

 portions of the waving lines above those which denote the common 

 origin of the changes, represent the counties distinguished by in- 

 crements ; and those below, the different decrements. The sums 

 of the lines indicating the changes for each county, must obviously 

 amount to the same constant quantity. The counties are arranged 

 alphabetically, and not in the order in which they are recorded in 

 the tables. 



By contrasting the lines denoting the different changes with 

 each other, it will be immediately seen how one is, in some mea- 

 sure, regulated by the other ; how, for example, if a county as 

 Cumberland, has -positive changes in the second and third divisions 

 of its population; how the class of agriculturists is immediately 

 distinguished by a negative change, equal to the sum of the pre- 

 ceding; or how, if like Monmouth, the first and second classes are 

 contrasted, and their variations are of an opposite kind, how the 

 third class undergoes a change, equal to the difference of the two ; 

 partaking of a positive or negative character, according to the na- 

 ture of the greater. The maximum increments and decrements are 

 also clearly displayed in it; and likewise those counties in which 

 the changes of their population have been the least. 



In Wales it will be observed, that with the exception of Cardigan, 

 the agricultural population of all the counties has diminished ; and 

 it is also remarkable, that the decrements in general are superior 

 in magnitude to those of England. The numerical results also for 

 the unproductive labourers in all the counties, excepting Flint, 

 have signs precisely the reverse of those attached to the class of 

 agriculture ; proving that the former counties have gained acces- 

 sions, partly, at least, from the latter. Cardigan having increased 

 both its agricultural and manufacturing population, has diminished 

 its unproductive members. Carmarthen, on the contrary, has 





