152 REPORT— 1889. 



compared a correction must be made for this circumstance. We havft 



then : — 



^ , , . . 1 . • • Total No. of births in ?/ 



Population in w oc population m x X — — — — ; — , — "^- 



^ ./ i- x' rpQta^^ jSIo. of births m x 



Average birth-rate in ?/' 



Average birth-rate in x 



Now, the last-written fraction may on certain suppositions be deter- 

 mined by taking a measure of the variations in birth-rate (at one epoch 

 compared with another) in each of the observed districts, with due 

 attention to the varying size of the districts, the different importance (for 

 the purpose in hand) of these rates. In other words, if the districts ara 

 named a, b, &c., we may write 



Average birth-rate in y 



Average birth-rate in x 



Population of a in ?/ x birth-rate of a in i/ 



+ population of & in 7/ X birth-rate of & in ?/ -|- &c; 



Population of a in ?/ x birth-rate of fi in a; 



-1- population oi b in y x birth-rate of h in .r-h&c.-' 



This is the analogue of Mr. Bourne's method, in which it will be seen 

 that there is postulated a certain constayicy in the proportions between tho 

 population of each district to that of the others and of the lohole country. 



Suppose a writer had employed the proportions furnished by the yeau 

 1883 in order to determine the relation between the birth-rate of that 

 year and of the year 1865.^ He, in effect, postulates the constancy of 

 proportions (between the different districts and the whole country) to 

 prevail over that period. It is not open, then, to him to complain of 

 another writer who employs the proportions furnished by the year 1875 

 in order to compare the population for a series of years between 1865 

 and 1883. But, if the use of those proportions is admissible, then the sort 

 of verification which the writer of the vexed passage under review appears- 

 to expect was not to be expected. 



In short, given the hypothesis which has been hinted metaphorically 

 here, and stated explicitly above, the method which Mr. Bourne has pro- 

 pounded has no great advantage over the other methods. That hypo- 

 thesis not being given, Mr. Bourne's method, equally with the others, 

 falls. Of the varied ramifications of the problem he has occupied a 

 particular, and no doubt an eminent, branch. He cannot hope that this 

 particular branch should stand when the others have fallen. One can. 

 only bring them down by striking at the root of the whole reasoning. 



From this class of methods we shall now proceed to a substitute for 

 them, which has recently been proposed by Sir Rawson Rawson. 



Section V. 



Sir Rawson Rawson'' s Method. 



Sir Rawson Rawson's original method may be contemplated under 

 two aspects, according as the primary object is to measure variations in 

 the volume of trade or — our peculiar care — in the value of the monetary 



' Compare the general formulEe given above, p. 145. 

 2 Cf. Brit. Assoc. Rej). 1885, p. 865 et seq. 



