230 KEPORT— 1888. 



Another illustration may make this point clearer. Suppose that we took 700 

 hexameters from the '^neid,' not en bloc from one or two books, as described in the 

 papers referred to, but by a perfectly random process from the whole poem indis- 

 criminately. Suppose (as is likely enough) that these samples being examined 

 should yield the same modulus for the proportion of dactyls as was afforded by the 

 actual specimens examined by the writer : namely '3 (for lines of four feet, the 

 almost unvarying last two feet of the hexameter being left out of account"). In 

 this case we may be fairly certain that the proportion of dactyls presented by the 

 sample, say '4, will not ditfer from the proportion in the whole ' ^neid ' by more 



.o 



than 3 x , say '035. He who carefully considers the verifications adduced 



V7U0 

 in the second of the papers referred to caimot reasonably doubt this proportion, or, 

 rather, will not feel more than the theoretical degree of uncertainty about it.' 



But when, as in the actual statistics to which reference has been made, the 

 specimens have not been selected with indiscriminate impartiality, then the induc- 

 tive hazard in inferring from a part to the whole becomes more serious. Even 

 then, however, the inference may be sufficiently safe if inspection has convinced us- 

 of the general homogeneity of the total aggregate concerning which we wish to 

 draw a conclusion. The 700 Virgilian lines examined by the writer, though far 

 from being perfect samples, seem still to justify an inference as to the constitution 

 of the whole '^neid.' There being in the whole poem some 9,900 lines, it is reason- 

 ably certain that a superior limit to number of dactyls in the '^neid ' is given by 

 the followuig formula, in which account is taken of the Jifth foot and of the 

 unfinished lines ; whose number we shall call n. 



Total number of dactyls in the '^Eneid ' is less than 



.o 



4(9900 — n)( '4 + 3 . — \ + number of dactj-ls in the n unfinished lines- 



+ (9900 — n — number of spondaic lines). 



We ought similarly to test the validity of the ratio which constitutes 

 the foundation of the Jevonian argument. We should break up the 

 aggregate of samples into some fifty parcels, observe the ratio for each 

 batch, and thence extricate the necessary coefBcient. Of course it would 

 be desirable to employ judgment in testing the worth of our result. We 

 might notice, for instance, whether the modulus derived from one half 

 our samples was much the same as that which the other half yielded. 

 We should observe whether the modulus for batches of 4,000 is as much 

 less as it ought to be than the modulus found for batches of 2,000. Such 

 inspections intelligently performed would suggest to what extent the- 

 general rule above exemplified might require some relaxation iu view of 

 the specially loose character of our materials. 



We shall thus determine the utmost extent of error whicli we are likely 



to commit in putting the observed ratio 



Number of samples bearing a certain date / Sj \ 



Total number of samjjles \ ^ S / 



. Number of coins of that date in circulation 



for the (unknown) ratio m"rr"i — ■ 1^ 



^ ^ iotal circulation 



Call this maximum of error (which may be either in excess or defect) 

 X. By means of this datum we can correct the superior limit (to the 

 circulation) obtained lately. 



That superior limit, it may be recollected, was — 

 Total number of samples 



Number of samples bearing a certain (recent) date 



X coins issued 



' One source of uncertainty is that the determination of the modulus from a 

 limited number of observations is liable to a certain error. 



