June 20, 1895] 



NA TURE 



175 



The extreme irregularity of the frequency of the different 

 terms of imprisonment forces itself on the attention. It 

 is impossible to believe that a judicial system acts fairly, 

 which, when it allots only 20 sentences to 6 years im- 

 prisonment, allots as many as 240 to 5 years, as few as 60 

 to 4 years, and as many as 360 to 3 years. Or that, 

 while there are 20 sentences to 19 months, there should 

 be 300 to 18, none to 17, 30 to 16, and 150 to 15. The 

 terms of weeks are distributed just as irregularly. Runs 

 of figures like these testify to some powerful cause of 

 disturbance which interferes with the orderly distribution 

 of punishment in conformity with penal deserts. 



On examining the diagram we are struck with the 

 apparent facility of drawing a smooth curve, that shall 

 cut off as much from the hill-tops of the irregular trace 

 as will fill their adjacent valleys. This has been done, 

 by eye, in the diagram, the small circles indicating the 

 smoothed values. Care has been taken that the sums of 

 the ordinates drawn to the smooth curves should be equal 

 to sums of those drawn to the traces, as is shown by the 

 totals in the bottom line of Table I. The smoothed 

 curves may therefore be accepted as an approximate 

 rendering of the general drift of the intentions of the 

 judges as a whole, and show that the sentences passed 



by them severally, ought to be made more appropriate 

 to the penal deserts of the prisoners than they are at 

 present. The steep sweeps of the cur\es afford a 

 strong testimony to the discriminative capacity of the 

 judges, for if their discrimination had been //// and the 

 sentences given at random, those steep curves would be 

 replaced by horizontal lines. We have now to discuss 

 the disturbing cause or causes that stand in the way of 

 appropriate sentences. 



The terms of imprisonment that are most frequently 

 awarded, fall into rhytlimic series. Beginning with the 

 sentences reckoned in months, we see that their maxima 

 of frequency arc at 3, 6, 9, 12, 15, and iS months, which 

 are separated from one another by the uniform inter\al 

 of 3 months, or a quarter of a year — a round figure that 

 must commend itself to the judge by its simplicity. 

 And we may in conscciuence be pretty sure that if the 

 year had happened to be divided into 10 periods instead 

 of 12, the exact equivalent of 3 months, which would 

 then have been 2i periods, would not have been used 

 in its place. If this supposition be correct, the same 

 penal deserts would have been treated differently to what 

 they arc now. 



Thus the precise position of the maxima has been 



NO. 1338, VOL. 52] 



apparently determined by numerical fancy, and it seems 

 that the irregularity of the trace is mainly due to the 

 award of sentences being usually in terms of the 

 3-monthly, but sometimes in that of the 1 -monthly, series. 

 The trustworthiness of this solution is tested by group- 

 ing the entries in sets of three, each set having one of the 

 maxima for its middle member, as shown in Table II. 

 (where, however, the first and last entries are perforce 

 limited to sets of two;. The agreement between the 

 recorded and the smoothed entries is now passably 

 good ; it would become somewhat closer if the smoothed 

 curve were revised by paying regard to the series of sets 

 of three, thereby taking facts into account that were 

 not utilised before. 



Table II. (derived from Table I.). 



This solution does not, however, account for all the 

 peculiarities of the irregular trace. For instance, in the 

 original table in the Blue-book, absolutely not a single 

 sentence of 17 months has been recorded, although 

 there are 32 sentences of 16 months, and 340 of 18. I 

 account for the absence of the number 17, by the un- 

 doubted fact that almost all persons have a disposition 

 to dwell upon certain numbers, and an indisposition to 

 use others, and that 1 7 is one of the latter. These curious 

 whimsies become conspicuous whenever calculators, who 

 are not forewarned, are set to record long series of measures, 

 entering them by estimation to the nearest decimal of the 

 divisions of the scale they use. Each figure from o to 9, 

 in the decimal place, ought then to occur with equal fre- 

 quency, but they never do ; there is always a run upon 

 some figures, while others are hardly, if ever, introduced. 

 The fancies in this respect of different persons differ 

 widely ; the biblical Jews, for e.xample, were fond of 40, 

 apparently employing it as a noun of indefinite multitude, 

 but it has no preferential use with us. On the other hand, 

 it is probable that a large and awkward prime number, 

 such as 17, would be generally in disfavour. 



As regards the sentences reckoned in years, they range 

 from 3 years upwards (those between 2 and 3 years being 

 here reckoned as 3 years, while those below 2 years are 

 reckoned, as above, in months). The maxima of fre- 

 quency in this group are at 3, 5, 7, and 10 years, showing 

 a tendency to a unit of 2 years at first, and then, presum- 

 ably guided by the habit of decimal notation, to jump 

 from 7 to 10. The bias due to decimal notation is 

 forcibly shown by some entries in the original table 

 which fall outside the limits of Table I. It there appears 

 that 7 sentences were awarded for 20 years, and 6 for 1 5 

 years, but absolutely none for the 4 intermediate years, 

 19, 18, 17, 16. It should be added that there were also 

 8 sentences for 14 and for 12 years respectively. Had 

 these appeared in Table I., they would have been entered 

 to their nearest tenths, that is as i in each case, but I 

 did not care to enlarge the table for the sake of including 

 these, comparatively few, additional cases. 



