SECT. 6.] Arrangement and Formation of the Series. 31 



of observations of a somewhat similar character have been 

 already referred to as collected and arranged by Quetelet. 

 From the nature of the case, however, there are not many 

 appropriate ones at hand; for when our object is, not to 

 illustrate a law which can be otherwise proved, but to 

 obtain actual direct proof of it, the collection of observations 

 and measurements ought to be made upon such a large 

 scale as to deter any but the most persevering computers 

 from undergoing the requisite labour. Some of the remarks 

 made in the course of the note on the opposite page will 

 serve to illustrate the difficulties which would lie in the way 

 of such a mode of proof. 



We are speaking here, it must be understood, only of 

 symmetrical curves : if there is asymmetry, i.e. if the Law of 

 Error is different on different sides of the mean, a com 

 paratively very small number of observations would suffice 

 to detect the fact. But, granted symmetry and rapid 

 decrease of frequency on each side of the mean, we could 

 generally select some one species of the exponential curve 

 which should pretty closely represent our statistics in the 

 neighbourhood of the mean. That is, where the statistics are 

 numerous we could secure agreement ; and where we could 

 not secure agreement the statistics would be comparatively 

 so scarce that we should have to continue the observations 

 for a very long time in order to prove the disagreement. 



6. Allowing the various statistics such credit as they 

 deserve, for their extent, appropriateness, accuracy and so 

 on, the general conclusion which will on the whole be drawn 

 by almost every one who takes the trouble to consult them, 

 is that they do, in large part, conform approximately to one 

 type or law, at any rate for all except the extreme values. 

 So much as this must be fully admitted. But that they do 

 not, indeed we may say that they cannot, always do so in 



