306 Mr. F. Y. Edgeworth on tlie Law of Error. 
absence of evidence to the contrary, that non-exponential laws 
of error of the kind considered in example 2 do occur in rerum 
naturd, that the u ancient solitary reign " of the exponential 
law of error should come to an end, and that the received for- 
mula for the probable error of the average requires modifi- 
cation. 
This conclusion will be best confirmed by considering the 
objections which may be brought against it. 
(1) There is, first, the direct appeal to experience — to regis- 
ters of observations, such as Airy has appended to his treatise. 
I find that there is no difficulty in ranging under a curve of 
the form v the observations which are registered 
by Airy, or those which are given under the article "Moyenne" 
in the ' Medical Cyclopaedia.' Quetelet's statistics of conscripts 
may be less accommodating; but the fact that the exponential 
law of error is verified in one case does not prove that it is 
universally true. 
In the sequel to this paper we shall be presented with an 
instance of a non-exponential form, if not in nature, at least 
in art — the art of measurement. The analogue in relation to 
the law of error of that incident of the method of least squares 
is the following: — Instead of the hypothesis with which we 
started*, of determinate elemental facility-curves, suppose a 
source of error consisting of a probability-curve with centre 
fixed but modulus varying at random between certain limits. 
Let there be taken an indefinite number of couples (or, mutatis 
mutandis, triplets &c.) of observations. Select all the couples 
which have the same difference, say b. Then the law of error for 
the mean of those couples is non-exponential. I do not know, 
however, that this method of selective generation has any exist- 
ence outside the sphere of art; and I notice it here chiefly for the 
interest of the hypothesis of elements with varying modulus, 
which in general leads to an (elemental) facility-function, not 
indeed with finite mean powers, yet unfamiliar — for instance, 
not at first sight included in the type given by DeMorgan 
(Encycl. Metrop. § 88). 
(2) An appeal may be made to a less specific experience, 
namely the factf that groups of actual errors do possess finite 
mean powers. But here the premises relate to actual facility- 
curves, which have somehow, in coming into existence, lost the 
tails attached to them by theory. The conclusion relates to 
the tail of the typical ideal curve. It would be equally easy, 
in the case of the orthodox curve, to name caudal properties 
* Above, page 301. 
t Cf. the passage in DeMorgan 's article just quoted. 
