154 Prof. F. Y. Edgeworrh on the 



of the nature of an error of observation " (Phil. Mag. p. 347). 

 Whether we are arguing that the average of errors-of -obser- 

 vation, or that the errors themselves (as sums of contributory 

 elements), are normally distributed, in both cases., the peculiar 

 character of Probability must be postulated. 



In the sequel of the passage just quoted (Congress, p. 168) 

 Professor Sampson's treatment of the disregarded unknowns 

 appears somewhat peculiar. My interpretation of his formula 

 y = sinf for the frequency-function of an observation was, I 

 think, very natural (Phil. Mag. vol. xxxv. p. 431). But, of 

 course, I accept the explanation which he has given (Phil. Mag. 

 p. 351) : " All values within the limits ± a would be equally 

 likely, and that is what the frequency-graph described would 

 imply " *. Yet I fail to see in what, respect this conception 

 has any advantage over Laplace's theory. Laplace also in 

 the very first section of his path-breaking chapter (11) 

 supposes that all values between the limits -f a and — a 

 would be equally likely. Laplace believed that the value of 

 each observation occurred according to determinate laws t \- 

 but he did not profess to know what these laws were. 



I am encouraged to surmise that nothing very paradoxical 

 is intended by the passage just quoted illustrating one of the 

 points for which novelty is claimed (Phil. Mag. p. 350), when 

 I consider the passages relating to., another point. Here, 

 too, there occur difficulties of interpretation. They are 

 largely due, I dare say, to the obtuseness of the interpreter,. 

 Yet the author has candidly taken to himself blame for 

 having thrown out collaterally one misleading statement 

 (Congress, p. 170 : Phil. Mag. p. 347). It is not the only 

 puzzling statement in the context. What are we to think of 

 the two statements with respect to the reproduction of form 

 (by the superposition of two functions of the same form) 

 made on the same page? (Congress, p. 170) : — " So far as I 

 can determine it, (reproduction) belongs with any generality 

 only' to the functions exp(a') and exp(a? 3 ) " (sic) ; and a few 

 lines below, "it will suffice to show that exp( — /r.r) and, of 

 course, also (exp — h 2 ,v' 2 ) cos (k.r + y) reproduce themselves.'' 



* The explanation continues (loc. cif.) : " If then we suppose that 

 errors are not of mysterious character, sui generis, but are simply the 

 mass of numberless neglected disturbances, each according to regular 

 law and order of its own, it is seen that we obtain the approximation to 

 Gauss's law which is necessary to begin with by the operation of neglecting 

 the circumstances and order of their origin and scheduling merely in 

 sequence of magnitude the number of times that each particular value 

 occurs.'' 



t The determinism of Laplace has often been noticed, especially by 

 Renouvier, JEssais de Critique generate. 



