336 



Mr. F. Y. Edgeworth on the 



table the first column represents degrees of the abscissa, mea- 

 suring each a tenth part of the Modulus. The remaining 



Modulus. 



Right Line. 



Parabola. 



First 



Exponential. 



Third 

 Exponential. 



o--i 











•1--2 



i 









•2--3 











•3--4 



m 





i 





•4--5 





i 





i 



•5--6 











■6--7 



i 





m 



m 



•7-*8 











•8-9 











•9-1 





m 









1-1-1 











11-1-2 



m 







1-2-1-3 





i 







columns show, for each of the rival curves, at which of those 

 degrees its critical points occur. Thus, in the second column 

 i opposite to the entry *l-*2 indicates that there is an inter- 

 section between the Right Line and the Probability- curve 

 at some point whose abscissa lies between a tenth and two 

 tenths of the Modulus. In the same column m indicates that, 

 somewhere between the points *3 and *4, the difference between 

 the ordinate of the Right Line and the Probability-curve 

 becomes a maximum. 



Having this clue, let us now examine the data of experience. 

 Let us take, as a first example, 470 observations (of the right 

 ascension of Sirius and Altair) made by Bradley, and discussed 

 by Bessel in his Fundamenta Astronomies (p. 20)*. We shall 

 first compare the fit of the rival curves in respect of some 

 selected ordinates, the points of comparison being determined 

 upon the principle above mentioned. 



We start with the datum (adopted from Bessel) that the 



* They are quoted by Chauvenet in his ' Manual of Astronomy/ and 

 also by Merriman in his ' Method of Least Squares/ 1885. 



