4 On thc Sy.stematic Fitting of Ciirves 



Now l is 9'5 ; hence the centre of thc normal curve is at "1425 beyond the 

 Start of the ränge wliii-li is 29 secs., i.e. 2S-8Ö75 secs. is the modal speed of the 

 group of trotters. 



If the normal curve bc 



y = z„e 





Whence we find 



and ultimately 



1 = log 2/ = log z, - ^^/ löge. 



log5„= 1-441,:31() X 1-300,583, 



2<7= = 



/-'löge 



l-441,31(Jx-27(i,G14' 



^0 = 9-14176, 0- = 7011,073. 



Thus thc requircd normal curve is 



2/ = i)14l70e-5-'''('''"-ö'-'')'. 



The "probable error" corresponding to the above valuc of o- is 4"7289, which 

 enables us to compare our resuits directly with Mr Galton's numbers. 



Likc Mr Galton wo have omitted from considcratioii the group of horses 

 with spceds betwccn 29 and 30 secs., for it incltidos a large nuniber of doubtful 

 trotters, whose speed is aliowod by grace to fall within the 30-second limit. 



The following are the actual determinations for four years of the 'centre' and 

 variability of American trotters. They are coini)arcd with Mr Galton's determina- 

 tions by inspection of the 'centre' and his calculatiou from this of the probable 

 error by quai'tiles. 



