666 



Prof. Karl Pearson on a General 



and striking circles with a pair of compasses, the folio wing- 

 circles were found without difficulty to give moderately 

 close fits : 



( x --2-Zy- + ( y -oy=(-2-i)\ 



(* 1 -2-3)»+(y l + -3)»=(2-4)», 



(,. 2 _ 2 -7) 2 +(y, + -8) 2 =(2-8)--', 

 (* 3 _2-4) 2 +(y 3 V7) i! =(2-r>)*. 



Here there are three constants 7t , £ , and r , the coordinates 

 of the centre and the radius, to be found. 



We have at once, using the first circle as a reference-circle : 



A 2 A=*5. 



A 2 &=--8, 



A,r=-3. 



The following are the ordinates found from the four circles : 





Observed. 



Reference Circle. 



Circle!. 



Circle 11. 



Circle III. 



.r=0 .. 











•386 



-■058 







x=l .. 



15 



1-844 



1-717 



1425 



1-371 



x=2 



1-8 



2191 



2-081 



1911 



1-708 



x=S .. 



2-0 



2049 



1-990 



1-984 



1-727 



.r=:4 .. 



1-5 



1-266 



1-394 



1-680 



1-221 



The ordinates show, what was indeed the fact, that our 

 trials were rough, i. e. 9 made without any attempt at great 

 exactitude ; actually they were four out of the first five 

 circles struck. "We now form the differences of the ordinates 

 and have : 





yo-y- 







Vx-y- 



y-r-y- 



y 3 ~y- 



x=0 



•386 



—•058 







x=l 



-•344 



-127 



—•419 



-473 



x=2 



-•391 



-•110 



•-•280 



-•423 



*=3 



-•049 



-053 



-065 



- -322 





+ •235 



+ •129 



+ •415 



-044 



From these we find at once by straightforward arithmetic 

 a f = -25645, <r, = '19833, <r 2 =-29462, o- 3 = :-31S83 ; 

 and fairly easily by using Crelle's Tables : 



i- 01 = -470,334, ?' 02 = -937,925, ^ ='815,868, ' 



• 23 = -679,835, 



■ 31 = -373,191 J 



= •403,317. 



