ON THE METHOD OF LEAST SQUARES. 21 



Consequently 



pdu = 



Now by Fourier's theorem 

 A "-A*tC---A 



= i f "k ( 



^ '- 



cos a 



which, replacing by a, becomes 



/M^r",. _cosa(--2/*)<fcu. 



r r 



I da i. . 



Therefore 



7 /i n 6?6 n r 7 r +o 7 r + 



lu = -^-\ dx de L ... 



" J f\ <* m > rr 



Now if w and e w are to vary together 



Jw = -tc?6 and therefore 



-| ! 00 / +00 / +00 



^ = 1 c^a J^... I d6 n <f> 1 e l ...<j) n n cosa(u-2,}j,6) ...... (5). 



I? J J -ao J -oo 



Arid finally, 



1 r+i r r +co r +0 



P=_| du\ da.} de...\ . d n 6 l 1 ...6 n 



7Tj_l J ^-oo /- 



Now let us suppose that equal positive and negative errors 

 are equally probable. In this case $e = (( e), and conse- 



quently, 



,* 



I $e sin apede = 0. 



J -oo 



Hence (6) will become 



2 rz / /+ r + * 



=- c?w cosaw^a ^ cos dfju l ede l . . . </> n 



TTJo Jo J-oo *- 



