384 



Mr. E. C. Snow on Restricted Lines and 



When the deviations are measured in a direction perpen- 

 dicular to the plane, the equation to determine Y m (the least 

 sum of the squares of these deviations) is, by § 5 above, 



o, 



the determinant being reversed for convenience in evalua- 

 tion, i. e. 







114 



187 



244 



114 



28526 -Y w 



46801 



64160 



187 



46801 



76827 -V w 



105264 



244 



64160 



105264 



144311-V 



107501 VJL-r 19413930V m -f 191936824 = 0, 



giving 



Then 

 do: 



and 



where 



V m = 10*49664. 



lUfi 



lUfi 28515-5 46801 



187//, 46801 76816-5 



244//, 64160 105264 



244/* 



64160 



105264 



144301-5 



7 "10 7 



l i-~F> h— -"J—* h— — -i-i 



! 00 



^00 



rfo 



^00 



l v x + l 2 y + h z = 



is the equation of the required plane. Since only the ratios 

 of Z 1? l 2 , and Z 3 are required, it is sufficient to find d 10 , d 20> and 

 d 30 (each of which contains /iasa factor). When we find 

 these ratios we must divide each by {^4 l%+ Z§} 5 in order to 

 have the sum of their squares unity. In this way we find 

 the equation of the plane is 



'8843a- -4632y--0582r=0. 



(*) 



The deviations of the results given by the formulae (0), 

 (f), (f), and (<£) from the actual values are (the deviation 

 being positive when the formula gives a value greater than 

 the actual value) : — 



