OUTLINES OF NATURAL PHILOSOPHY. 



Suppose, for example, that the formula 

 (121) sin x (65.5) sin 2# = */, 



was reduced into a table, and that by a compari- 

 son with observation, it was required to correct 

 the quantities 121, and 65.5, that is, A and B, 

 according to the former notation. 



Suppose also that the observations were made when 

 the values of x were 30, 4-5, 60, 75, 90, 105, 

 120 ; and that the errors in the Tables were in 

 these instances found to be -f- .3 1 8, .334-, .083, 

 + .04 4-, -f- 05, .021, .084; then, calling a an(J 

 b the corrections on A and B> we have 



.500 a + .866 b = + .318 

 .707 a + 1.000 b = .334 



.866 a + .866 b = .083 



.966 a + .500 b = + .044 



1.000 a + = + .05 



.966 > .5006 ;= .021 



.866 a .866 b = .084. 



By adding all these equations together, 

 5.971 a + 1.0766 = .299. 



Then, ordering all the seven original equations, so 

 that the terms involving b shall be affirmative, we 

 obtain 



2.207 a -f 4.598 b = + .1. 

 From these, a = .0527, and b = + .047^ 



This 



