378 Mr. E. C. Snow on Restricted Lines and 



to express a relationship between the percentage of carbon 

 present and the solidifying point of the alloy should 

 pass through the fixed point (0 %, 1505° C). Up to 

 2 % °f carbon a straight line seems to be the most likely 

 fit. The two methods will therefore be applied to get a line 

 to pass through the point (0 %, 1505° C.) and to fit the 

 series of observations. It will be seen from the figure that 

 up to a percentage of carbon of 0*5 % * ne results are ir- 

 regular, but from that point up to 2 % the ^irregularities 

 are small and within the limits of experimental error. 



Measuring x positively from zero and y negatively from 

 1505, we find 



S(.r') = 19-0176, 

 $>{xy) = 3138-41, 

 SQ/ 2 ) = 624986. 



By the first method the equation of the line (measured 

 from 0%and 1505 c C.) is 



V = S o / f? • * or tf = 180-801*. 



The relationship between the temperature of solidification 

 and percentage of carbon present is therefore 



T= 1505- 180-801 x. 



If we apply the second method, we find 



tan0= - -0110035, 

 whence 



and 



f = 89° 41' 



tan f=181-80843, 



which gives the relationship 



T = 1505-181-808*. 



The actual temperatures obtained from the two formulae 

 are given in columns 3 and 4 of Table I. ^ We see that, to 

 the nearest degree, there is no difference in the results up 

 to 0*5 % o £ carbon, and the difference beyond that point 

 U small. The two lines cannot be distinguished on a diagram 

 of the size shown. The line OP in the diagram represents, 



