454 



PRACTICAL MATHEMATICS 



point it will be necessary to find the values of x, y, and s ; the value 

 of .9 can be found by drawing the tangent to the curve at the point 

 and measuring its slope in the usual way. When a sufficient number 

 of values has been obtained, plot the following three curves on the 

 same sheet of squared paper, so adjusting the scales that the curves 

 practically cover the same space. 



Curve I. y vertically, xs horizontally ; for the law y = a + bx n . 



11 

 Curve II. - vertically, x horizontally ; for the law y = b (x + a) n . 



S 



Curve III. y vertically, .9 horizontally ; for the law y = a + be. 



Then select the curve which most nearly approaches a straight 

 line, and this will indicate the most suitable law. 



This method is open to the objection that there is no way of 

 drawing the correct tangent to a curve, but, if reasonable care is 

 taken in drawing the tangent, the errors should not be great enough 

 to make the discrimination impossible. 



221. Example. The following values of x and y give a number 

 of points on a curve obtained by bending a thin spline of wood. 

 Find the law of the curve. 



The curve was drawn to a large scale on a sheet of drawing paper, 

 tangents drawn to the curve at the above points, and the values of 

 the slope determined. 



Tabulating the results 



