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THE SLOPE of a curve at any given point is repre- . In many physical chemical measuresented by d~ -d.r. ments the function, y = f ( x ) , cannot be determined dY IS . desired. In such instances y is directly but dx . determined by: plotted against x and dY - IS dx (1) Application of a straight edge to draw the tanAY can easily be obgent to the curve at the point x. Ax tained for this straight line. Various devices have been developed to draw the tangent more accurately.'

against x as chords. The smooth curve drawn through the midpoints* of these chords represents the slope for value of x. An examDle follows: AY -

Y

%

AX

1

2

4--2

.

2 - 1

2

x - -

4

3

3

9

4.5

15

Thus the slope at x

8-

=

2

-

7

3.5

-

9 - - 1 - 4 3.5 3 15 - 9 5-

2 3

-

3.2 is 3.9.

REFERENCES

DANIELS: Chaps. IX, XXI. LIPU: "Graphical and mechanical computation," John Wiley &Sons, New York City, 1918. LEWISAND RANDALL:"Thermodynamics and the free energy of chemical substances," McGraw-Hill Book Co., Inc., New York City, 1923, pp. 36, 266, 269-75.

7--

6.-

5.-

PROBLEMS

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