Simple Substitution.
A method of obtaining a resistance equal to that of a standard. The
standard is put in circuit with a galvanometer and the deflection is
noted. For the standard another wire is substituted and its length
altered until the same deflection is produced. The two resistances are
then evidently identical. The standard can be again substituted to
confirm the result.
Sine Curve.
If we imagine a point moved back and forth synchronously with a
pendulum, and if such point made a mark upon paper, it would trace the
same line over and over again. If now the paper were drawn steadily
along at right angles to the line of motion of the point, then the point
would trace upon it a line like the profile of a wave. Such line is a
sine curve. It derives its name from the following construction. Let a
straight line be drawn, and laid off in fractions, such as degrees, of
the perimeter of a circle of given diameter. Then on each division of
the line let a perpendicular be erected equal in height to the sine of
the angle of the circle corresponding to that division; then if the
extremities of such lines be united by a curve such curve will be a sine
curve.
In such a curve the abscissas are proportional to the times, while the
ordinates are proportional to the sines of angles, which angles are
themselves proportional to the times. The ordinates pass through
positive and negative values alternately, while the abscissas are always
positive.
Any number of sine curves can be constructed by varying the diameter of
the original circle, or by giving to the abscissas a value which is a
multiple of the true length of the divisions of circle. If the pendulum
method of construction were used this would be attained by giving a
greater or less velocity to the paper as drawn under the pendulum.