Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/370

338 part of the motion of another point which moves with uniform angular velocity in a logarithmic spiral.

733.] The equation of the spiral is

To determine the horizontal motion, we put where $$a$$ is the value of $$x$$ for the point of equilibrium.

If we draw $$BSD$$ making an angle $$\alpha$$ with the vertical, then the tangents $$BX$$, $$DY$$, $$GZ$$, &c. will be vertical, and $$X$$, $$Y$$, $$Z$$, &c. will be the extremities of successive oscillations.

734.] The observations which are made on vibrating bodies are—

The quantities which we have to determine are—

735.] Let $$x_1$$, $$x_2$$, $$x_3$$ be the observed scale-readings, corresponding to the elongations $$X$$, $$Y$$, $$Z$$, and let $$a$$ be the reading at the position of equilibrium, $$S$$, and let $$r_1$$ be the value of $$SB$$,

From these values we find

When $$x_3$$ does not differ much from $$x_1$$ we may use as an approximate formula