It may be shown to be the locus of the vertex of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.
Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to BC and through the corresponding points on the radius AB.
It has now been firmly established, both experimentally and mathematically, that coronae are due to diffraction by the minute particles of moisture and dust suspended in the atmosphere, and the radii of the rings depend on the size of the diffracting particles.
With increase of speeds this matter has become important as an element of comfort in passenger traffic. As a first approximation, the centre-line of a railway may be plotted out as a number of portions of circles, with intervening straight tangents connecting them, when the abruptness of the changes of direction will depend on the radii of the circular portions.
He investigated the optical constants of the eye, measured by his invention, the ophthalmometer, the radii of curvature of the crystalline lens for near and far vision, explained the mechanism of accommodation by which the eye can focus within certain limits, discussed the phenomena of colour vision, and gave a luminous account of the movements of the eyeballs so as to secure single vision with two eyes.
Since e is a line of insensible magnitude compared with the dimensions of the mass of liquid and the principal radii of curvature of its surface, the volume of the shell whose surface is S and thickness will be and that of the interior space will be V - SE.
An epicycloid in which the radii of the fixed and rolling circles are equal.
The longitudes, latitudes and radii vectores of a planet, being algebraically expressed as the sum of an infinite periodic series of the kind we have been describing, it follows that the problem of finding their co-ordinates at any moment is solved by computing these expressions.
It is the envelope of circles described on the central radii of an ellipse as diameters.
The resistance to motion round a curve has not been so systematically studied that any definite rule can be formulated applicable to all classes of rolling stock and all radii of curves.