68 SCIENTIFIC APPARATUS. 



circle, a curve having various properties in relation to two internal 

 points or foci, which replace as it were the one centre of a circle. 

 In the case of the ellipse described by a planet, the sun is in one 

 of these foci ; in the case of the moon, the earth is one focus. So 

 much for the geometrical description of the motion. Kepler 

 further observed that a line drawn from the sun to a planet, or 

 from the earth to the moon, and supposed to move round with the 

 moving body, would sweep out equal areas in equal times. These 

 two laws, called Kepler's first and second laws, complete the 

 kinematic description of elliptic motion ; but to obtain formulae fit 

 for computation, it was necessary to calculate from these laws the 

 various harmonic components of the motion to and from the sun, 

 and round it ; this calculation has much occupied the attention of 

 mathematicians. 



The laws of rotatory motion of rigid bodies are somewhat 

 difficult to describe without mathematical symbols, but they are 

 thoroughly known. Examples of them are given by the apparatus 

 called a gyroscope, and the motion of the earth ; and an applica- 

 tion of the former to prove the nature of the latter, made by 

 Foucault, is one of the most beautiful experiments belonging 

 entirely to dynamics. 



Rotation. Next in simplicity after the translation of a rigid body, 

 come two kinds of motion which are at first sight very different, 

 but between which a closer observation discovers very striking ana- 

 logies. These are the motion of rotation about a fixed point, and 

 the motion of sliding on a fixed plane. The first of these is most 

 easily produced in practice by what is well known as a ball-and- 

 socket joint ; that is to say, a body ending in a portion of a 

 spherical surface which can move about in a spherical cavity of 

 the same size. The centre of the spherical surface is then a fixed 

 point, and the motion is reduced to the sliding of one sphere 

 inside another. In the same way, if we consider, for instance, the 

 motion of a flat-iron on an ironing-board, we may see that this is 

 not a pure translation, for the iron is frequently turned round as 



