The species of Linnaeus were supposed to represent a series of steps in a scale of ascending complexity, and it was thought possible thus to arrange the animal kingdom in a single series - the orders within the classes succeeding one another in regular gradation, and the classes succeeding one another in a similar rectilinear progression.

The investigation of caustics, being based on the assumption of the rectilinear propagation of light, and the validity of the experimental laws of reflection and refraction, is essentially of a geometrical nature, and as such it attracted the attention of the mathematicians of the 17th and succeeding centuries, more notably John Bernoulli, G.

That this is actually the case is proved by experiments on the interference of polarized light, from which it may be deduced that the polarization-vector of a train of plane waves of plane polarized light executes rectilinear vibrations in the plane of the waves.

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The circles in the centre indicate a rectilinear series of indicate the five turns of the spiral, scales and two lateral secondand show the insertion of each of the ary spirals, one turning from leaves.

Atwood's published works, exclusive of papers contributed to the Philosophical Transactions, for one of which he obtained the Copley medal, are as follows: - Analysis of a Course of Lectures on the Principles of Natural Philosophy (Cambridge, 1784); Treatise on the Rectilinear Motion and Rotation of Bodies (Cambridge, 1784), which gives some interesting experiments, by means of which mechanical truths can be ocularly exhibited and demonstrated, and describes the machine, since called by Atwood's name, for verifying experimentally the laws of simple acceleration of motion; Review of the Statutes and Ordinances of Assize which have been established in England from the 4th year of King John, 1202, to the 37th of his present Majesty (London, 1801), a work of some historical research; Dissertation on the Construction and Properties of Arches (London, 1801), with supplement, pt.

The telautograph is on a similar principle to the Cowper apparatus, the motion of the transmitting pencil or stylus used in writing being resolved by a system of levers into two component rectilinear motions, which are used to control and vary the currents in two distinct electrical circuits.

This we can only do by conceiving them as originally moving through intelligible space in rectilinear paths and with uniform velocities.

The next stage is geometrical mensuration, where geometrical methods are applied to determine the areas of plane rectilinear figures and the volumes of solids with plane faces.

It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an ellipse of very small eccentricity, and a true parabolic figure can thus be obtained.

The parallel motion known by his name is a three-bar linkage, which gives a very close approximation to exact rectilinear motion, but in spite of all his efforts he failed to devise one that produced absolutely true rectilinear motion.