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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 Excerpt:...point, and are refracted at a surface of revolution about an axis through the point; to find an (aplanatic) surface which will refract them to a given point on the axis, i.e. to construct an aplanatic lens. Scholium. The above methods are applicable when the rays are refracted at more surfaces. In constructing optical instruments it is preferable to use only lenses whose surfaces are spherical, not only because they can be made more readily and accurately, but also because rays incident obliquely would be refracted to a point more accurately than by spheroidal lenses. It is chromatism, however, that is the real obstacle to perfecting practical optics, and unless the errors thence arising can be corrected, " labor omnis in caeteris corrigendis imperite " collocabitur." Book II. On The Motion Of Bodies In Eesisting Mediums. The second book is devoted to the discussion of the motion of bodies in resisting mediums. It is divided into nine sections as follows: Section I.--On the motion of bodies in a medium luhose resistance varies directly as the velocity. Prop. 1. If a body be resisted in the ratio of its velocity the momentum lost by the resistance is proportional to the space traversed. Lemma 1. Quantities proportional to their differences are continually proportional. That is, if a: a--b=b: b--c = c: c--d, etc., then a:b = b: cc: d, etc.: see lemma 2 of the tract Be Motu quoted above (p. 36). Prop. 2. If a body move under the action of no external force in a homogeneous medium whose resistance varies as the velocity, and the time of motion be divided into a number of equal intervals, then the velocities at the beginnings of those intervals are in a geometrical progression, and the spaces described in each of those intervals are as those veloc...