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A typical breast cancer, for example, will have 10 to 20 chromosome aberrations.

Consider the aberrations which may arise from the representation by a system of wide aperture with monochromatic light, i.e.

Once grant the above definition of disease, and even the most trivial aberrations from the normal must be regarded as diseased conditions, quite irrespective of whether, when structural, they interfere with the function of the part or not.

The aberrations can also be expressed by means of the "characteristic function " of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order.

If, in the first place, monochromatic aberrations be neglected - in other words, the Gaussian theory be accepted - then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction.