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By Altshuller

The ebook is aimed to start with on the engineer. however it is usually understandable to those that don't paintings with expertise. the rules of controlling pondering within the resolution of artistic difficulties (the ideas and never concrete formulae and principles) might be transposed to the association of artistic pondering in any sphere of human a,ctivity. consequently, the e-book is acceptable for a large readership. it really is was hoping that between those that learn it there'll be a few who are looking to take it additional and interact themselves within the look for new sorts of the keep watch over of inventive pondering in know-how, technology, and artwork. What may be extra pleasing than the invention of the character of gifted idea and changing this pondering from occasional and fleeting flashes right into a strong and controllable hearth of data.

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U'2 = dl . N . u2 and this form of the equation enables us to determine the longitudinal magnification for any centred system, in close analogy with the same stage in the development of the theorem of Lagrange. For a first surface we shall have dl{ . N{ . u{2 = dl; . N l . u l 2, and for a second surface dl; . N; . u? = dl 2 • N 2 . u~. Obviously the axial image dt{ by the first surface acts as the axial object for the second, therefore dl{ ::::: d12; and as N{ ::::: N 2 and u{ ::::: U 2 by the fundamental conventions, the left of the first equation is identical with the right of the second; hence FUNDAMENTAL EQUATIONS 45 and it is evident that these arguments can be repeated any number of times, thus [19] leading to the general theorem of longitudinal magnification dl k .

For particularly erratic computers equation (7) supplies also by far the safest and surest check against errors caused by applying the refractive indices wrongly in the main calculation; such computers (who may be excellent designers in spite of their liability to numerical mistakes) will therefore be wise to adopt (7) instead of the simpler check depending on (6) as a regular part of their computing formulae. When (7) is used the V' for closing the standard calculation and for computing (5)** is of course determined as the starting value of V plus twice the value of t (1 - 1') obtained from (7) ; as in all optical calculations, the sign of all the quantities must be carefully watched.

Every computer therefore should be extremely careful in putting in the given quantities. Our optical formulae provide an ugly trap in this respect in the introduction of the refractive index which enters only once, namely in obtaining sin l' from sin I by equation (2). No one would doubt for a moment that the introduction of a wrong value of NfN' would necessarily lead to a wrong result which would nevertheless satisfy any check that could be applied to it, simply because the result so obtained is the right one for the indices actually used.

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