## Smithsonian Miscellaneous CollectionsSmithsonian Institution, 1925 - Science |

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angle animal appear approximation birds brown cave coefficients collection column complete computed convergent coördinates cos x cos² cosh curl curvature curve decimal places Denoted designs determinant differential equation direction elements elliptic equal Example expressed feathers figure Formula four functions given gives groups head House integral interval Island known Limit lower method Mimbres normal obtained origin Photograph plane polar positive pottery radius represents respect result roots shows side sin x sin² sinh SMITHSONIAN sn² solution Suppose surface Table tail taken tangent tanh transformation unit upper Valley values variable vector wings y₁

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Page 235 - I is encountered in its simplest form, not as the elliptic arc, but in the expression of the time in the pendulum motion of finite oscillation, unrestricted to the small invisible motion of elementary treatment. The compound pendulum, as of a clock, is replaced by its two equivalent particles, one at 0 in the centre of suspension, and the other at the centre of oscillation, P; the particles are adjusted so as to have the same total weight as the pendulum, the same centre of gravity at G, and the...

Page 201 - Society, 15, p. 40i, 1916. 9.9 References to Bessel Functions. Nielsen: Handbuch der Theorie der Cylinder Funktionen. Leipzig, 1904. The notation and definitions given by Nielsen have been adopted in the present collection of formulae. The only difference is that Nielsen uses an upper index, /-(*)> to denote the order, where the m<jre usual custom of writing /n(*) is here employed. In place of H\n and HI" used by Nielsen for the cylinder functions of the third kind, Hnl and Hn1\ are employed in this...

Page 60 - ... officially connected were in the field during the fiscal year, and only one of them is known to be still active. Nor has any been organized during the year except a botanical expedition which is about to start as the year closes. This expedition was made possible by a cooperative arrangement between the New York Botanical Garden, the Gray Herbarium of Harvard University, the Bureau of Plant Industry of the Department of Agriculture, and the National Museum, the latter's share consisting in allowing...

Page 77 - ... that have not yet been touched. The possibilities In this field are very great. The caverns of the Dordogne region are for the most part comparatively small, while those in the department of Arriege are immense caves of a most spectacular nature. Of the former class are the grottoes of Font du Gaume, Combarelles, La Mouthe, Marsoulas, Montesquieu, and others. Of the latter class are the immense caves in the neighborhood of Foix, as for example, Salignac, Ussat, and Niaux. The tunnel of Mas d'Azil...

Page 56 - The cosine and sine of the sum of any number of angles in terms of the sine and cosine of the angles are given by the real and imaginary parts of cos (*i + xt +. . . . + xn) + 2 sin (xi + x.

Page 5 - Any term may be obtained from the leading term : ann by keeping the first suffixes unchanged and permuting the second suffixes among i, 2, 3, . . . ., я. The sign of any term is determined by the number of inversions from the second suffixes of the leading term, being positive if there is an even number of inversions and negative if there is an odd number of inversions. 1.341 The coefficient of...

Page 152 - X is a function of x alone and Y is a function of y alone. Introducing Eq.(5.3) into Eq.(5.1), there follows d2X d2Y Y — - +X — - = 0 (5.4a) dx2 dy2 or separating the variables...