## Smithsonian Miscellaneous CollectionsSmithsonian Institution, 1925 - Science |

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a₁ absolutely convergent angle animal axes axial vector B. A. Report b₁ birds C₁ cave coefficients convergent convergent series coördinates cos² cosh coth curl curve decimal places Denoted determinant differential equation direction cosines dy dx elliptic functions elliptic integral feathers figure Formula g-table given hyperbolic Hyperbolic Functions interval o.1 Isolobodon Jahnke and Emde Jo(x kiva linear Mimbres Osborn collection particular integral perpendicular Photograph Pipe Shrine House plane polar positive integer Pueblo rectangular sin x sin² sinh SMITHSONIAN TABLES sn² solution surface tail tangent tanh Theorem uniformly convergent variable wwwww x₁ xn+1 y₁ ΙΟ ди ду дх

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Page 241 - 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 207 - 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 66 - ... 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 83 - ... 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 8 - 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 156 - 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...