This white plaster model of the outer shell of a Fresnel wave surface for a biaxial crystal consists of two pieces that fit together. It is hollowed out and missing an octant and a half-octant. Parts of two small and two larger circles are drawn on the surface. The elliptical wooden stand is painted black. A paper tag on the model reads: Fresnel'sche Wellenfläche. (/) Verl. v. L. Brill. 6. Ser. Nr. 1a. A mark on the bottom of the stand reads: VI.1a
An example of the inner shell of this wave surface, L Brill No. 160. Ser. 6 No. 1b, is the collection as 1982.0795.24, which is part of another copy of Brill No. 160.
This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
This white plaster model has a rectangular base, four concave sides, and a flat top. No curves are indicated on it. It goes with 1985.0112.120.
The model was designed in 1877 by Walter Dyck under the supervision of Ludwig Brill at the technical high school in Munich. It shows the locus of centers of principal curvature of a one-sheeted hyperboloid (that is to say, the envelope or caustic of reflected rays). A tag on the base of the model reads: 153. Another tag reads Centrafläche des Hyperboloids. (/) Verl. v. L. Brill. 1. Ser. Nr. IIIa.
This example of the model was exhibited at the German Educational Exhibit at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It there was purchased by Wesleyan University in Connecticut, and subsequently was donated to the Smithsonian.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 3, 86.
In 1881, Gottlieb Herting, then a student in the technical high school in Munich where he worked under the direction of Alexander Brill, designed a set of eleven plaster models of surfaces of revolution. Herting would spend the rest of his career teaching mathematics and physics at an advanced high school (gymnasium) in Augsburg. The models would be published by Ludwig Brill of Darmstadt in 1885 as his Series 10, 30 (lettered a through l and given Brill numbers 113 to 123). A twelfth model in the series was designed by another Brill student, Sievert. This is letter “k” in that series. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago, where it was purchased by Wesleyan University.
The plaster model shows a surface of revolution generated by the revolution of a cubic parabola. The equation of the surface is z3 = a3 (x - a). The fragments of a number tag remaining on the model are illegible.
References:
Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 22,76.
J. C. Poggendorff, J.C. Poggendorffs biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften . . ., vol. 4, Barth, 1904, p. 626.
“Asymptotic Curves,” website of the Mathematical Institute, Oxford University, accessed September 5, 2017.
This white plaster model of a third order surface has a square base and three peaks, one larger than the other two. Various lines are indicated. A paper tag on the base reads: 41. Another paper tag reads: Fl. 3 Ord. mit bipl. Knotenpunkt B4 (/) Verl. v. L. Brill 7. Ser. Nr. 12. Brill's catalog indicates that model 41 (series 7, No. 12 - 1985.0112.032) is the real part of the surface and model 42 (Series 7, No. 13 - 1985.0112.033) is the imaginary part.
This model, along with all the models of Series 7, is on the design of Carl Rodenberg of the technical high school in Munich.. It was first published by Brill in 1881.
The object was exhibited at the German Educational Exhibit at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It there was purchased by Wesleyan University in Connecticut, and subsequently was donated to the Smithsonian.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p.14, 61.
Accession file.
G. Fischer, Mathematical Models, Braunschweig: Vieweg, 1986, vol. 1, p. 24, vol. 2, pp. 12-14. This object is presently missing a piece shown in Fishcer's photograph.
These hollow wooden stands are painted black. They are for Brill models once part of the Wesleyan University collections that did not survive to be given to the Smithsonian. The first model is elliptical and is for Brill model #2. The second is also elliptical and is for model #3. The third is elliptical and for model #102. The fourth, received in 2 pieces, is elliptical and for model 103. The fifth and sixth are elliptical and for models 105 and 107. The seventh is elliptical and for model 108. The eighth is elliptical and for model 161. The ninth is circular and is the stand for model 204. Four of these stands have dimensions: 19.5 cm. x 16 cm. x 2 cm. Three of these stands have dimensions: 16 cm. x 12 cm. x 1 cm. One stand measures: 12.5 cm. x 10.5 cm. x 1.5 cm. One stand measures: 10.2 cm. x 10.2 cm. d. x 1.4 cm. h.
Each of these three identical white plaster models has the dimensions given. Each model has eight triangular faces for sides and a parallelogram for the base. There is a line segment indicated which stretches across four triangles on each model. A diagonal is indicated on the parallelogram. Two of these models can be arranged together to form a polyhedron congruent to two of model 1985.0112.0172.
This is one of a series of models designed by A. Schoenflies in Göttingen to illustrate the regular partition of space. Schoenflies designed “stones" which could be arranged into larger blocks (sometimes with congruent stones and sometimes using stones that were mirror images of one another). The series was first published by Brill in 1891. The plaster stones that comprise the object with museum number 1985.0112.174 could be arranged to form a block with museum number 1985.0112.162. A model of this block and stones at the University of Göttingen (#330 in their collection) has three stones and a block. The Smithsonian collections include three such stones (these objects) and a block
This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, pp. 46-47, 90-91.
A Schoenflies, “Uber Reguläre Gebietstheilungen des Raumes,” Nachrichten von der Königl. Gesellschaft der Wissenschaften, #9, June 27, 1888, pp. 223-237.
Göttingen Collection of Mathematical Models, presently online at http://modellsammlung.uni-goettingen.de/, accessed September 6, 2019.
This white plaster model of a third order surface (Hesse's surface) has a nearly square base on which a four-sided curved surface sits in the center. Above this are three symmetrically arranged pieces held up by metal rods. Two pieces detached from the center are intended to go at the top. One of these is broken. An incomplete paper tag reads: [ . . .] 6.
The model is one in a series designed by Carl Rodenberg of the technical high school in Darmstadt that was first published in 1880.
This example of the model was exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. p. 15, 64
Groeningen University website, accessed September 3, 2019.
In 1880, Ernst Lange, a student at the mathematical institute of the technical high school in Munich, working under the direction of Felix Klein, designed four plaster models of space curves of degree three drawn on cylinders with cross sections that were conic sections. All of these curves represented the intersection of a surface of degree two with the cylinder shown.
This model, the first in the series, shows the intersection of a cone with an elliptic cylinder. The curve of intersection, called a cubic ellipse, is incised on the model. A paper tag on the model reads: Raumcurve 3. Ordnung. (/) Verl. v. L. Brill. 6. Ser. Nr. XIXa.
Compare 1985.0112.061, 1990.0571.24, and 1990.0571.25. For another curve drawn on an elliptic cylinder, see 1982.0795.32
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p. 13, 73-74.
E. Lange, Mathematische Modelle XIX. Die vier Arten der Raumcurven dritter Ordnung, pp. 1-2. A copy of this document is available online through the website of the Göttingen collection of mathematical models. Accessed November 13, 2017.
Mathematics Institute of Oxford University website. This indicates that the intersecting surfaces are an elliptic cylinder and a hyperbolic parabola.
Ulf Hashagen, Walther von Dyck (1856-1934): Mathematik, Technik und Wissenschaftsorganisation an der TH München, Stuttgart: Franz Steiner, 2003, p. 90, 100, 102.
This hollow white plaster model of a third order surface has three rolling symmetric peaks around a central peak. The tip of the peak is missing. This model, along with all the models of Series 7, is on the design of Carl Rodenberg of the technical high school in Munich. It was first published by Brill in 1880. A paper tag at the base reads: 33. Another tag reads: Fl. 3. Ord. mit 4 reellen con. Knpktn. (/) Verl. v. L. Brill 7 . Ser. Nr. 4.
This example was exhibited at the German Educational Exhibit at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It there was purchased by Wesleyan University in Connecticut, and subsequently was donated to the Smithsonian.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p. 14, 61..
Accession file.
Online University of Tubingen collection of Brill models.
G. Fischer, Mathematical Models, Braunschweig: Vieweg, 1986, vol. 1, p.. 17, vol. 2, pp. 12-14.
500 DIESER ENTWURF ODER WENIGER / 100 PFENNIG 100 / ALT CORBACH-DALWIGKERTOR (1840)
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[[strikethrough]][[?]] 500 ODER WENIGER [[/strikethrough]] / 100 PFENNIG 100 / HELLE KLEINE / BRÜHMANN / GUT-SCHEIN DES SPORT VEREINS COR-BACH 1909 / GÜLTIGKEIT BEI ALLEN VERANSTALT- / JUNGEN DES VEREIN'S BIS ZUM 30.9.1999 / LOUIS KOCH-HALBERSTADT.
The kit consists of a Leica 1(A) camera (Serial no. 4495) with 50mm f/3.5 Elmar lens and lens cap, a small dial rangefinder, two reloadable film cassettes in case, and a brown leather case to hold all the items. Model 1(A) Leicas were not fitted with a rangefinder for focusing, so from the very beginning Leitz (the manufacturer) sold an accessory rangefinder that fitted into the camera shoe. The rangefinder in this kit was the first design type sold by Leitz in 1925.
The kit also includes a small tubular case that contains two 35mm film cassettes. In the early Leica days preloaded 35mm film cassettes were not available and the camera users had to load their own cassettes from bulk film. From the beginning 36 exposures was the standard length of film. This kit would enable the user to shoot 72 exposures before resorting to a darkroom for reloading.
The whole kit fits into a custom leather case in excellent condition.
HAUPT / UND HANDELS / STADT / FRANKFURT A.O. / 25 / FRANKFURT / 25 / [[IMAGE]]A COAT OF ARMS DEPICTING A HERALDIC EAGLE, A ROOSTER, AND TWO TOWERS. [[/IMAGE]] / A.O. / MAGISTRAT / [[SIGNATURES]] / DIESER GUTSCHEIN VERLIERT / SEINE GÜLTIGKEIT DREI / MONATE NACH ÖFFENTLICHER AUF/ FORDERUNG DES MAGISTRATES / ZUR ZAHLUNG BEI DEN STÄDTISCHEN KASSEN
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AUCH DIESER NOTGELD / WISCH WARD AUS DER NOT GEBOR'N / ALS UNSER GOLD VERLOR'N. / NOT MACHT ERFINDERISCH. / 25 / PF / [[image]]Town hall of Frankfurt an der Oder surrounded by a cloud or dust [[/image]] / RATHAUS FRANKFURT A.D.ODER V.NORDEN / JOCHEM