Beck’s Improved National Monocular Microscope is a compound instrument with coarse and fine focus, circular stage, sub-stage bar that holds condenser and mirror and that can swing around the stage, inclination joint, and tri-leg base. This example came from the U.S. Military Academy. The inscription on the base reads “R. & J. BECK / LONDON & PHILADELPHIA.” The serial number 10198 appears on the back of one foot. There is a strong wooden box, and small wooden box holding 3 objectives and 3 eyepieces.
R. & J. Beck began in business, as such, in 1865, and by 1877 had established an American shop under the leadership of W. H. Walmsley.
Ref: R. & J. Beck, An Illustrated Catalogue of Microscopes and Accessories (Philadelphia, 1891), pp. 18-19.
Patent model for Hamilton L. Smith, “Improvement in Microscopes,” U.S. Patent 52901 (1866). Hamilton Lanphere Smith (1819-1903) was a graduate of Yale College who taught natural philosophy and astronomy at Kenyon College in Gambier, Ohio, from 1853 to 1868, and then moved to Hobart College in Geneva, N.Y. Smith was also an avid microscopist. His invention, he claimed “consists in the use of a movable reflector inserted into the tube of a microscope and arranged so as to transmit the light down through the lens on the object in such a manner that by the action of said lens or object glass of the microscope the light is condensed on the object to be viewed, and an object viewed as opaque will be illuminated for the microscope.”
This heavy compound monocular microscope has a push-pull focus, square stage, sub-stage aperture ring, sub-stage mirror, and tri-leg base. The “Lerebours Opticien / Place du Pont Neuf N. 13 / à Paris” inscription on the tube refers to the firm begun by Noël Marie Lerebours (1762-1840) and continued by his son, Noël Marie Paymal Lerebours (1807–1873). This was purchased for the U.S. Military Academy in 1829. That was one year before the first achromatic microscope lenses were produced, in England.
From its infancy, timekeeping has depended on astronomy. The motion of celestial bodies relative to the rotating Earth provided the most precise measure of time until the mid-twentieth century, when quartz and atomic clocks proved more constant. Until that time, mechanical observatory clocks were set and continuously corrected to agree with astronomical observations.
The application of electricity to observatory timepieces in the late 1840s revolutionized the way American astronomers noted the exact movement of celestial events. U.S. Coast Survey teams devised a method to telegraph clock beats, both within an observatory and over long distances, and to record both the beats and the moment of observation simultaneously. British astronomers dubbed it the "American method of astronomical observation" and promptly adopted it themselves.
Transmitting clock beats by telegraph not only provided astronomers with a means of recording the exact moment of astronomical observations but also gave surveyors a means of determining longitude. Because the Earth rotates on its axis every twenty-four hours, longitude and time are equivalent (fifteen degrees of longitude equals one hour).
In 1849 William Cranch Bond, then director of the Harvard College Observatory, devised an important improvement for clocks employed in the "American method." He constructed several versions of break-circuit devices—electrical contracts and insulators attached to the mechanical clock movement—for telegraphing clock beats once a second. The Bond regulator shown in the forground incorporates such a device. Bond's son Richard designed the accompanying drum chronograph, an instrument that touched a pen to a paper-wrapped cylinder to record both the beats of the clock and the instant of a celestial event, signaled when an observer pressed a telegraph key.
From its infancy, timekeeping has depended on astronomy. The motion of celestial bodies relative to the rotating Earth provided the most precise measure of time until the mid-twentieth century, when quartz and atomic clocks proved more constant. Until that time, mechanical observatory clocks were set and continuously corrected to agree with astronomical observations.
The application of electricity to observatory timepieces in the late 1840s revolutionized the way American astronomers noted the exact movement of celestial events. U.S. Coast Survey teams devised a method to telegraph clock beats, both within an observatory and over long distances, and to record both the beats and the moment of observation simultaneously. British astronomers dubbed it the "American method of astronomical observation" and promptly adopted it themselves.
Transmitting clock beats by telegraph not only provided astronomers with a means of recording the exact moment of astronomical observations but also gave surveyors a means of determining longitude. Because the Earth rotates on its axis every twenty-four hours, longitude and time are equivalent (fifteen degrees of longitude equals one hour).
In 1849 William Cranch Bond, then director of the Harvard College Observatory, devised an important improvement for clocks employed in the "American method." He constructed several versions of break-circuit devices—electrical contracts and insulators attached to the mechanical clock movement—for telegraphing clock beats once a second. The Bond regulator shown here incorporates such a device. Bond's son Richard designed the accompanying drum chronograph, an instrument that touched a pen to a paper-wrapped cylinder to record both the beats of the clock and the instant of a celestial event, signaled when an observer pressed a telegraph key.
The horizontal line is represented by the wire coming out of the vertical plane at c’. The second line would run from point a on the horizontal plane to b’ on the vertical, however the black string that should represent this line is missing. The two lines intersect at point (m, m’) at the bend in the wire. Lines cd and ab are the projections of the lines on the horizontal plane, with line nm perpendicular to cd at m. By rotating about these three lines as in relief 25, the angle between the given lines is shown on the horizontal plane as angle aM2D1.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Plane APA’ and point (m, m’) are given. Construct the line on the plane with largest slope or inclination from the horizontal. Theory says that this line would be perpendicular to the horizontal trace of the plane, line PA. So the result is the black string from point c on the horizontal plane to point A’ on the vertical plane. The red string from point A is in the plane; the red string from point d forms the plane perpendicular to plane APA’ that the line lies on. All three lines meet at point (m, m’).
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Suppose one is given plane APA’ and point (m, m’) not on the plane. To find the distance, one must find the perpendicular from the point to the plane. This is done by finding the shortest vertical and horizontal distances from the point to the plane. Segment mn on the horizontal plane is the projection of the shortest distance of point (m, m’) to the plane horizontally, often referred to as the perpendicular foot. Line de’ (red string) is the image of this foot up onto the plane. Likewise, segment m’n’ is the vertical perpendicular foot and its image on the plane is the wire coming out of the horizontal plane. Point (n, n’) where these two lines meet is the perpendicular from (m,m’) to the plane, and thus the shortest distance.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
For the discussion that follows, the following conventions will be used to explain the location of points in each model. Any point in space can be denoted by a coordinate triple (x,y,z). This is the three-dimensional version of the (x,y) plane from Euclidian geometry learned in high school. For our purposes, the x-axis will be the horizontal line stretching left and right at the fold of each relief. The y-axis will be on the horizontal plane (paper card) of each model, appearing to be coming out of the plane of each image. The z-axis will be the vertical axis of each relief and lies on the vertical plane (paper card) of each relief. In all of the reliefs, the x-coordinate is irrelevant since each projection will be with respect to the y and z planes. When needed, a point will be referred to in two coordinates only (y,z), leaving off the x-coordinate for brevity. Positive will be the forward or upward direction and negative values will be behind or below the cards of each relief.
In each relief, a point of interest that is on the vertical or horizontal plane will be marked by a letter and a small hole or dot. Points in space are shown by the bend in a wire that pierces the cards at the y and z intercepts (a,0) and (0,b) respectively and will be denoted (a, b). Lines are shown by black or red strings threaded between points on the cards or by wires and will be denoted by the point on the horizontal plan followed by the point on the vertical plane, such as ab. The title of each relief is actually a construction. For example, relief seven is entitled “line perpendicular to a plane.” This is actually a task, “construct a line perpendicular to a given plane in space.” Following Jullien, we will assume the directions are to construct the item in question. There are many projections shown for the construction of each item. For simplicity, I have only described the relevant items in each model, leaving out all the mathematical details. It would take a whole textbook on the topic to rigorously go through each model. And that is the point of the models, to supplement the textbook Jullien wrote. The reliefs slowly progress from simple to complex, starting with the depiction of points and lines and ending with the construction of a pyramid, guiding the students through the constructions of descriptive geometry. The progression of the reliefs follows the textbook.
In this particular model, nine points are shown for all the possible combinations of a positive, negative or zero value for y or z. For example, the first point on the left shows a point with both y and z coordinates positive.
Reference:
A. Jullien, Cours élémentaire de géométrie descriptive. . ., Paris: Gauthier-Villars, 1875. There were editions of this book as late as 1887.
The two planes are APA’ and BQB’, both perpendicular to the vertical plane. As can be seen in the relief, the horizontal images are the parallel lines PA and QB. Each red string represent a line on each plane that is perpendicular to intersection of the plane with the horizontal plane. These lines meet at (m, m’). The locus of all such intersection points is the horizontal line (wire) coming out of the vertical plane. By rotating (m, m’) about segment sm, the image of the angle of intersection of the planes is given by angle sM1n.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
This relief shows four more special cases of lines. It is one of two reliefs that are about twice as long as the rest. The wires and strings are missing, so it is difficult to visualize the representations. (Note that the wire coming out of the horizontal plane on the far right is not correct, it is in fact one of the support pieces. This is how the relief was configured when it arrived at the Smithsonian.)
Figure 1 on the left shows the vertical and horizontal projections of two lines as well as the intersection of the two lines projected onto the vertical plane.
Figure 2 shows the angle of inclination of the line with the horizontal plane by rotating it down onto the horizontal plane.
Figure 3 shows the angle of a line coming up through the horizontal plane with the vertical, again by rotating it onto the horizontal.
Figure 4 shows the vertical projection of a line and the horizontal projection of its vertical component.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Point (m, m’) is rotated about line ab. Point n on the horizontal plane is the foot of the perpendicular from the point to line ab. Point M1 is the result of rotation of the point about line nm; M2 is the result of rotation about line ab.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
The faces of model include five squares arranged as in the sides of a prism, with pentagonal pyramids of five equilateral triangles each rising from both ends. Its faces total ten equilateral triangles and five squares.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
This model is an extension of a truncated dodecahedron. On two of decagonal faces, the decagon serves as the base of a figure with a regular pentagon on top and five squares and fiveequilateral triangles below. These "augmented" sides are opposite one another. The faces of the model total thrity equilateral triangles, ten squares, two regular pentagons, and ten regular decagons.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
This model has a regular pentagon on the top, a round of five equilateral triangles, a round of five regular pentagons and five equilateral triangles, a round of ten squares, and a regular decagon on the bottom. Hence its faces total of six regular pentagons, ten equilateral triangles, ten squares, and a regular decagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.