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PRECISION SPHEREOMETER, French, mid-19th century. Standing 6-1/2" tall, made of brass with a steel lead screw, the spherometer has three tapered legs, central pin on the fine thread precision screw, and "micrometer" readout with vertical scale graduated every half-millimeter, and circular scale (on a six-spoked ring) graduated every 0.001 millimeter (!) The central pin presses against an upper double lever arm with very high amplification factor, so that repeatable positive contact is reliably indicated. The instrument thus measures the central height, and therefore the sphericity, of a surface. Condition is fine noting nicks around the scale edge, and crazing to the original lacquer finish. The most sophisticated early mechanical spherometer we have seen. (6401) $695.

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THE HERBERT SMITH CRYSTAL REFRACTOMETER, English, c.1910, signed "J.H. Steward Ltd., London, No. 549." Made of black enameled and clear lacquered squiggle-worked brass, 3-1/4" (8 cm) overall, the refractometer has a complex prism of high refractive index glass, internal calibration scale reading directly in refractive index of the sample, and right angle focusing eyepiece. Condition is fine complete with the original mahogany case, plus a list of mineral refractive indices. In use one places the flat surface of a natural or a polished crystal against the top surface of the instrument, illuminates through the window below preferably with monochromatic light, and reads the answer at the critical edge separating partially from totally internally reflected light. A fine miniature instrument for the identification of minerals, gem stones, etc. (8312) $1150.

UNUSUAL HANGING SPRING SCALE, French, 18th century, the 5-3/8" (14 cm) wide brass frame decoratively pierced and engraved, and divided non-linearly in units from 5 to 60. It has a central suspension point, and is mounted to the rear with a large elliptical steel spring connected by linkage to the iron pointer, and hung with suspension hook. Condition is fine, the brass with a dark patina, the iron with some surface rust. This unusual scale has a primitive charm, and is not described in the standard references. But a search finds several related examples, one in the Musee des Arts et Metiers in Paris, one in the Musee Le Secq des Tournelles in Rouen (graduated 0 to 27), one in the Museum of the History of Science in Oxford (graduated 1 to 70), and finally one in a private collection (graduated 0 to 64). No two are the same, but all have the frame of opposed "C" shapes, floral decor, distinctive early numeral shapes (zig-zag "3" for example), and elliptical spring. The graduations on the present one correspond rather closely to pounds of pull, specifically to the French pounds ("livres" or "livres poids de marc") used in Paris and several other French cities in the 18th century. (These were about 7% heavier than the English avoirdupois pounds.) (8364) $1495.

PHOTOGRAPHIC PRIZE MEDALS, English, 1880's. The two medals, which came to us from the same Byrne family source, are described briefly as follows:

1) Silver 1-1/2", O.D., Derby Corp. Art Gallery 1882 VR, Industrial Art Prize Medal. No inscription; wonderfully designed and super-detailed.

2) Bronze 1-3/4", one side with bust of James Watt, Royal Cornwall Polytechnic Society, First Class, edge engraved "Byrne & Co., for portraits on China, 1881."

The winner's name is engraved around the edge of the latter. The photographers Byrne & Co. are found in 1883 and 1900 directories at 1 Clarence Terrace, in the London Borough of Richmond upon Thames (home to Hampton Court Palace, Ham House, Kew Gardens, etc.) Condition is fine. $400./the pair

EXQUISITE SILVER SECTOR, Continental, possibly Italian, c. early 18th century, bearing a punch mark, and with lovely shaped ends, and roses engraved to the hinge. Overall length is 4" (10 cm) closed, and the sector is beautifully engraved with doubled sector scales "Arithmetica, Geometrica, Cubica, Gradus Quadrantis." Additional scales give "demy Pied Roy," i.e., half the French linear measure of the King's Foot with subdivisions in inches and twelfths; 'Reinlendscher. 1/2 Fusz," i.e., half the Rhineland foot, likewise subdivided; and reminders of the sizes of one-pound cannon balls of iron, and of lead. The words are all beautifully hand engraved with flourishes, and the tiny numerals are all hand punched. Interestingly, the scales and their names are all read with the hinge to the right, rather than to the left as on typical French and English designs. Condition is very fine.

This is a diminutive example of an elegant form occasionally seen in brass; the design, execution, and terminal shaping may be compared with a Dutch sector by Metz (Tesseract Catalogue 46 Item 45) and with a c. 1700 Continental sector (Catalogue 71 Item 36). The only example we have seen in silver. (8267) $4800.

EDWARD FAGE'S MASTERPIECE -- THE UNIVERSAL SECTOR INVENTED BY SAMUEL FOSTER, English, 1669, signed "Edward Fage fecit, Thomas Hatton 1669." Measuring 9-1/2" (24 cm) long (closed), the sector is made of very thick (7/16") boxwood with inset three-leaf hinge of sturdy brass. The surfaces are covered with hand-divided and punch-marked mathematical scales -- more numerous and of greater variety than we have seen on another sector. The 18" long outer edge has Numbers (i.e., logarithmically divided), Sines, and Tangents. The inner edge has four proportional linear scales, labeled "Repre: Feet/Inches." On the sides we find sector scales of Solids, Lines, Sines, Superficies, Inscribed Bodies, Equat. Bodies, Chords, Sines, Secants, Tangents, Vers. Sine, Seg. Cir., Seg. Sph., etc. Further scales give Metalls, Dry Measure, Ale Measure, Wine Measure, Inches, calendrical scales from January to July and back again (with Julian vernal equinox of about 10 March), and even twin Zodiac scales with punch marks for all the Houses. Inset center-punched brass pins are located at prominent points on many scales, for use with dividers. Fage must have misplaced his little "s" punch along the way, as many (but not all) plural words end in a "3" punch, the "3" usually forward but sometimes backward! Condition is fine but for old stains and some areas of inner edge damage.

With this instrument, a pair of dividers, and a piece of paper, one can perform almost any computation required in the applied mathematics of the 17th century. The maker, Edward Fage, worked at the sign of the Sugar Loaf in Hosier Lane, West Smithfield, London. He had apprenticed to Anthony Thompson (who worked c. 1645 - 1665), gaining his freedom in the Clockmakers Company 1667/8 and in the Stationers Company 1669. Although Fage took over from Thompson, he seems to have had a terribly brief but stellar career, c. 1667 - 1673 (see Clifton). He specialized in mathematical instrument making, especially in producing complex divided scales, and was recommended by various authors at the time, including William Leybourn (1669) for a carpenter's rule, Samuel Sturmy (1669) for "all sorts of Mathematicall Instruments" and Simon Jones (1670) for gauging rods (see Bryden, 1992). The Compleat Gunner, published 1672, includes a plate of a very sophisticated gunners scale bearing Fage's name and address as maker, and Fage is credited, in an appendix to the fifth edition of Gunter's Works (1673), with communicating the construction details of Samuel Foster's newly invented quadrant. We also note that his master, Anthony Thompson, had a high reputation for mathematical scales, and that he, too, is known to have constructed sectors with the unusual inclusion of Zodiacal scales. Turning again to Edmund Gunter and Samuel Foster (each serving at times as Professor of Astronomy at Gresham College in London), we find the present sector well described within Gunter's compiled works, in a separate section "The Sector Altered; and Other Scales Added, with the Description and Use thereof,...Invented and written by Mr. Samuel Foster...Published by W(illiam) L(eybourn), Printed by Andrew Clark, 1673." In 37 pages Foster explains his sector in great detail, including its many uses in astronomy (e.g., to find the sun's altitude throughout the day given its place in the Zodiac and one's latitude). The description matches perfectly the present instrument.

Dated English sectors of any form are rare, and the present instrument is among the earliest. We are aware of three pre-Gunter Elizabethan ones in brass (see G. Turner, 2000). The British Museum holds one which is "probably English," signed "E.B." and dated 1625, plus the only other known (to us) example of Foster's design, that made by Anthony Thompson and dated 1665 (see Ward, 1981).

Our sector was made in 1669 for one Thomas Hatton. While the name is not uncommon, it could refer to Sir Thomas Hatton, baronet, Member of Parliament for Cambridgeshire 1674 - 1679, and in the lineage of the former Christopher H., Lord Chancellor to Queen Elizabeth I, or perhaps to the Thomas H. of Tewkesbury, heir to the Maryland (in the American colonies) fortune of his brother John H.

An important survival. (8355) $18,500.

RARE FRENCH GUNNER'S CALIPERS, c. 1800, signed "Baradelle a Paris," 7-1/2" (19 cm) long (closed), of brass with finely inset steel tips. One side is engraved with a linear scale of (French) inches and twelfths; diagonal lines for "Canon en Bronce:" (using the Spanish spelling of "bronze"!) and calibrated 1, 2, 3, 4, 6, 8, 12, 16, 18, 24, and 36, for direct readout when placing the calipers on the inside diameter of the cannon bore; a circular scale around the hinge, similarly calibrated and labeled "Boulet," for direct readout when placing the calipers on the outside diameter of a cannon ball. The other side has an edge scale of decimeters, centimeters, and millimeters, and diagonal lines for "Canon en Fer." Condition is very fine throughout.

We have seen only three other French gunner's calipers; this form seems adapted from the English style, never widely adopted in France. Bion describes a curious French form of gunnery calipers, but then devotes two full pages to a detailed description of the "Englifh Callipers" or "Gunners Compaffes." The maker was one of the important French family of mathematical instrument makers (see Marcelin, and Tesseract Catalogue 84, Item 20). (8347) $6500.

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VARIABLE ANGLE MIRRORS, German, c. 1900, signed on a plaque "Physikalische Werkstatten, Aktiengesellschaft, Gottingen." The 6-1/4" (16 cm) square machined brass main plate supports two plane mirrors in blackened brass frames, one mirror fixed, the other hinged about a vertical axis and clampable to any position along a scale divided 0 to 90 degrees. As the angle decreases the number of reflected images seen in the pair of mirrors increases. Placing a small colorful object in the center, one sees two images at 90 degrees (mirrors orthogonal), but literally dozens of images at less than 10 degrees. It is the effect of the kaleidoscope; even Brewster had designed one with this sort of variable mirror angle. Here the assembly is in fine condition, mounted on its turned wood stand. (8324) $895.