Prepared by V. Frederick Rickey on 28 November 2012 and 11 December 2012.

I would like to thank Jennifer Lee of the Columbia Library for making these objects available for my study,

The accession numbers below refer to a "Catalog of the Smith Collection of Mathematical Instruments" which contains 271 items. For example the first item below has the accession number (148) 27-628. The first number, 148, indicates the order of the items in a spreadsheet which I obtained from the Rare Book Room. The second, 27, refers to the David Eugene Smith (1860-1944) Collection. The third, 658, identifies the object.

All of the sectors are brass.

NB. These are just raw notes. As I do more research, I will add notes and references about the makers and the design and use of the scales.

DESmith (148) 27-658. The rectangular arms are 4 5/8 long (12.5 cm) and each is 3/4 in wide (2 cm), not counting the circular hinge. The hinge has a flower on both sides.

On the side with the accession number, hinge at right, the scales are:

Fortificat. 1 to 12. Numbering starts at the hinge. Large space between 3 and 4 (why?).

Chord. 1 to 90

Cir: Divid. 3 to 10, with larger numbers near the joint.

Lin Recta. 2 to 5.

Written on the two arms, letters divided between them: Circumf extrema accomd rat secan [space] Diam. Quite hard to read as the arms do not go tightly together.

On rthe bottom arm: Divideni, Cir Divid 4 to 10, Chord, Fortificat All as above. There are scratches from using dividers.

Now the reverse: These are all double scales, with with corresponding scales in corresponding positions on the arms.

Short line at top right: 1 Lb Then symbol for mars (circle with arrow pointing to the left, i.e., iron). No marks on the scale.

Lin Metall followed by signs of the zodiac (too small to read). The first is iron.

Arithm: 10 to 100 even divisions. The numbers start near the hinge.

Geome: 10 to 100. Larger spaces between smaller numbers.

Cubic. 10 to 60 Much larger spaces.

Now the lower arm: Cubic, Geome, Arithm, Lin Metall as before.

The card with this reads: "Sector Compsses. / Sector compasses, English. First described by Galileo, 1606. Nearly a century ago Benjamin Pike, Jr., had a shop at 294 Broadway. From this he issued a small book on mathematical instrumets. "The Sector --- of all mathematical instruments that have been contrived to facilitate the art of drawing, there is none so extensive in its use as the sector. It is a universal scale. It not only contains the most useful lines, but also by its nature renters them of general application."

DESmith (149) 27-588. Sector compasses. Signed piece, made by Butterfield, Paris

Hinge at left decorated with petals on both sides (just a doodle). Rectangular arms., each is 6 1/2 inches long (6.5 cm) and 7/16 wide (1.4 cm). Signed "Butterfield" near the hinge on the top arm, "Paris" on the bottom.

Top scale not labeled: 8, 10, 14, 18, 20, 24, 30(?), 36, 40, 48, 60, 64.

Les Cordes. 10 to 180. Distance from 0 to 60 is not quite the same as from 60 to 180.

Another scale of chords, but just to 60. The scale of the two is different. The second scale has a larger radius (60). The advantage of the larger scale is that it is somewhat more accurate.

At right "les Solides" one word on each arm. Then a sun symbol on both arms. Then in boxes: "Les Metas???" (one word on each scale). Then 4 zodiacal/alchemical symbols, standing for Silver, Brass, Iron, and Tin.

The lower arm:

The two scales of chords repeated.

The last lineis "Calibre des pieces" (written upside down) and then 1/4, 1/2, 1, 2, 4, 6. This continues on the upper arm: 8, 10, etc.

Now the reverse (hinge on left). On top edge, upside down: "Poids des boules: 1/4, 1/2, 1, 2, 4, 6. and this continues 8, . . . 64 as before, but on the bottom of the lower limb.

Lés parties Eqales. 10 to 200 by 10s. On both arms: les Plans / les poligons 12, 11, 10, 9, 8, 7, 6, 5. The numerals are half on each arm. The next looks like a line of chords to 60, but unmarked. Lower arm repeats in reverse order except for the last line which is best viewed when the sector is

opened to its full length.

NB. This is almost an exact duplicate of (153) 27-594. The sides with the maker's names are virtually the same. Of course the names are different, and there are minor differences in craftsmanship. For example, on the scale of chords, the division lines between 130 and 180 are laid out slightly differently and the spacing is not quite the same. On the other side, 27-594 has "Egalles" whereas 27-588 has "Egales". The only other difference I noted is that 27-594 has "les plans / les" on the upper arm and "poligones / les plans" on the lower, while, 27-588 has simply "les Plans" on the upper arm and "les poligones" on the lower. Might this be an indication that 27-588 was made later.

Need to see if Butterfield and Chapatot were the "same" firm.

DESmith (150) 27-350. Sector compasses. Signed piece, made by Butterfield, Paris

Rectangular arms that are each 4 3/8 (11 cm) inches by 1/2 (1.2 cm); the hinge has a flower.

The side with the accession number will be called the obverse. On the inside is the scale of "les" "Ploigones" with one word on each arm. This double scale goes from 3 to 12. Next is a double scale of "Les Partes Egales" (with one "l"), going from 10 to 120. Outer most is a scale of "Calibre des pieces" (written up-side-down on the lower arm), but there are no number on this arm. The upper arm has 4, 8, 12, 216, 24.

On the inner arms of the obverse, is a double scale of "les" "Metaux" (this is quite clear so this is certainly the correct spelling). There are starburst to the left and then the symbols (on each arm) for silver, brass, iron and tin. There is a double scale of "les Cordes" going from 10 to 90. Up-side-down on the outer edge of the upper arm is "Poids des boultes" and then the scale is on the outside of the lower arm: 4, 8, 12, 16, 24.

This is signed near the hinge "Butterfield" "Paris" with one word on each arm.

DESmith (151) 27-585. Sector Compasses. 18th century. French.

Rectangular arms 6 7/16 inches (16.3 cm) by 9/16 (1.4 cm). Undecorated hinge.

The side with the accession number will be designated the obverse. It is quite simple, with only two double scales. The innermost is "les poligones", which is on the left, awasy from the hinge, goes from 4 througt 12. "Les parties Esgalles" goes from 10 (0 would be at the joint) to 200. This scale is 61/4 long (15.8 cm).

When the scale opens there is a decorative piece 3.3 cm long attached to the upper arm that slips into a grove in the lower. This is the only such thing that I noted, as most of the sectors don't open. There is also a pin near the end that is attached to the upper arm and fits into a hole in the lower. Other sectors have similar pins.

The reverse has only one double scale marked from 10 to 180 (there is no space for the numbers 160 and 170, but there are marks for them on the scale). At the end of the upper scale is "des ct" ("l"?), and on the lower "aye". Might this be the maker?

DESmith (152) 27-586. Sector compasses, 18th century, signed by Chapotot, Paris.

The rectangular arms of this sector are 6 3/8 inches (16.2 cm) by 1/2 (1.3 cm).

The obverse (with the accession number) has the hinge at the left and three double scales. Innermost is "Les Poligones" going from 4 to 12; "Les Plans" 5, 10, 20, 30, 40, 50, 60; and outermost "Les Parties Esgalles" (two "l"s; when did the French spelling change?).

On the end of the reverse, away from the hinge, is a double scale annotated on each arm as: sunburst, "Les Metaux" lead, silver, brass, iron and tin (using symbols). Next is a double scale of "Les Solides: 1, 5, 10, 30, 40, 50, 60. Finally there is a double scale of "Les Cordes" going from to to 180 (although 160 and 170 are not enumerated). On the upper arm near the hinge is "Vne ?????" followed by the symbol of iron. The bottom arm is stamped (not engraved as in 27594) "CHAPOTOT A PARIS".

Is this an earlier model than (153) 27-594? They are almost identical.

DESmith (153) 27-594. 18th century, signed by Chapotot, Paris.

A rectangular sector, with a design on the hinge. 6 7/16 inches (16.3 cm) by 9/16 (1.5), for each arm. Not counting the hinge.

The innermost double scale is "Les polygone", with one word on each arm; extends from 4 to 12.

Moving outwards is a doubles scale, i.e., repeated on each arm, of "les plans" going from 10 to 60.

Next is a double scale from 10 to 200. These are marked on each arm, in a fancy script, "Les parties Egalles".

Finally, on the outer edges is the "poids des boulets" with the numbers 1/4, 1/2, 3/4, 1, 2, 4, 6 (all of this is upside-down), When the sector is open to a straight line, this scale continues on the lower arm: 8, 10, 14, 18, 20, 24, 30, 36, 40, 48, 55, 60, 64.

On the reverse, near the hinge on the right is "Chapotot" and "Paris", with one word on each arm. The innermost scale is "Les" "Solides", with one word on each arm; each word is followed by the symbol for the sun. To the right of this is a double scale for "Les" "Metasoc" (?): lead the symbol is split between the arms; the remaining are on both arms): silver, brass, Iron, and tin (of course, the astrological symbols are used. See Bion, 17??, p. 52 for a key to the symbols. Moving outward, the next double scale is marked 5, 10, 20, 30, 40, 50, 60. The next double scale is "Les Cordes" (this is on both arms), going from 10 to 180.

Finally, on the outer edge of the lower arm is "Calibres des pieces" followed by the numbers 1/4, 1/2, 3/4, 1, 2, 4, 6. This contiues on the upper arm (with the joint at the left): 8, 10, 14, 18, 20, 24, 30, 36, 40, 48, 55, 60, 64. When the sector is completely open this is a single scale. While the number are the same as on the obverse, the length of the scales are not.

NB. This is almost an exact duplicate of (149) 27-588.

DESmith (154) 27-590. Sector Compasses. 18th century. French.

Rectangular arms, with the circular joint not included in the measurements. Length 6 3/8 inches (16.3 cm) by 15/16 (1.5 cm). This brass instrument is haavier than the others as it is thicker.

The side with the accession number has the joint at the left and only two scales. The inner one is "Les" "Poligones" (one word on each arm), going from 3 to 12; as usual the smallest number is opposite the hinge. The outer scale is "Les Cordes" (repeated on both arms); it goes form 10 to 180, with only marks for 160, 170, and 180 as there is just not enough room for them.

The reverse has only two scales, both double. The outer one is "Les parties Egalles" and goes from 10 to 200. The inner scale, which is away from the hinge begins with a sun, the "Les" on the upper arm and "Metaux" on the lower. These words are followed by the symbols for lead, silver, brass, iron and tin.

I do not know how they chose the distances between these symbols. Perhaps the sun is where you are to place one end of your dividers.

DESmith (155) 27-591. Sector compasses. 18th century. French.

Rectangular with the circular hinge sticking out on the left, 6 1/4 inches (15.9 cm) by 1/2 (1.4 cm), not counting the hinge.

The side with the accession number has but two scales. The outer one, "Partes" "Egalés" (with one word on each arm), going form 10 to 190. This is the first time I have seen a clear accent on "Egalés". The inner scale is "les" "Poligones"(with one word on each arm), from 4 to 1[2] (the 2 is missing on the 12). The numerals are written across the two arms.

The reverse has two scales. The outer is "les" "Cordes" and the inner "les" "Métaux". The cordes run from 10 to 110, with marks to 150, but no numerals. The metals are silver, brass, iron, and tin. The symbols for the metals are drawn more freely than on the other scales in this collection. There are no stars (presumably from which one should measure).

DESmith (156) 27-349. Sector Compasses. 18th century, signed by Brière, Paris.

Rectangular rule with arms 6 7/16 inches (16.3 cm) by 9/16 (1.4 cm). Flower at the joint.

The obverse (with the accession number) has a decorative piece attached to the upper arm that fits into a slot in the lower arm. There are two pegs attached to the upper arm that fit into holes in the edge of the lower. This is similar to (151) 27-585. Near the hinge on the lower arm is scratched "HEINZ" (the H and E are a ligature); this is almost certainly the owner at one time.

The obverse has three double scales plus a "Calibre des pieces", upside-down on the lower arm, and continuing 4, 8, 12, 16, 24 at the top of the upper arm. The innermost scale is "Les" "poligones", with one word on each arm. The scale runs from 3 to 6 with the numbers on each arm, and then from 7 to 12 with the top half of the numbers on the upper arm and the rest on the lower. This arrangement seems novel. Next is an unmarked scale of chords from 10 to 60. Finally there is a scale of equal parts form 10 to 200 with "Les Partice" on the upper arm and "Egales" on the lower arm; both are near the hinge.

The reverse is inscribed "Briére" on the upper arm; "Paris" on the lower. Note that I am reading the accent differently than that typed on the card that is wrapped up with the sector (and is used in the heading for this object). Up-side-down on the upper arm is "Poides des boulets" and the numbers 4, 8, 12, 16, 24 on the lower arm, so that this reads as one line when the sector is fully opened. At the end away from the joint, on the upper arm, is "les *", the star representing a sun, and then "les" followed by the symbols for silver, brass, iron, and tin (these symbols are written a bit differently from sector to sector), but the last three of these are written horizontally, which has not occurred on any other scale. There are two double scales, a scale of chords from 10 to 60 and marked "les Cordes", with one word on each arm, from 10 to 60. There is a longer scale of chords marked from 10 to to 140, and then marks to indicate angles of 150, 160, 170, and 180. On the shorter scale the distance between 10 and 20 degrees is 2.3 cm, while it is only 1.4 cm on the longer scale.

Is the word "Cordes" both singular and plural?

DESmith (157) 27-593. Sector Compasses. 18th century. French.

Rectangular arms 6 in (15.3 cm) by 1/2 in (1.3 cm). Flower on the hinge, which is on the left end when the accession number is up.

At the right is a scale with only 5 marks. On the top arm is "Les" and the bottom is "Meraux" (?). On the left is "Les" on the top arm, and "COBDES" (?) on the lower. I can't make sense of the marks on this scale; there are some letters (D and B, widely spaced) are clear. Can't read the numbers. Double Scale of equal parts from 10 to 120.

Where the arms join is a scale of "Les Poligones" with one word on each arm. The scale goes from 4 to 10. At the right end, away from the hinge would be 3, but it is not marked.

Moving out from the center, there is a scale of equal parts marked from 10 to 180. Near the hinge is "PRTHES" on the top arm and "B G ALES" on the bottom. I can't make sense of the scales at the outside of the arms.

DESmith (158) 27-589. Sector compasses. 17th century, Italian.

The design of this instrument is quite different than the others. There is a circular hinge, but it is surrounded with brass to that end is rectangular. the other end is decorative. Overall length is 4 3/4 inches (12.2 cm) by 15/16 (2cm). The length includes the decorative end and the material surrounding the joint; the width is the total for both arms.There is one pin to align the arms, but no decorative piece between them.

The side with the accession number will be called the obverse. The hinge is on the right! There are three double scales, "Solid.", "Part. AEq"where A and E form a ligature, and "Plan." These are alos indicated by small drawings at their left ends: a cube, the fraction 2/2, and a square filled with horizontal lines. There are two more double scales, "Fig. Reg." and "Met." The metals are written perpendicular to their scale. Starting closes to the joint they are: aur, mer, plu, cup, fer, sta, mag.

There are five double scales on the reverse. Starting from the inside they are "Plan. AEq", with a triangle at the left; "Grad. Circ." with a cone; and "Quad. Segm." with a quarter circle in a square. The final two are "Corp. Reg."and, finally "Trans. Corp."

The numbers on the scale are too small for my poor eyes, even with a magnifying glass, and a lupe is even worse. Sadness.

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DESmith (134) 27-348. Diagonal scale, German workmanship giving the Paris and Rhenish feet. 18th or early 19th century.

At the left end of this brass rectangular scale (7 11/16 by 1 1/8 inches) is inscribed "1/2 Rheinh Fuss". The scale is 17 units long plus the diagonal unit. The obverse (with the accession number) has "1/2 Par Fuss" at the end (the first "s" is the old style that extends below the line). There are 11 units on this scale, plus the diagonal unit. For ease of use, the fifth line up is marked with a cross at units 1, 3, 5, 7, 9, 11.

DESmith (135) 27-345. Diagonal scale, German, 18th century.

Rectangular brass scale, 6 5/16 inches long and 7/8 inch wide with a decorative handle (a plant or tree with performations) that is 1 1/8 inches long. This diagonal scale has a length of 100 (counting the diagonal portion). 10 units = 9/16 inch. Nicely made. On the obverse (where the accession number is) there is an unfinished diagonal scale that if faint. There are no numbers on it.

DESmith (136) 27-274. Brass diagonal and trigonometric scale. German workmanship of 1773. It is signed by the maker "Inventor Roppelt 1773".

A brass square 3 3/16 inches on a side. The reverse is blank (except for the accession number). There is a diagonal scale running from one corner to the opposite one. 30 units are 1 15/16 inches. The scale is 40 units long with another 10 for the diagonal scale. Above the scale is inscribed "Inventor" and below is "Roppelt 1773". Along the edge, to the left of "Inventor" is "1/2 Tangens". "45" is at the top and "1/2 Tangens" is to the right. At he left corner os "0" and at the right "45"; these are outside of the diagonal scale. At the bottom left near the edge is "1/2 Radius", "0" is at the bottom and "1/2 Tangens" at the right. There are no markings to indicate how this could be used as a trigonometrical scale.

DESmith (144) 27-344. English protractor and diagonal scale. A signed piece made by Cox and Son, London.

A brass rectangle with beveled edges, 6 by 1 3/4 inches. Inscribed near the bottom "Cox & Son. London". Under this, precisely in the middle of the bottom edge is a mark indicating the center of the protractor (or, center of the circle on which it is based). There are two scales of angles around the two ends and top edge of this protractor. The outer scale starts on the lower left and the angles 10, 20 are marked. 30 is at the corner, and then across the top we find 40, 50, 60, . . . , 150. Down the right side there is 160 and 170. 180 would be at the lower right corner, but it is not labeled. The inner scale is similar but runs counterclockwise from the lower right. The obverse has five scales of equal parts: 50, 45 40, 35, 30 parts to the inch. These are of length 11, 14, 21, 18, and 16 respectively. At the right of the 50 scale is a scale of chords ("Cho") going up to 90 degrees. Below it is another scale of chords ("C") also going up to 90 degrees. The first has length 2 15/16 inches and the second 2/16. Below this is a double diagonal scale one with twice the unit of the other. A lovely instrument.

DESmith (205) 27-281. German proportional compass of the 18th century.

Wooden. 12 5/8 inches long. The metal points are about half an inch long and sharp. There are no markings on it. The two arms are held together by a wooden block and metal screw that can be adjusted as desired.

DESmith (207) 27-326. A set of drawing instruments in a shagreen case. German workmanship of the 18th century.

The hard case is 6 3/4 by 2 1/2 by 1 1/2 and contains 12 instruments (there is a blank hole, so one has been lost; A parallel rule, perhaps). Of particular interest to me are:

(1) A rectangular sector made of ivory with an undecorated brass hinge 6 by 1/14 inches. Along the top an bottom is a ruler of 12 inches when the sector is completely open. The following scales are repeated on both arms: L, S, C, Pol. L is a linear scale going from 1 to 10 with each unit divided into 10 parts. S is marked (from the hinge) 10, 20, 30, 40, 50, 60; this makes me think it is a log-sine scale, but this needs further investigation. C is a scale of chords up to 60 degrees. Pol deals with the construction of regular polygons with 4 to 12 sides. The other side has S, T, and T scales on both arms and T, S, and N on the lower arm. I am perplexed.

(2) Another ivory scale, with equal parts scales for 20, 25, 30, 35, 40, 45, 50. A curious feature of all of these scales is that for 45. The marking are 1, 2, . . ., 9, 10, 1, 2, 3, . . . 9, 20, 1, 2, 3, 4. To prevent crowding the tens digit has been omitted. The other side has three scales: From 1 to 6 (and divided into tenths) where the unit is about 1/32 less than an inch (shrinkage?). The next scale goes from 10 to 60 (again the units are divided into tenths) where the unit is longer, 1 3/16 in. Since this is a German scale could one of these be Rhenish feet? Finally there is a double diagonal scale. The right end of this scale has a curvilinear end which is similar to that pictured on the cover of the 2002 reprint of John Robertson's A Treatise of such Mathematical Instruments as are usually put into a Portable Case, Indivisible College Press, Woodbridge, Virginia.

(3) A wooden scale, 1 5/16 wide, with scales of equal parts with 15, 20, 25, 30 units to the inch (?). Another scale at the top marked "C" and numbered fro 10 to 90. It does not look like a scale of chords to me. The reverse has two rules with unequal units as in item (2). There is also a double diagonal scale.

(4) Another wooden scale but only 13/16 wide. This has a double diagonal scale with the unit half that in item 3. as well as equal parts fro 25, 30, 35, 40 and a C scale.

(5) The other instruments are dividers, compasses, pens, etc.

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