**Catalog of Olivier Models**

**Bell 2. **This model is currently stored in the departmental
library in the bottom of case 3. Richard Bell describes this as follows:

(2) Intersection of Two Conoids

-- has original plate and gold plate

-- good working condition

What Bell calls the "gold plate" is on the front of the model and reads "Intersection of Two Conoids." You can see it in Figure bell-2:

In the *Mathematical Dictionary and Cyclopedia of Mathematical Science*
by Charles Davies and William G. Peck, 1855, we find on p. 127:

CONOID. [Gr. xxx, from xxx, a cone, and xxx, form]. A warped surface which may be generated by a straight line moving in such a manner as to touch a straight line and curve, and continue parallel to a given plane.

This dictionary entry continues, but this much suffices to show that the "gold plate" on this model is incorrect. This is good evidence that these plates were added at a much later date. Also arguing for a later addition is the fact that these gold labels are in English, while the original labels brass are in French or Latin. This model really consists of two frusta of cones:

FRUS'TUM. [From

frusto, to break]. A piece or part of a solid separated from the rest.Frustum of a Pyramid or Cone. In Geometry, the part contained between the base and a plane parallel to the base between it and the vertex. In general, the frustum of any solid body is that portion of the body lying between any two parallel planes which intersect the body. . . . [Davies and Peck, 1855, p. 263]

**Bell 4. ** This model is currently stored in room 246 Thayer,
Professor Rickey's office. It is not in a case. Bell's description of this model
is as follows:

(4) Right Conoid

-- no original plate

-- has gold plate

-- cardboard inside to separate rows of weights

-- good working condition

Something is amiss here. One can see in the picture below that there is an "original plate" to use the phrase that Bell uses in other descriptions, but there is no "gold plate" on this model. Instead there are paper labels affixed with Scotch Tape on both the front and rear of the case which read "Right Conoid." Perhaps Bell got his notes mixed up and simply switched the names of the two plates in his write up. The model does have the cardboard inside (see Figure Bell4-?). Both the original plate and the paper label can be seen clearly in Figures Bell4-1 and Bell4-2. The wine cork in the picture comes from a bottle of 1996 Chateau Olivier, which is a lovely Grand Cru Classé de Graves.

Figure Bell4-1. Figure Bell4-2.

Calling this a "Right Conoid" is undoubtedly an error of nomenclature made by some later individual. The bottom portions on both sides are indeed right conoids, but they are not the essential part of the model. Note the straight line generator which is parallel to the base; also note the cut-out in the base just below this generator so that the strings can extend into the base and hide the weights which keep them taut. Of course the bottom portion of this model can be used to illustrate conoids, but it is much more likely that the straight line generator simply provided a convenient way to guide the strings into the case which conceals the lead weights.

Figure Bell4-3. Figure Bell4-4.

In Figure Bell4-3, the top and left rings have been adjusted so that one has a truncated right circular cylinder on the left and a truncated cone on the right. Figure Bell4-4 is a "back" view of the top of the model. Note the set screws that can be used to hold the rings in the desired orientation.

Figure Bell4-5 is a back view of the model which shows the straight line directrix of the conoid.

**Physical description: **The wooden base of the Olivier model
Bell-4 is 50 cm wide, 27 cm deep and 27 cm high. It is supported by four round
feet at the corners, so that it is 2 cm off the table. The bronze frame, which
is 19 cm high, is attached to the base in two places. This frame is a triangle
with a base of 41 cm. 33 cm up from the base there is a cross bar that is 13 cm
long; thus the top of the frame is a large letter "A". The frame is
made of brass that is 2 cm wide and 0.5 cm thick (thickness being measured from
back to front). At the three corners of the upper triangle of this A there are
rings that are mounted orthogonally to the bronze frame and that can be turned.
The two bottom rings are circles of diameter 12 cm and are drilled so that the
strings can pass through them. These circles of string have a diameter of 10 cm.
When both of these circles are horizontal they come within 0.5 cm of each other.
The top ring is an ellipse with a major axis of 16.5 cm and a minor axis of 12
cm; thus it sticks out from the A the same 12 cm as the two circles below it.
This ellipse can also be titled to any angle. There are 72 threads passing
through each ring. The strings on the left are black, those on the right, white.
They appear to be fishing line.

**Bell 10.** In room 246 in the top of case 4.

I am beginning to suspect that Bell-10 is misstrung. When you turn the wheels at the top the strings touch one another and don't stay straight. I suspect one of the wheels is mounted backwards and so turns the wrong direction.

**Bell 15.** Currently stored in the bottom of case 4 in room 246 of
Thayer.

**Bell 20. ** Located on the upper shelf of case 1 in the Mathematics
Conference Room.

This model (and perhaps all of our models) has been restrung. But this model is clearly not strung as originally planned. Both the top and bottom horizontal plates of the model have a circular disk that has two concentric circles of holes punched in it. Presently threads only go through the outer circle of holes. In addition the top of the wooden base is cut out so that two lines of weights can be hidden by the case, but no threads go through these cuts.

**Bell 23.** Located in the top of case 5 in room 248 Thayer. Bell
describes this as follows:

(23) Untitled

-- has original plate

-- no gold plate or other identification

-- cracked on top right hand side of box

-- uneven base

-- old cardboard inside box to contain weights

This model differs from Bell-15 in that there are no slits on the side supports, so the lower plate cannot move up an down. Also, the design of the lower plate is considerably different.

The picture below from the 1957 Howitzer has a light colored blemish on the left side of the case (the side facing us in the picture; note the original plate at the top --- it determines the front). This is not on model Bell-23 today and Bell-23 shows no signs of having been repaired or revarnished.

From the 1957 *Howitzer*,
p. 83..

The caption
on the page facing this picture reads: "Captain MacWherter points out the
characteristics of the hyperboloid to Charlie Williams, Bill Clark and Leo
Keefe." Curiously, CPT MacWherter is not in the picture of the Mathematics
Department on p. 125 of the same 1957 *Howitzer*.

http://www.dean.usma.edu/math/research/history/olivier/default.htm Amy's page on the models.