Device for Reading Double-Alignment Nomographs
J.
G. Roof, Shell Development Co., Houston, Tex.
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HEN a nomograph relates only three variables, a single setting of an index line will generally obtain a reading of the value sought. An opaque straightedge for alignment is unsatisfactory, as parallax is difficult to avoid, and extrapolation from the last plotted value to the edge of the rule is difficult, especially on nonlinear scales. A narrow, well defined line on the lower surface of a transparent rule or parallel to the long edge of a transparent drafting triangle facilitates reading of a nomograph (1). An equation relating four variables is often presented as a double-alignment nomograph with a pivot axis. The advantages of a transparent rule can be incorporated into a simple device for reading such nomographs.
spool is pressed down against the nomograph. On its lower face the spool is scribed with two lines along diameters a t right angles. The top flange of the spool is a separate disk of plastic, attached to the core by pressing the two pieces together after solvent has been added to soften the two pieces. If care is taken, no air bubbles are formed a t the interface. The core of the spool should be made slightly longer than might seem necessary, to extend above the body of the guide when the solvent is being added; otherwise solvent may touch the body and roughen the wall of the slot. The slot may be enlarged a t one end, keyhole fashion, to permit placing the previously assembled spool in the slot; a retaining plug can then be placed in the enlarged end.
The guide (Figure 1) is essentially a transparent plastic rule having a line scribed longitudinally on the lower side, with a cross-hair pivot arrangement that permits shifting the pivot point within a range of about 2 inches along a n extension of the index line, and rotating the rule about the pivot point. The device is assembled from four parts: body, spool core with lower flange, upper flange, and rubber O-ring. The spool fits within a longitudinal slot near one end of the body. The body is recessed on the lower side around the slot to sufficient depth to accept the lower flange of the spool and allow it to slide along the slot without objectionable drag by the O-ring. This O-ring is recessed in a circular groove in the lower flange of the spool, protruding only far enough to furnish a firm fix when the
APPLICATION
In connection with one set of nomographs used in the determination of cyclic carbon in petroleum distillates ( 3 ) the guide is first placed on the nomograph so the index line passes through the determined values of the refractive index, n D , and the density, d, of the test material, and the pivot axis, 100 y, crosses the slot of the guide (Figure 2). Then the body of the guide is held firmly against the nomograph -chile the intersection of the spool cross hairs is brought to the pivot axis by sliding the spool along its slot. The spool is pressed down firmly to fix its position on the pivot axis, and the body is rotated until the index line passes through the determined value of the molecular weight, M ,of the test mate-
rial. The cyclic carbon content is estimated directly from the intersection of the index line with the per cent CE scale corresponding to positive or negative values of y. I n this application it may be necessary to rotate the body of the guide as much as 180" between the two settings For maximum convenience, doublealignment nomographs can be arranged to minimize rotation, by "folding" so the pivot axis lies to one side of all other scales on the chart. Such rearrangement of Figure 2 leads to that shom-n in Figure 3. The nomograph is more compact, the necessity of swinging the body of the guide through the vertical is eliminated, and rotation through more than 90" is rare. When a chart is folded, it is desirable to indicate the sets of axes to be used simultaneously. Even when a two-color press is available, all axes and graduations should be printed in one color, to avoid errors in color register, but one pair of axes can bear titles and numbers in a second color. When printing in two colors is impractical, a broad line may be drawn parallel to each of the second pair of axes to set them off prominently (Figure 3). Chance of error may be serious when the numerical values on the chart are more nearly the same on two or more axes. If it is inexpedient to fold a nomograph to give an external pivot axis, with proportional charts of the s i n g l e 4 or double-N type (2), a reading guide of adequate length with a pivot slot near the center of the body should be considered.
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DIMENSIONS INCHES
Nomograph guide
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SCHEMATIC N O M O G R A P H A F T E R VAN l r E S AND VAN WESTEN
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NO. 5, M A Y 1959
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I N D E X LINE
Example of folded nomo-
The device appears to have certain operating advantages over the nomograph compasses described by Van Nes
and Van Westen ( 3 ) . Essentially, their guide consists of two opaque straightedges connected by a n open-center hinge fitted with a transparent windon-, which has cross hairs that mark the intersection of extensions of the two index lines, regardless of the angle subtended. Simultaneous setting of the first arm upon three values is requiredthe straightedge passes through the proper values, in the present example, of n D and d, while the intersection of the cross hairs must fall upon the y axis. Once this first arm is properly placed, it is held in position while the second arm is rotated until its edge crosses the proper value of 111; the corresponding value of per cent C E is then read. After the nomograph compass has been placed in its final position, a check reading on all five axes is possible. The present device is trans-
parent, and the initial setting is made on only two points rather than three simultaneously. If one is willing to forego the latter convenience, the spool can be fitted into a closely fitting circular hole rather than the slot, simplifying the machine work required for construction. LITERATURE CITED
(1) Allcock, H. J., Jones, R. J., “The Nomograph,” 3rd ed., p. 40, Sir Isaac Pitman &- Sons, London, 1946.
(2) Davis, D. S., “Empirical Equations and ,h;omography,” p. 125, hlcGrawHill, New York, 1943. (3) Tan Nes, K., Van Westen, H. A,, “Aspects of the Constitution of Rlinera1 Oils,” p. 347, Elsevier, Amsterdam, 1951.
PUBLICATION 159, Exploration and Production Research Division, Shell Dewlopment Co., Houston. Tex.
Machine for Preparing Phosphors for the Fluorometric Determination of Uranium R. E. Stevens, W. H. Wood, K. G. Goetz, and C. A. Horr, U. S. Geological Survey, Denver, Colo.
of uranium are S usually determined by measuring the fluorescence of a sodium or lithium M ~ L L QUASTITIES
fluoride-uranium phosphor. A serious handicap has been the difficulty of preparing the phosphors. When the flux is melted by manually holding a container of platinum or gold over a n open flame, conditions of heating and cooling cannot be readily duplicated and fluorescence may vary widely. Sadowski and Gentry ( 5 ) describe a fusion rack which prepares one phosphor a t a time over a flame. Racks for preparing a large number of phosphors at one time have been used (1, 4, 7 , 8 ) . The equipment consists of a single large burner over which 20 small dishes ( i/le-inch internal diameter) containing uranium and flux can be heated at once. There is no adequate provision for stirring the melt. Variations in heat over different parts of the burner and in cooling rate from outside to inside positions are compensated by random arrangement of the unknowns, standards, and blanks. Although these racks are suitable for use with small dishes, they are not practical for supporting a large number of the larger dishes used by many laboratories. Thatcher has designed a support for preparing three phosphors at a time in a muffle furnace (6). The melts are swirled by a n externally mounted motor, which swings the support for the dishes in the furnace. Preparation of the phosphors in a muffle furnace is not completely satisfactory, however. because of the greater solubility of the platinum in the flux in the oxidizing 962
ANALYTICAL CHEMISTRY
atmosphere of the furnace, with consequent variability of results, as recognized by most users of the fluorometric method for uranium. Recently Michelson ( 3 ) described a device for dran-ing the dish through a n electric tube furnace or burner a t a repeatable rate. The machine described here was designed for use in the procedures described by Grimaldi, May, and Fletcher (2), in which 2 grams of flux (45.5 parts by weight of sodium carbonate, 45.5 parts by weight of potassium carbonate, and 9 parts by weight of
sodium fluoride) are used for making the phosphor, with platinum dishes of 38mm. inside diameter. The 4-mm. flat lip around each dish holds the dish in a horizontal position in the mountings provided in the machine. Phosphors prepared a t one time in the machine show good reproducibility and separate runs show good agreement, \There precise values are wanted, each run can be standardized by including blanks and phosphors of known uranium content. The machine eliminates the tedious hand preparation of phosphors
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Figure 1.
Cutaway drawing of machine in inclined position
Showing motor, mounting of dishes, inclining lever, etc., but only parts of dishes and mounting rods
