ASHL,EY A N D E M L E Y ON THE S I Z E S OF GRAIN
OF MINERALS.
87
much of the carbon tetrachloride has been lost through the results have given valuable indications, except evaporation during the process of solution, when a that the reaction with common rosin is so intense drop or two more should be added to produce the spread that if present in the mixture in any considerable ing effect above referred to, Then immediately in amount it is apt to mask the other color indications. Perhaps it would be well to state also that the a n adjacent cavity of the plate a cc. or so of solution B is placed and the bromine vapors evolved are al- presence of more than traces of water, alcohol or lowed to impinge upon the surface of the solution in ether interfere with the sensitiveness of the colorthe other cavity. Sometimes it is necessary to blow reactions. --_--a gentle current of air in the proper direction to accomplish this satisfactorily, or both cavities may ERRORS IN DETERMINING THE SIZES OF GRAIN OF be covered by a watch crystal of suitable size. MINERALS AND THE USE OF SURFACE FACTORS.' The color reactions begin almost immediately By HARRISON E. ASHLEYAND WARRENE. EMLEY. with the contact of the bromine vapors and are best Received December 27, 1910. observed upon the flat portion of the test-plate. In In the clayworking industry, the size of the micromost cases they last long enough for satisfactory scopic grains is of great importance in regard to observation ; the changes in colors are practically over, plasticity, rate of vitrification, warping, cracking, however, in a period varying from five to ten minutes. appearance, etc. This led us to a study of methods The sensitiveness and reliability of this reaction of determining the size of grain and of expressing the for detecting minute amounts of rosin in admixture results numerically. with various substances led me to apply the same Diameters.-The size of microscopic particles is reaction to some other of the more common resins used usually expressed in diameters. When we looked a t in commerce, especially the varnish gums, and I our irregular clay particles, the effort to make them have stated below in tabular form the results of my appear circular and then to read the diameter by the observations, first giving that already observed by eye-piece micrometer exceeded the power of our imaginaFoerster in the case of colophony. nation. Equivalent Rectangle.-We were able, however, to Co1ophowy.-First green, then rapidly blue and violet ; latter lasts considerable time, then slowly construct mentally an equivalent rectangle, and to changes to purple, and finally a deep indigo in all read its length and breadth. Mr. A. V. Bleininger had previously done this and parts. as the square root Damunar.-Brown to lilac-brown, forms rather represented the size of particle ___slowly; gradually changes into a distinct reddish of an area: 2/ length X breadth. A. brown (maroon). Volume of Graiw.-The question remained, however, Elemi.-Indigo-blue, forms a t once, quite permanent ; whether or not the depth of the grain bears a constant gradually deepens in color, sometimes becoming ratio to this figure. purplish, but generally remaining a dark rich indigo. Round Grains.-The round grained mineral with Kauri.-Azure-blue, changing rapidly to purple which we are familiar is the Illinois glass sand through violet shades. Later, a t point farthest from from Wedron and Ottawa. We were quite surprised bromine vapors a dark olive-green forms. Manila Gum (spirit-soluble).-A very faint brownish Mlcroscopt fiengthx breadti green forms slowly; changes gradually to violet and finally purple. At point farthest from bromine vapors " (length x breadth)' a chocolate-brown usually is produced. Mastic.-Reddish brown, becoming almost a carmine WedronSand F;r&y nearest bromine vapors. A coffee-brown tint is produced a t the far side of the test. Vot. by Microscope cumrn. cc. Sawdarac.-Lilac forms almost immediately and is quite permanent ; gradually changes t o a violet, '1 becoming violet-brown farthest from bromine vapors. Shellac, (when pure.)-Gives no colorations. Fig 1. Zanzibar Copal.-A light brown forms slowly, later brownish violet and finally a chocolate-brown to find it showing parallel rounded edges like a loaf of yeast bread. 28 grains of this sand were measured mixed with some violet. and their individual volumes calculated on the asOf course the intensity of the colors and tints is sumption Volume (length X breadth) 3/*. B. t o a degree dependent upon the concentration of the The weight of the same 28 grains was divided b y resin in the solvent solution A, but a little experience in the application of the test with materials of known the specific gravity of quartz, also t o obtain the purity will soon give one the ability t o interpret the volume. The results were: Volume by microscope.. . . . . . 21.38 cu. mm. indications without difficulty. Volume by weight. . . . . . . . . . 11.84 cu. mm. In conclusion, I should state that I have not tested thoroughly the reliability of the color-reactions where . Evidently the depth averages a little less than several of those giving characteristic colors have half expression A for this sand. been in admixture, but in a few cases that were tried 1 By permission of the Director of the BureauIof Standards.
Edge by Vol.
(A) (0)
'!
Vol, by Wight
21.38 I 1.84
No.2 ,6898
,2203
T H E JOURNAL OF INDUSTRIAL AND ENGINEERING CHEMISTRY.
88
Sharp Grains.-A No. 2 fire-clay from Nelsonville, O., leaves sharp irregular fragments on a zo-mesh sieve. 50 of these grains showed:
Volume by microscope.. , . 0 . 6 8 9 8 cc. Volume by weight . . . . . . . 0 . 2 2 03 cc. Here the depth is approximately one-third of expression A. Flat Grains.-Evidently flat-grained minerals, like kaolin and mica, would give ratios far greater than these two cases. This leads us to be very skeptical of most calculations based on the diameter of mineral grains as measured by the microscope. Correct Size Measuremevtts.-Zsigmondyl computed the size of gold particles from the concentration of the solution, the specific gravity of gold, and the observed number of particles in a measured volume, obtaining results free from objection. He made no conjecture as to shape of particle, avoided the use of the word “diameters,” and assumed a cubical-shaped particle for computation purposes. This seems the most feasible procedure. Group Classification of Clays.--Seger,z the founder of the scientific study of clayworking problems, found it convenient to classify the grains of natural clays in groups between definite size limits as follows:
...........
Coarse sand. Fine sand.. , , , , , , , Silt.. Rock dust Clay..
Purdy surface factor.
Average diameter. Over 0.333 mm.
. . . , , 0.333-0.040 mm. .................. 0.040-0.025 mm. .............. 0.025-0.010 mm. ................. 0.100- 0.000 mm.
............
0,1865 0.0325
5.36 30.77 57.14 200 . O O
0.0175
0.0050
Arithmetical Mean.-Mellor3 says: “A trial obtained by subdividing a given fraction shows that the arithmetical mean of the extreme diameters, namely, (d, d z ) , may be less or greater than the true average diameter. The validity of the arithmetical mean has been called in question by A. Heath4 and by A. S. Cushman and P. Hubbard.6 The deviation is greatest when the adjacent fractions are very large in proportion t o the fraction under investigation.” Other Means.-Among other possibilities mentioned by Mellor are the geometrical mean, 2/d,d,; E. J
+
Laschinger’s
“average
diameter,
and Mellor’s average diameter,”
1Ed,
Feb.,
1911
All of these formulas are equally as true for cubes as for spheres, save those involving length and breadth. Law of Variation ~ P Za Group.-To investigate the reliability of duplicate measurements, we plot a sort of probability or variation curve, in which the measure-
Sand 07 20 M e s h
Wedron
1,IO
+
1.00
.90 80 1s” ‘ Individual
I I determim 21 ations. Fig. 2 .
ments are plotted as ordinates, the lowest measurement having zero as abscissa, the next lowest P, the
3.0 q0.z
Fireclay,
I\) elsonville, 0.
On20 Mesh
&
2.4
j(d,a+-d zij: 4
Von Reytt,6 using round-hole sieves, found ‘the diameter of the mean particle passed by one sieve and retained by the next to be 0.87 times the diameter of the mean sieve hole. As Von Reytt’s results were obtained on so much larger particles, it is questionable whether we are justified in including them in the table below. 1 2
Zsigmondy-Alexander, ”Colloids and the Ultramicroscope” (1909)’ “Collected Writings, American Ceramic Society translation,” p .
43 (1902). a Pottery Gazette, 35, 789; Trans. Eng. Cer. Soc., 9, 94 (1910). 4 Trans. Eltg. Cer. Soc., 3, 23 (1904). J . Ant. Chem. Soc., 29, 589 (1907). @Richards.Ore Dressiltg, 1, 305; Oest. Zeit., 36, 229, 246, 255, 268.
283 (1888).
2.0 7197111.
edge
1.4
t!
t 3 82
12
24 Fig. 3.
36
48%
ASHLEY AND E M L E Y ON T H E SIZES OF GRAIN OF MINERALS.
Best Meam-On the 3 forms of curve so found, the average edge (assuming cubical particles) is given in the above table, calculated by each of the methods, and also from direct measurement. All apply well to the straight line (Wedron) save Von Reytt’s. Mellor’s mean is least satisfactory for the elutriation residues, and the arithmetical mean nearly as bad. The geometrical and Laschinger means have deviations of different sign for the two kinds of elutriation residues. Von Reytt’s simple empirical device seems (perhaps by chance) to give best results, and would have given better had a smaller constant than 0.87 been employed. By examining grains by the methods given above i t should be possible to accumulate data showing what form of mean is most reliable. Surface Factors.-For many chemical and ceramic purposes, the activity of a material is considered proportional to its area. For computing the area, surface factors are employed:
