GKAPHIC METHOD. 142 GKAPHITE. curve in the annexed figure represents the sums paid by the I'nited States Government for pen- sions in VMriniis years as follows (1)V ten millions of dollars): 1802. O.S; 1803, 1; 1804, 5; 1805, 8; 1870, 28; 1880, 57; 1890, 100; 1891, 119; 1892, 141 1894, 141 1890. 139 1898. 140 In al{ [graphic
- 1893, 158;
- 1895. 141;
- 1897. 141;
1899, 139. f e b r a the method of cd form, massive, or even in hexagonal crys- tals, but its greasy feel, softness, and black streak enable it to be easily distinguished. While black lead is the popular name, it is misleading, for graphite is nearly pure carbon, with only 1 or 2 per cent, of impurities, as can be seen from the following analyses: representing equations may be illustrated thus : To represent the equation i/ = a; — 1, X may have the values: — 1, 0, 1, ^ ... In which cases i/ will have the values . — 2, — 1, 0. 1 . . . Plotting the correspond- ing values of x and y as rectangular co- ordinates (see Coordinates), the line 1 is called the graph of the equation y = ^ — 1- Similarly the graph of the equation 2j^ — 3^"= 10 is as Fig. 3. shown in Fig. 3, the corresponding values of x and 2/ being X = ± -^^, ± ■/&. dz -i/f. ^ Vs. ■ ■ • 2/ = 0, ± ^Q, ± 1/3. ±V2.--- In mechanics the condition of equilibrium of a system of concurrent plane forces may be ex- pressed by the closing of a broken line; e.g. the forces fj, f,, ft, acting at the point P. are in equilibrium when the three lines f/, f,'. f/, paral- lel to f„ /,, f,, form a triangle. Such polygons are called funicular polygons. The analytic rep- Fio. 4. resentation of the forces is very simply effected by means of complex numbers. Another use of the graphic method may be seen in the case of the hodograph (q.v.). GBAPHITE ( from Gk. ypa^ij, graphs, writing, from 7/)d0ei>', graphein, to write). Black Lead, or Plumbago. A dark steel-gray to black mineral, having a black streak, hardness of 1.2. and specific gravity of 2.25 to 2.27. It crystallizes in the hexagonal system, and may occur in foliat- Analyses of Geaphite Carbou Ash VolatUe % 98.817 97.026 % .28 1.78 % .90 594 Brougham Can Although widely distributed, graphite rarely occurs alone in large deposits, but is usuallv mixed with other minerals, so that it requires special treatment after mining to separate it from the accompanying rock. It is usually found in crystalline metamorphie rocks, such as lime- stones, gneisses, or schists, and especially those of Pre-Cambrian age; still deposits are known to occur in the Carboniferous. It has also been found in small quantities in meteorites. Two forms of graphite are recognized, viz. the crys- talline or true graphite, and the amorphous or graphitic anthracite. The deposits form veins, disseminations, or beds. On account of the chemi- cal similarity to anthracite coal, many have con- sidered graphite to be of organic origin, and some have taken its presence in Pre-Cambrian rocks as an indication of the existence of plant life at that time. The organic theory is correct, how- ever, in only a few instances : e.g. when beds of coal are found passing into graphitic anthracite as the result of intense metamorphism in cer- tain parts of the deposit. The Rhode Island and Bavarian graphite is of this nature. In vein deposits or disseminations in gneissie rocks, it is more probable that it has originally been in- troduced into the rock in the form of a liquid hydrocarl)on, which has subsequently been con- verted into graphite; while in other cases, as in Ceylon, Weinschenk believes that the graphite is of volcanic origin, and due to the reaction be- tween carbon dio.xide and cyanogen compounds. In some limestones which have been subjected to contact metamorphism the carbonaceous matter has been changed to graphite. The chief commercial sources of graphite are Ceylon and Austria-Hungary, smaller amounts being produced in Bavaria, Italy, Siberia, Mexico, Japan, Canada, and the United States. The Ceylon deposits, which are worked entirely by natives, are of great extent, and masses of solid graphite weighing several hundred pounds are sometimes found. The Canadian graphite occurs in Laurcntian rocks, notably in the vicinity of Brougham, and has been obtained in lumps of large size. In the United States ci"j-stalline graphite is mined near Hague, N. Y., and to a considerable extent in Chester County, Pa. At the former locality it occurs in a bed of quartzite inclosed between gneiss. Other localities in the United States are Alabama, Wyoming, North Carolina. Wisconsin, Michigan, and Rhode Island. That obtained from the last two localities is amorphous graphite. Graphite is used in the manufacture of lead pencils, lubricants, stove-blacking, paint, refrac- tory crucibles, and foundry facings. For pencils and lubricants the best grades have to be em- ployed, and in the manufacture of crucibles.
