A further mechanical test, forming a part of the scheme of investigation, is the resistance of the paper to rubbing. This test is an altogether empirical one, as the following brief description will show:—A piece of the paper, about 6 inches square, crumpled by successive folding in two directions at right angles, is grasped by the thumb and forefinger of each hand, at a distance of 3–4 inches apart. It is then rubbed upon itself across the thumbs a given number of times (seven is the number chosen) and held up to the light. If no holes are visible, the rubbing is repeated. The number of times necessary to repeat the rubbing until holes appear is the measure of the resistance. A sufficient uniformity in the results of this test has been observed to make it the basis of a classification of papers, in regard to their resistance to such disintegration; they are divided into the following eight groups, beginning with the lowest:— 0. Extremely weak. 1. Very weak. 2. Weak. 3. Medium. 4. Moderately strong. 5. Strong. 6. Very strong. 7. Extremely strong. The classification of papers on the results of these tests cannot be more lucidly given than in the following scheme, under which the results are officially recorded:— _Class_. 1 2 3 4 5 6 _a._ Mean breaking length (metres) not less than 6000 5000 4000 3000 2000 1000 _b._ Mean elongation (per cent.) at fracture not less than 4·5 4 3 2·5 2 1·5 _c._ Resistance to rubbing 6 6 5 4 3 1 {198} This classification is based on the results of some hundreds of observations. It is interesting to note the differences observed in the numbers for _a_ and _b_ according to the direction for the test in which the paper is cut, i.e. in the direction in which it was run on the paper machine, or at right angles (see Chap. XI. p. 171). The mean ratio for the breaking lengths (strains) may be taken as 1 : 1·6, i.e. the paper is about 40 per cent.[16] weaker across the web; the elongation under strain on the other hand is about double. [Footnote 16: In the statement of results the mean of the numbers obtained in the two directions is given.] It is also of interest to note the influence of the glazing process (p. 167) upon the quality of the paper as determined by these tests. First, we must notice the effect of the treatment upon the substance of the paper itself. The mean reduction of thickness is 23 per cent. On the other hand, the reduction of weight, calculated per unit of surface (square metre), is 6·7 per cent., whence we may infer an increase of surface, flattening out, in the process. These quantities, but more particularly the latter, will doubtless vary with the various methods of glazing and with the materials of which the paper is composed.