as 16 lbs. ; but if the piece had been cut up into four strips, only one of them would break at 16 lbs., the others breaking at higher figures, say 17, 18, and 18 for example This would give an average of 171⁄2 lbs.

The following experimental result serves to illustrate this point:

A brown paper of good quality, substance 29 lbs. double crown, was examined, various lengths of constant width (inch) being tested. Table XI. gives the figures for each length, five tests being made in each case.

(2) The necessity of having a definite width for the test piece.-Theoretically width should have no influence on the breaking strain, since a 2-inch strip might be expected to stand double the breaking strain of a 1-inch strip. As a matter of common experience, it frequently happens that the wider strips favour a higher result. The following tests show the variations of an actual case: Examined a common printing, 28 lb. double crown, testing strips of varying width on a constant length of 3 inches (between the clamps). Each figure recorded is the mean of five tests.

(3) The influence of the conditions under which the tension is applied to the paper.-Usually the tension is applied at a constant rate, the speed of the machine being carefully regulated as far as possible. This method, however, takes no account of the variation in stretch exhibited by papers or by the same paper in the two directions of the sheet. Very little investigation has been made as to the proper conditions for the rate of application of the tension in the case of paper. If one paper has twice the percentage stretch of another, and both are tested in a machine in which the rate of speed is constant, then the former would take a longer time to break. The exact effect of varying times ought to be thoroughly investigated.

(4) Influence of moisture in the air.-The moisture of the air has considerable effect upon the strength and elasticity of a paper. As the proportion of moisture in the air increases, so the strength decreases, and the stretch of the paper under tension increases. This question has been very fully studied by Herzberg, who gives the results of an interesting investigation with a good writing paper made of rags, sized with rosin, and 'tested under varying conditions of moisture. (See Table XIII.)

Machine direction of paper.-The strength of paper is never absolutely the same in both directions of the sheet, even in the best hand-made papers. With machine-made papers the difference is usually very marked, the strength being greatest in what is known as the machine direction-that is, the direction in which the wet pulp is travelling on the wire during its formation into paper. When the sheet of paper under examination is a normal sample, so that it may be assumed the edges are cut strictly parallel to the machine direction, as is usually the case, the two directions are readily identified by the differences in the tests for strength. If the sample is irregular in shape, without any folds, and the directions cannot be determined by a close examination of the appearance of the sheet when held up to the light, the machine direction may be detected by floating a circular disc on water for a few seconds. The paper

is carefully removed so that the upper surface is not wetted, and placed on the back of the hand. The paper curls up into a cylinder, the axis of which is parallel to the machine direction of the sheet.

If two strips, each 3 or 4 inches long and about 1 inch wide, cut from the machine and cross directions respectively, are held together between the thumb and finger at the ends, and allowed to move freely, they behave in a peculiar manner, as shown in Fig. 96. (1) When the lower strip is that cut in the machine direction, the two pieces hang close together.

Per cent.

Per cent.

Kilos.

Kilos.

Kilos.

Per cent.

Per cent.

Per cent.

Km.

Km.

100

21.5

3:07

69.7

2.83

6.8

14.1

11.5

2.41

80.7

Relative
Humidity of
the Air.

Moisture

contained in
the Paper.

Fig. 96.-Determination of the Machine
Direction of Papers.

(2) When the lower strip is that cut in the cross direction, it falls away from the upper strip.

The explanation of this test is obvious enough.

Breaking Length. The strength of a paper may also be recorded by calculating the "breaking length," or the length of paper which, if suspended, would break of its own weight. The data necessary for this calculation are (1) the exact weight of the strip tested, (2) its length, (3) the breaking-strain as found by trial. In the absence of a delicate balance for weighing the strip, the figure may be calculated approximately from the weight of the The following example will serve to show the method of arriving at the breaking length from these data:

ream.

Example. A paper of substance 20" by 30", 72 lbs. (480 sheets), is tested for breaking strain on a strip i inch wide and 5 inches long, and breaks at 60 lbs.

Since the ream weighs 72 lbs., the weight of a strip 5" by 1" can be found. 480 x 20 x 30 square inches weigh 72 lbs.

If for the 60 lbs. weight necessary to break the paper a length of paper weighing 60 lbs. be substituted, fracture of the suspended length would take place.

8

1

As lb. is the weight of a strip 5 inches long, 60 lbs. is that of a strip 240,000 inches long, which is the breaking length, viz., 6666.6 yards.

The rule for finding the breaking length is therefore: multiply the breakingstrain recorded on the testing-machine by the length of the strip tested, that is by the length of the piece between the clamps on the apparatus, and divide the product by the weight of the strip.

Bursting-strain.-Machines which register the strength of paper in terms of the pressure necessary to break a sheet fastened between two horizontal clamps are useful because no special precautions are required in adjusting the paper, whereas in the tension machines great care must be exercised not only in cutting the strip to an exact width with edges clear and free of notches, but also in the adjustment of the paper so as to secure correct alignment in the machine between the clamps.

Mullen's machine.-This is one of the most useful appliances of this type. It consists of a small hydraulic cylinder with a pressure-gauge attached. The paper is clamped over one end of a cylinder filled with glycerine, having a flexible rubber diaphragm between the liquid and the paper. The liquid is supposed to conform perfectly to any irregularity in the paper, and thus the pressure acts uniformly. (Fig. 97.)

Southworth's machine. This works on the same principle as Mullen's, but the pressure is transmitted through a metal piston, which is forced upwards through the sheet of paper. (Fig. 98.)

Woolley's machine.-This is a diaphragm apparatus in which the piston is forced downwards through the paper. The strength of the paper is registered on a scale of arbitrary degrees, whereas in the other machines the pressure is recorded in pounds per square inch. (Fig. 98A.)

Elasticity and Stretch.-These terms are usually applied to the behaviour of paper as it elongates when under the influence of tension on a paper-testing machine. The term stretch is also frequently applied by printers to the behaviour of paper when it expands on becoming moist. The use of the word

in this double sense is rather misleading, and it would be better to confine the word "stretch" as meaning the elongation of paper when submitted to tension, and to describe the behaviour of paper when moistened, by the term "expansion."

The stretch of a paper is automatically registered by most paper-testing machines when the paper is examined for strength. Since it varies with the length of paper tested the amount of elasticity or stretch is recorded in terms of the percentage elongation which results from the tension applied. Thus if the elongation on a four-inch strip at the moment of fracture is three thirty-seconds of an inch, then the percentage elongation is 2.3.

There are many interesting points to be observed in connection with the behaviour of a paper when it is stretched.

(1) The paper always stretches least in the stronger direction, and the greatest percentage stretch is found in the weaker direction. In a machinemade paper the maximum stretch is found in the cross direction, and the minimum stretch in the machine direction. This is also true to a limited extent of hand-made papers. It is usually assumed that the strength of a hand-made paper is the same in both directions of the sheet, but as a matter of fact there is always a uniform difference, though not so marked as in the case of machinemade papers.