Various bases for the starting point in screen scales have been proposed. As the United States Government has standardized the 200-mesh sieve made from 0.0021-in. wire, having an opening of 0.0029 in., this sieve has been adopted as the base of the Tyler standard screen scale.

The 100-mesh and the 20-mesh sieves in this scale also come within specifications adopted by the Bureau of Standards, so that there are three sieves in the series which have been standardized by the Bureau.

The ratio between different sizes of the screen scale has been taken as 1.414 or the square root of 2, as recommended by Rittinger in his work on ore dressing. The niceness of this will be apparent from the following: Taking 0.0029 in. or 0.074 mm., the opening in the 200-mesh sieve as the base or starting point, the diameter of each successive opening is exactly 1.414 times the opening in the previous sieve. It also makes the area of surface of each successive opening in the scale just double that of the next finer or half that of the next coarser sieve. In other words, the diameters of the successive sizes have a constant ratio of 1.414 while the areas of the successive openings have a constant ratio of 2.

This constant ratio in the openings is shown drawn to scale, Fig. 67. To illustrate : the opening 0.093 in. in the (8-mesh) sieve is 1.414 times the opening in the preceding sieve 0.065 in. (10-mesh). The area of the opening in 0.093 in. (8-mesh) sieve is twice that of 0.065-in. (10-mesh) and just half the area of the opening in the 0.131-in. (6-mesh) sieve.

Another advantage in this selection of ratio is that by skipping every other screen, you have a ratio of diameter of 2 to 1 , by skipping two sizes you have a ratio of 3 to 1 (approximately), and by skipping three sizes, you get a ratio* of 4 to 1, so that in selecting a screen scale for concentrating work, for instance, you can pick out from the table without any calculation a 1.414, 2, 33 or 4 to 1 ratio of opening.

The screen scale in the following table is based on an opening of 0.0029 in. and increases in series in the ratio of the fourth root of 2 or 1,189, the factor recommended by Prof. Richards in his work on ore dressing.