Tyler (Taylor) standard screen scale: what is the ratio of the actual mesh opening (aperture) of a screen to that of the next smaller screen in the series?

Introduction / Context:
The Tyler (often called Taylor) standard screen scale uses a geometric progression for sieve apertures. Recognizing the fixed ratio between successive openings helps interpolate sizes and relate mesh counts to actual openings.

Given Data / Assumptions:

• Standard Tyler scale based on a geometric series.
• Successive opening ratio is constant.

Concept / Approach:
The aperture size in the Tyler scale decreases by a constant factor between adjacent sieves. The factor is the square root of 2 (≈1.414) for one step. Hence the opening of a given sieve is √2 times the opening of the next smaller sieve.

Step-by-Step Solution:
Aperture progression: a_n = a_0 / (√2)^n.Therefore, a_n / a_{n+1} = √2 ≈ 1.414.

Why Other Options Are Wrong:
2.0 and 3.0: far larger than the accepted ratio; would create overly coarse steps.1.50: close, but not the standardized √2.

Final Answer:
√2 ≈ 1.414