A Refresher of the Original Bloch's Law Paper (Bloch, July 1885)

Abstract

In 1885, Adolphe-Moïse Bloch asked the following simple question "Is there a law describing the relationship between the duration of a light and its perceived intensity?" Based on a series of experiments using a Foucault regulator and a candle, Bloch concluded that "when the lighting duration varies from 0.00173 to 0.0518 seconds (…) the [visible] light is markedly in inverse proportion to its duration"-his famous law. As this law pertains to the more general and hotly debated question of accumulation of sensory information over time, it is timely to offer the public a full translation of Bloch's original paper (from French) and to present it within the context of contemporary research.

Keywords: detection; drift-diffusion; information accumulation; linear systems; temporal integration; transfer function.

Figure 1.

Different “regulators.” (a) The James Watt (1736–1819) regulator. Two shafts link two heavy balls to a vertical rod whose rotatory motion is driven by a steam engine through a lever. As the angular speed increases, the centrifugal force moves the balls further apart while the sliding collar rises along the rod thereby acting on the lever to decrease the steam admission. The opposite occurs when the angular speed is too slow. (b) One of Foucault’s regulators built for the imperial marine. Such regulators were little if at all affected by the gravity. Highly sensitive springs provided the restoring force. Steam admission was regulated by levers (not shown) integral with the sliding collar. (c) A Foucault blade regulator built by Eichens in 1867. Here the rotation of the aluminium blades whose gap increases with their angular speed is proportionally slowed down by the opposition of the air. The counterweights were meant to increase the sensitivity.

Figure 2.

Bouguier’s simplest photometer presumably used to compare the brightness of two light sources, one at a fixed distance from the screen (the candle) and the other at a variable distance modulated so that the perceived lightings of the two half-screens appear equal. It is required that both areas be illuminated at the same angle, for the intensity of illumination depends essentially on the angle at which the rays arrive (from http://mpec.sc.mahidol.ac.th/radok/physmath/PHYSICS/l2.htm).