122 Dr. S. P. Thompson on Photometry, 



II. Periodic Principle in Photometry. 



It is a familiar fact to every person who is accustomed to 

 use the Bunsen photometer that the most convenient way of 

 taking observations is to swing the carriage which supports 

 the screen and mirrors backwards and forwards through a 

 continually-decreasing distance about the position of balance. 

 That position is ultimately found by the eye noting the suc- 

 cessive departures from equality produced by rapid small 

 displacements on either side of the position of balance. If 

 these inequalities can be made equal inter se, the zero will lie 

 midway ; for though the intensity of illumination (assuming 

 the sources of light as points) varies inversely as the square 

 of the distance, the change of intensity for a small change of 

 distance will (irrespective of sign) be the same, to within a 

 small quantity of the next higher order, whether the displace- 

 ment be toward the standard light or from it. For, taking 

 the initial distance as unity when the illumination is i, then 

 (neglecting small quantities of higher orders), when the dis- 

 tance 1 is made 1 + Br, the proportional change of illumina- 



2Sr 

 tion is +-z — ^- ; or, the change of illumination is approxi- 

 mately inversely proportional to the distance, and is approxi- 

 mately proportional directly, but with contrary sign, to the 

 displacement. 



It is a consequence of the law of fatigue that the eye is 

 much more sensitive to small differences of illumination when 

 these are successively produced than when they are constant 

 in amount. Hence it is easier to estimate the true zero 

 position on the photometer by these successive movements 

 than by simply trying to put the carriage at zero. A 

 difference due to a displacement of two millimetres of the 

 stationary carriage might fail to be perceived. But the eye 

 cannot fail to detect the difference when the carriage is 

 quickly swung to and fro over the distance of two millimetres 

 on either side of the zero ; and, judging of the two inequalities 

 on either side, and altering the adjustment until the two 

 inequalities are themselves equal, the zero is determined. 

 As a piece of pure physics, this method of successively 

 approximating to a zero, ill-defined in itself, by means of 

 equal errors on either side, may be compared with the method 

 of Joule for determining the temperature of minimum volume 

 of water. 



In the researches of Abney and Festing on the photometry 

 of colour, the same principle of estimating the position of 

 balance by producing rapid movements giving successive 



