14 Mr. Francis Galton [Jan. 27, 



just-perceptible increment of sensation, has been taken at the average 

 of 1 per cent, for light, 6 per cent, for muscular effort, 33 per cent, 

 for sound and warmth ; also 33 per cent, for pressure upon most parts 

 of the body, and as high as 16 per cent, upon the finger tips. But 

 these values must not be trusted too far; they cease to be exact 

 towards the two ends of the scale. 



A mechanical arrangement clearly illustrates the consequences of 

 Weber's law. It includes an axle to which is fixed a wheel, a part 

 of a logarithmic spiral, and an index hand. This portion of the 

 machine is carefully balanced, so that it will remain steady in any 

 position in which it is set, while a small force is sufficient to cause it to 

 turn ; behind all is a card with equal graduations upon it, over which 

 the index travels. A string, with a scale pan at one end and a 

 counterpoise at the other, is wrapped round the wheel. A string 

 fastened to the axle passes over the logarithmic arm, and a ball is 

 fastened to its free end. The varying weights put in the scale pan 

 will now represent varying amounts of stimulus, and the graduations 

 to which the index points, represent the corresponding variations of 

 sensation. 



I exhibit a diagrammatic model of the apparatus, much too rough 

 to give exact indications, but still sufficient for rough explanatory 

 purposes. 



Owing to the obvious properties of a spiral, the more the axle to 

 which it is fixed is rotated in the direction of its concave side, the 

 further does the point at which the string is hanging travel away 

 from the axis, and the leverage exerted by the weight of the ball will 

 increase. Whatever be the weight in the scale pan, there is within 

 the working range of the apparatus some position of the beam at 

 which that weight will be counterbalanced by the ball. The pro- 

 perty of the logarithmic spiral is that equal degrees of rotation 

 correspond to equal percentage increments of leverage. Hence, when 

 percentage increments of weight are successively placed in the scale 

 pan, the index attached to the beam will successively travel over 

 equal divisions of the scale, in accordance with Weber's formula. 



The progressive increase in the effective length of the logarithmic 

 arm is small at first, but is seen soon to augment rapidly, and then to 

 become extravagant. We thus gain a vivid insight through this 

 piece of mechanism into the enormous increase of stimulus, when 

 it is already large, that is required to produce a fresh increment of 

 sensation, and how soon the time must arrive when the organ of 

 sense, like the machine, will break down under the strain rather than 

 admit of being goaded farther. 



The result of all this is, that although the senses may perceive 

 very small stimuli, and can endure very large ones without suffering 

 damage, the number of units in the scale of sensation is comparatively 

 small. The hugest increase of good fortune will not make a man 

 who is already well off many degrees happier than before; the 

 utmost torture that can be applied to him will not give much greater 



