SENSATION AND PERCEPTION 127 



quantity of a there is just so much, and neither more nor less, 

 quantity of b. There is an independent variable a and there is 

 another variable b the occurrence and magnitude of which depends 

 on a. Now if w^e do not know from experience or investigation 

 that the relation of functionality holds for two variables we cannot 

 assert it a priori. Thus pure carbon burns in oxygen with the 

 generation of heat and for so much carbon that is burned there 

 will be just so much heat generated, and we can predict that this 

 will happen from our experience. But we do not know that 

 some hitherto unknown substance will burn in oxygen nor can 

 we predict, even after establishing the bare fact of the combustion, 

 that there will be a definite quantity of heat resultant from the 

 combustion. 



In the relation of physico-mathematical functionality the terms 

 a and b in the equation b = f{a) are stated in the same denomina- 

 tions or are reducible to the same denominations. Thus a gram of 

 pure carbon when burned in pure oxygen generates just so many 

 calories of heat. Then the quantity of heat in calories, ^, in the 

 above equation is a definite linear function of the number of grams 

 of carbon, a, each gram generating just so much heat. Again 

 the momentum of a projectile, b, fired from a gun in standard 

 conditions, is a function of the charge of explosive. When the 

 latter is fired, just so much kinetic energy is developed. Kinetic 

 energy is to be stated in terms of mass and velocity and the 

 momentum of the projectile, when it leaves the muzzle of the 

 gun, is also stated in terms of mass and velocity. 



Simple dependence. We know, /row experience^ that a sensation 

 is had by us when some particular receptor, or nerve, or nervous 

 centre, is stimulated. (A noise comes from atmospheric vibrations 

 impinging on the auditory organ, or from tinnitus aurium, when 

 the auditory centre is otherwise stimulated, or from an overdose 

 of quinine.) The sensation " depends on " one or other of these 

 antecedent events, but the sensation cannot be expressed in 

 terms of the motions of the molecules of the atmosphere or 

 of the motions of the atoms, molecules, etc., of quinine : it has 

 nothing in common with these " causes," though it depends on 

 them. 



Statistical dependence. Here there is a cause, or series of causes, 

 but there is no one definite effect. When a pack of cards is 

 shuffled (or thrown into " disorder ") and when the pack is cut 



