3i6 REPORTS ON THE STATE OF SCIENCE, ETC. 



and so on, which is not necessarily a member of the group of phenomena 

 we are perceiving at any given moment ; whereas by relative extensions 

 we mean relative not to an external fixed standard but to the other extensions 

 of the same magnitude within the perceived group of phenomena. In a 

 relation structure composed of lengths, those relations involving absolute 

 extension determine what we vaguely call the size of the structure while 

 those involving only relative extensions, in this case the ratios of the various 

 lengths, determine what we call the shape of the structure. Of two such 

 structures it may happen that the relations involving absolute lengths are 

 different but that all the relations involving the ratios of lengths are identical. 

 The two structures are of the same shape but of different sizes. The terms 

 size and shape are so convenient for discriminating between properties 

 depending on absolute extension and those depending on relative extension 

 that it will be useful for our present discussion to extend them to apply 

 to relation structures involving any extensive magnitude. We may use 

 the term relation-shape to signify the sum total of those properties of a 

 relation structure involving any extensive magnitude which depends only 

 on the relative extensions of the samples of the magnitude comprising the 

 structure, and relation-size to signify the sum total of those properties of 

 the structure which depend on the absolute extensions. For instance, 

 consider a .simple relation structure involving two masses A and B of 20 

 and 30 gm. As this particular structure does not include the universal 

 standard gram, the relations of the masses A and B to this standard are not 

 part of the structure, so the masses of A and B are absolute extensions of 

 the magnitude mass. Of course the symbols 20 gm. and 30 gm. used to 

 denote these absolute masses are meaningless unless we determine the 

 relation between each mass and the standard gram, but this is determined 

 from the examination of other relation structures of which the standard 

 gram is a part. So long as attention is confined to our present structure 

 the masses are absolute. Relations exhibited by this structure include 

 (i) B - A = io gm.) {z) B + A = 50 gm. ; (3) BjA = 1-5. If we 

 have another structure involving masses C and D of, say, 40 and 60 gm., 

 the corresponding relations are : (i) D — C = 20 gm. ; (2) Z) + C = 

 100 gm. ; (3) D/C = 1-5. Relations (i) and (2) involve absolute masses ; 

 relation (3) only relative masses. These two structures have the same 

 relation-shape but diflFer in relation-size. In the same way, two relation 

 structures involving, say, brightnesses, may have the same relation-shape 

 provided the ratios of the brightnesses comprising one structure are the 

 same as the corresponding ratios in the other structure, but will differ in 

 relation-size if the absolute brightnesses of the corresponding members of 

 each structure are not equal. 



Of the physical relations constituting a relation structure of the kind we 

 call an object, the relation-sizes are properties of the body just as much as 

 the relation-shapes ; but they are not of equal importance for intuitive 

 recognition. The complete relation structure of an object can never be 

 perceived on any single occasion. It is a synthesis of many relations 

 observed in diflFerent ways at diflFerent times, and usually involves several 

 of our senses. We can never see a house ; we can only see the visual 

 relations exhibited by the particular bit of the outside or inside of it which 

 comes within the field of view at one instant. In order to become 

 acquainted with all the visible properties of a house we have to perform 

 numerous acts of seeing at different times and in diflFerent conditions. 

 Even then we have not apprehended the whole house : we have to feel 

 all over it for such tactile relations as it may exhibit — hardness or softness 

 of its various parts, roughness or smoothness, etc. — and perform all sorts 



