312 REPORTS ON THE STATE OF SCIENCE, ETC. 



intensity may be constructed. The underlying assumptions are that a 

 sense-distance is the difference between the sensation intensities corre- 

 sponding to its terminal stimuli, and that the difference between the sensa- 

 tion intensities corresponding to the lowest and highest of a series of unequal 

 stimuli is the sum of the sense-distances between the adjacent pairs of the 

 series. For this to be possible sense-distances must be samples of the same 

 magnitude as sensation intensity. Let us examine the proposed criterion 

 of equality. We define as equal the sense-distances between pairs of 

 unequal stimuli which satisfy a certain subjective criterion. It is un- 

 desirable to attempt to define this criterion at the moment because the words 

 we choose to define it tend to invest it with some one of a number of alterna- 

 tive interpretations. Suffice it to say that there is a condition which the 

 observer attempts to satisfy in experiments of this kind. For our present 

 purpose the nature of this condition is immaterial, the essential point is that 

 the practical operation of producing equal samples of sense-distance neces- 

 sarily involves at least three stimuli of different apparent intensities, whereas 

 the operation of producing equal samples of sensation intensity involves 

 only stimuli of the same apparent intensity. We see therefore that sense- 

 distance, whatever it may be, is not the same kind of magnitude for the 

 purposes of measurement as sensation intensity. The one cannot be 

 expressed on any scale applicable to the other, and it is meaningless to regard 

 them as quantities of the same measurable magnitude. 



It may be objected that this applies with equal force to the difference of 

 two samples of any magnitude. We cannot produce an example of equal 

 differences of length, for instance, without at least three objects of unequal 

 length while the operation of producing equal lengths involves only objects 

 which appear equal by our criterion of equality for length. The analogy 

 is illusory. Difference of lengths as something expressible on a quantitative 

 scale derives its significance from the association of number and length 

 established by the practical criteria of equality and addition which define 

 length as a magnitude. It merely means the length which must be added 

 to the smaller of two lengths in order to make a new length equal to the 

 larger of the original pair. We cannot define a process of subtraction 

 independently of a process of addition. We cannot construct a scale of 

 length from units of difference-of-length defined by operations other than 

 those involved in defining equality and addition for length. Similarly we 

 cannot give any quantitative significance to difference-of-sensation-intensity 

 unless we already have practical criteria both of equality and addition for 

 sensation intensity ; for all that difference-of-sensation-intensity means, 

 if it means anything, is the sensation intensity which, when added to the 

 smaller of two given sensation intensities, will produce a new intensity 

 equal to the larger. 



The mean -gradation series as a basis for determining a relation between 

 sensation intensity and stimulus intensity has therefore the same defect as 

 the j.n.d. series. The proposed criterion of equality is not the one applicable 

 to sensation intensities. Thus if sense distance is a magnitude, it must be a 

 different magnitude from sensation intensity. 



Further, as with the j.n.d. series, the proposed criterion of equality is not 

 a legitimate one for defining aiiy magnitude. Each sense distance in the 

 series is defined for practical purposes by a pair of dissimilar stimuli, a 

 different pair being applicable in each case. No symmetrical transitive 

 relation can be constructed from such material, therefore no criterion of 

 equality appropriate to measurement can be formulated for sense-distances. 

 So whatever sense-distance may be it is not a measurable magnitude ! 

 Thus if we examine by what right the word equal is applied to the pheno- 



