360 PROCEEDINGS OF THE AMERICAN ACADEMY. 



by its contrast with the ground-tone upon which it has been drawn. If 

 the ground-tone is white paper, the value having the greatest attractive 

 force is black ; if the ground-tone is a half-tone between white and black, 

 the forces of white and of black are equal. What is the result of all 

 these forces of attraction, as they act upon the eye? The eye is held at 

 rest at their centre of equilibrium. Where is that centre ? In order to 

 answer this question, we must bring the values into a scale-relationship 

 upon a common ground-tone, otherwise we have no means of measuring 

 their respective contrasts, or the forces of attraction which depend upon 

 their contrasts. Make a scale of seventeen values, exclusive of white and 

 black, in seventeen circles of half an inch radius, in a straight line, half 

 an inch apart, and upon a ground-tone of the middle value. Be sure that 

 the values are at etjual intervals of equal contrasts. In order to get 

 them into the perfect scale-relation which this implies, establish the ex- 

 tremes first, then the mean between the extremes, tlien intermediates, until 

 the scale is complete. The interval or contrast between value and value 

 may be great or small; the scale may be central in pitch, high in pitch, 

 or low. It is central in pitch when its middle value is at the half-point 

 between white and black. Considering the scale of values which you have 

 produced, you observe what you have observed before, that each value is 

 a force of attraction, that this force, other things being equal, depends 

 upon the contrast with the ground-tone. The only value which has no 

 force of attraction is the central one of the scale, the value which coincides 

 with the ffround-tone and cannot be distinguished from it. Lookinor at the 

 scale again, pick out the values which have the same force of attraction. 

 They will be those at equal distances from the half-tone, which is the 

 ground-tone, making equal contrasts with it. In order to distinguish the 

 different values of the scale, we will call the middle value zero (0). 

 The values above the middle value we will call 1, 2, 3, etc., above. The 

 values below the middle we will call 1, 2, 3, etc., below. The values 

 above can be written thus: X, 2, 3, etc.; the values below thus: T, 2, 3, 

 etc. The values having the same force of attraction are, then, those 



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havinof the same numbers: ,i -r> o' etc. The numbers are the measures 

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of the contrasts, and of the forces of attraction depending upon the con- 

 trasts. If now we scatter our seventeen values over the ground-tone of 

 the middle value we shall be able to discover the centre of equilibrium of 

 their forces, that is to say, the point where the eye is held by them. AVe 

 have simply to remember the familiar principle of balance ; that equal 

 attractions balance at equal distances on a line connecting their centres; 



