592 



NATURE 



[October 20. 1892 



«ye, and held horizontal nearly on a level with the eye, the 

 true relations will appear. Fig. 1 1 is valuable for its con- 

 clusive demonstration that the deviation is proportional 

 to the angle ; the increasing angles gradually bend the 

 straight lines away from one another, and give them 

 the gradual change of direction of curves. These and 

 other forms of illusion are all included in the generaliza- 

 tion that the sides of an angle are deviated towards the 

 direction of that angle.^ 



The psychological principle with which this general- 



ization may be correlated is the law of relativity. This 

 law emphasizes the fact that a sense-impression is not 

 the same when presented alone and when in connection 

 with other related sense-impressions. We cannot judge 

 the direction of lines independently of that of the angles 

 whose sides they form. As a further illustration of this 

 principle it may be shown that angles will affect the 

 apparent lengths of lines as well as their apparent direc- 

 tions. If in Fig. 12 we compare the horizontal portion 

 -of the uppermost figure with that of the lowest, it is 



.almost impossible to believe that they are of equal length. 

 The intermediate horizontal lines seem intermediate in 

 length, and thus illustrate the fact that the apparent length 

 of the horizontal lines is directly proportional to the size of 

 the angles at their extremities. The illusion would persist 

 if we converted these figures into truncated pyramids by 

 adding a line parallel to the horizontal line, and would 



' The reader is referred to the original paper for further illustration of 

 this dictum, as well as for explanations of apparent exceptions and a dis- 

 .cussion of the conditions affecting it. 



NO. TTQ9. VOT,. 46] 



then illustrate the fact that equal lines may be made to 

 appear unequal by the effect of the areas whose contours 

 they help to form. A converse effect is illustrated in 

 Fig. 13. Here the upper figure seems larger than the 

 lower, because its larger parallel side is brought into 

 juxtaposition with the smaller parallel side of the lower 

 figure. This illusion and others show especially well 

 when cut out of paper and held against suitable back- 

 grounds. As the figures are moved about one another 

 the upper constantly becomes the larger. More than 

 two figures may be used, and a variety of such contrasts 

 may be formed. 



The subject is by no means fully considered in these 

 illustrations, nor is the explanation offered as final or 

 adequate. If it seems to direct investigation into fruitful 

 paths its chief purpose will be accomplished. 



THE NEW SATELLITE OF JUPITER. 



'T^HE new number of the Astronomical Journal cox\- 

 -*■ tains Mr. Barnard's account of his discovery of this 

 additional member of our system. We make the follow- 

 ing extracts :— " Nothing of special importance was 

 encountered until the night of September 9, when, in 

 carefully examining the immediate region of the planet 

 Jupiter, I detected an exceedingly small star close to the 

 planet, and near the third satellite. I at once suspected 

 this to be a new satellite. I at once measured the dis- 

 tance and position-angle of the object with reference to 

 satellite three. I then tried to get measures referred to 

 Jupiter, but found that one of the wires had got broken 

 out and the other loosened. Before anything further 

 could be done the object disappeared in the glare about 

 Jupiter. Though I was positive the object was a new 

 satellite, I had only the one set of measures, which was 

 hardly proof enough for announcement. I replaced the 

 wires the next morning. The next night with the great 

 telescope being Prof. Schaeberle's, he very kindly gave 

 the instrument up to me, and I had the pleasure of veri- 

 fying the discovery, and secured a good set of measures 

 at elongation. In these observations, and those of the 

 succeeding night, only distances from the following limb 

 of Jupiter could be measured. These were observed with 

 the wires set perpendicular to the belts. The planet was 

 thrown outside the field, the satellite bisected, and then 

 the limb brought in and bisected also. This method 

 would not permit any measures from the poles of the 

 planet for latitude. On the 12th I inserted a strip of 

 mica, carefully smoked, in front of the field-lens, for 

 occulting the planet. This served admirably, permitting 

 the satellite and planet to be both seen at once, and 

 measures from the polar limbs could be made with great 

 ease. The observations of the satellite from the 12th 

 were all thus made. 



" To avoid any personal equation I have on each night 

 measured the diameters of the planet, for use in reducing 

 the observations to the centre of Jupiter. Since the 12th, 

 these have been measured through the smoked mica, so 

 as to avoid introducing any error from the reduced 

 brightness of the planet. The diameters were measured 

 by the method of double distances. Just what the mag- 

 nitude of the satellite is, it is at present quite impossible 

 to tell. Taking into consideration its position, however, 

 in the glare of Jupiter, it would, perhaps, not be fainter 

 than the thirteenth magnitude. It will only be possible 

 to settle this question with any certainty by waiting until 

 some small star of the same magnitude is seen close to 

 Jupiter, and then after determining its magnitude when 

 away from the planet. In general the satellite has been 

 faint— much more difficult than the satellites of Mars. 

 On the 13th inst., however, when the air was very clear, 

 it was quite easy. 



" It is scarcely probable that this satellite will be seen 



