24 Deceptive Figures. 



outside the true one. But now I could scarcely persuade 

 myself that I had not by mistake drawn the convexities of the 

 curves the wrong way; in other words, that the curvilinear 

 pentagon I had drawn was not a true pentagon, and its sides 

 the chords of a curvilinear pentagon inside the true one. I 

 had, in fact, to take a tracing of the curvilinear pentagon 

 before I could form a satisfactory conception of its real 

 shape. 



This illusion seems to have a direct bearing on the question 

 of the square-shouldered figure sometimes assumed by Saturn. 

 We see that a series of concentric, similar, and symmetrically 

 disposed curved lines, give to a straight line crossing them an 

 appearance of curvature in a direction opposite to that of the 

 curved lines. Hence a line drawn with a certain slight curva- 

 ture in the same direction as the curvature of the concentric 

 lines would appear straight, and a line with a greater curva- 

 ture would appear to have its curvature diminished. Further, 

 if such a line were continued beyond the concentric lines, the 

 alteration of curvature would disappear at a short distance 

 from the concentric lines. Hence IjI's observation of the 

 flattening of Saturn's equator, and his determination of a 

 maximum diameter and curvature at latitude 43° (not far from 

 the apparent intersection of the ring's outer boundary with 

 the outline of the disc) seems to be satisfactorily explained. 

 Yet it cannot be denied that there are grave objections to the 

 optical explanation of the phenomenon. One would expect 

 that the illusion would be perceptible in pictures of Saturn ; 

 that it would be always observable, or, if it be supposed to 

 depend on the extent to which the rings are open; that it 

 would always be noticed when the rings are open to a particu- 

 lar extent ; that it would disappear when the rings are closed ; 

 that it would not affect micrometrical measurement — or, if it 

 affected such measurement in one case, that it would do so in 

 all cases. A perusal of Mr. Webb's review of the evidence 

 (pp. 250-252 of the May number of the Intellectual Observer) 

 will suffice to show that not one of these conditions is fulfilled. 



I venture with great diffidence to offer some considerations 

 which seem to point to a different solution of the difficulty. 



If we assumed, either that the atmospheres bear any pro- 

 portion to the masses of planets, or that any provision is made 

 by increased depth of atmosphere for diminution of solar heat, 

 we might fairly suppose that the height of Saturn's atmosphere 

 is nine or ten times as great as that of our own atmosphere. 

 Now the earth's atmosphere has been supposed to extend to a 

 height of from 100 to 150 miles (Nichol's Cyclopaedia of the 

 Physical Sciences, Art. "Atmosphere"); but taking the more 

 moderate estimate of 50 miles, the height of Saturn's atmo- 



