OP ARTS AND SCIENCES. 431 



To solve this equation, its first member was placed equal to ?h, and 

 various values of h substituted ; a curve was then constructed with m 

 and h as coordinates, and a few trials readily gave the value of h cor- 

 responding to m =z 0. This affords an easy means of solving many 

 equations not readily treated by the usual methods. The value of h 

 thus found was a little less than unity. Substituting h = 1 gives 

 log a = — .5835, a = .2 GOO, log b = .5835, and b = 3.833. Or, if the 

 effect of the solar atmosphere resembles that of a homogeneous atmos- 

 phere, its height must equal the radius of the sun, and its opacity be 

 such that the light in the centre is only .26 of what it would be were 

 the atmosphere removed ; or the sun's brightness in the latter case 

 would be throughout 3.8 times its present brightness at the centre. 

 Substituting these values of a, b, and h in our first equation, gives 



log y = .5835 — .5835 (^4: — x' — \/l — x-), 



in which, by substituting various values of (c, we deduce the corre- 

 sponding values of y, the light at various points of the sun's disk. In 

 Table I., the column headed Theor. gives the amount of light computed 

 by this formula, and the last column the differences from the mean ob- 

 servations, M. Three other theoretical values were computed for these 

 points, but those given in the table were retained as agreeing most 

 nearly with observation. From these it appeared that a considerable 

 variation in h did not alter the amount of light very materially, that a 

 diminutive change of A of one-tenth increased the light between x = .G 

 and x = .d only half a per cent, and for other values of x altered y 

 still less. Moreover, the differences in the last column of the table 

 are evidently too regular to be due to accidental error, but rather show 

 a real variation from theory, due to the fact that the atmosphere is not 

 really homogeneous. We might assume that the law of the density is 

 the same as that of the earth's atmosphere, or that, the height being 

 taken in arithmetical progression, the densities will vary geometrically. 

 But this leads to an equation which cannot be integrated, and, more- 

 over, cannot be correct in fact, since it assumes that the temperature 

 is uniform throughout. The great heat near the surface, by expand- 

 ing the atmosphere in contact with it, diminishes its density, thus 

 rendering it more nearly homogeneous than the above law would re- 

 quire ; this effect is, however, counteracted by the tendency of the 

 heavier ijases to descend. 



It is a matter of interest to know not merely how much light is cut 

 off by the atmosphere at the centre of the sun's disk, but also how 

 much the whole light of the sun will be reduced by the same cause. 



