Mr. J. J. Waterston on Solar Radiation. 503 



Let N, fig. 5, be the position of the -p. ^ 



observer, Z his zenith, and N S the direc- g# 



tion of the sun. Draw parallel lines 

 a b, cd y &c. ; now ac :bd : : rad. : sec. 

 sun's zenith distance ; so that the thick- 

 ness of each stratum varies as the 

 secant; and if the physical condition 

 of the stratum do not alter between 

 two observations*, we may take the 

 secant as the representative of the 

 collective thickness of the absorbing 

 medium traversed by the sun's rays, 

 except at such low altitudes when the curvature of the earth 

 as well as refraction may be expected to introduce uncer- 

 tainty. The minimum value of the secant is radius; but we 

 may imagine the sun's rays to pass through a similarly con- 

 stituted atmosphere in which the thickness of the same layers 

 proportionally diminishes from unity or radius to zero. The 

 reciprocal of r diminishes for values below radius at the same 

 rate as for values above radius, attains at zero the extra atmo- 

 spheric limit, which, in all climates and seasons, ought to be 

 determined by the inverse square of our planet's distance from 

 the sun in its orbit, and should not vary beyond T T n th of its 

 mean value. 



* But the very absorption of the sun's rays must promote change in 

 physical condition. Is the law for a constant physical condition thereby 

 masked ? I believe that during an interval of one or two hours it is not 

 sensibly disturbed, for the following reason : the absorption of the sun's 

 heat by the aqueous particles in the atmosphere would tend to diminish 

 their number, and thus 'augment r beyond the value assigned by the law 

 for the condition constant. The later of the observations taken in the 

 forenoon of August 21, projected in fig. 3, may thus be suspected to give 

 too high values for r ; and if so, the lower points on the left-hand side would 

 require to be removed higher up, and the trend of the points continued 

 towards the vertical axis would intersect it at a point which would give a 

 value to R less than 67°. But this is impossible, because in India r exceeds 

 this amount. The trend must therefore be the other way ; and as the 

 scale of r diminishes rapidly downwards, and as R is certainly a constant 

 quantity in all climates, a very slight depression of the trend (the dotted line 

 in fig. 3), such as may be due to fault of observation, would intersect 

 the axis at a point giving a sufficiently probable value of R. In short, R 

 is a fixed point in the axis towards which the projected points of a conse- 

 cutive series of observations, wherfever taken, must trend, whether by straight 

 or curve, if the physical condition of the atmosphere is undisturbed. The 

 line of the consecutive series of the 21st is straight, and points, within 

 moderate limits of inaccuracy, to a probable value of R. On the other 

 hand, if the effect of the sun's rays was to diminish the diathcrmity of the 

 atmosphere, and the observations were quite accurate, the points would be 

 conformable, and indicate a disturbance of physical condition. 



