on the Temperature of the Sun, 545 



Now let us notice the values which were obtained for a and 

 b. The values of b in each day's observations were found to 

 increase with the value of e ; but on different days, for one 

 and the same value of € we have different values of b. These 

 facts have been noticed by former observers. 



As I have already said, b represents the ratio between the 

 quantity of rays which arrive at the face of the pile at the 

 place of observation, after having traversed perpendicularly 

 the depth e = 1 of the atmosphere, and the rays which it would 

 receive if the atmosphere did not exist, i. e. if e were equal to 0. 

 It is obvious that if the hygrometric state of the air were dif- 

 ferent on the different days, the values of b obtained by means 

 of the formula corresponding to one and the same value of e 

 would also be different. 



It is in accordance with the laws of absorption that b should 

 increase as e increases. In short, the absorption of rays which 

 pass through a transparent body is greater in the first strata 

 than in the subsequent ones. The observations of 20th Sep- 

 tember, 24th October, 21st October, and 22nd December show 

 that, beyond a certain thickness e, the coefficient of absorption 

 becomes constant. 



Let us now consider the values of a. Each of these values 

 represents, in the units chosen for the curve, the true quantity 

 of heat which falls on the unit of surface at the limits of the 

 atmosphere. We see, nevertheless, that as e diminishes the 

 value of a increases ; and it is evident that, if we had been able 

 to make experiments with less thicknesses of e, we should have 

 had greater values for a. If we express the values of a gra- 

 phically, taking for abscissae the arithmetic means of the values 

 of e (which are found in the last column of the preceding 

 Table) which have been employed in the calculation of each 

 of the values of a, and for ordinates the corresponding values 

 of a, we find that the different points thus determined arrange 

 themselves with very few exceptions in a straight line. The 

 more favourable the condition of the atmosphere on the day 

 of observation, the more marked is this regularity. 



Consequently, since a more exact method was required, I 

 decided to take as the true value of a that portion of the axis 

 of the ordinates which lies between the origin and the point of 

 contact of the above-mentioned straight line with the same 

 axis. In order to obtain greater accuracy, I determined by the 

 method of least squares the equation of the line a=ra + we, 

 which approaches nearest to the points representing the values 

 of a corresponding to the different mean values of e ; and I took 

 for the value of the quantity sought the number m. This cal- 

 culation was made for several curves obtained under very dif- 

 ferent conditions, and gave for m such results as, if we take 

 into consideration the causes which necessarily influence 



