Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/15

(the earth). The values of ${\text{A}}$ reduced in this manner are tabulated below under the heading ${\text{N}}$.

⟨Angle..⟩.	40°.	39.45.	39.30.	39.15.	39.0.	38.45.	38.30.	38.15.	38.0.	37.45.	37.30.
⟨Angle.${\text{M}}$ ....⟩..	3.4	11.6	24.8	45.9	84.0	121.7	161	189	210	210	188
⟨Angle.${\text{N}}$ ....⟩..	3.1	10.1	11.3	13.7	18.0	18.1	11.2	19.6	44.4	59	170

⟨Angle.⟩..	37.15°.	37.0.	36.45.	36.30.	36.15.	36.0.	35.45.	35.30.	35.15	35.0.	Sum.	P.c.
⟨Angle${\text{M}}$ ...⟩...	147	105	103	99	60	51	65	62	43	39	2023	100
⟨Angle.${\text{N}}$ ....⟩..	75.5	62.9	56.4	51.4	39.1	37.9	39.2	37.6	36.0	28.7	743.2	37.2

For angles less than 37° one finds, in the manner above described, numbers that are a little inferior to the tabulated ones, which are found by means of the absorption-coefficients of Table I. and the values of ${\text{N}}$. In this way the sum of the ${\text{M}}$'s is a little greater (6.8 per cent.) than it would be according to the calculation given above. This non-agreement results probably from the circumstance that the spectrum in the observations was not quite pure.

The value 37.2 may possibly be affected with a relatively great error in consequence of the uncertainty of the ${\text{M}}$-values. In the following calculations it is not so much the value 37.2 that plays the important part, but rather the diminution of the value caused by increasing the quantities ${\text{K}}$ and ${\text{W}}$. For comparison, it may be mentioned that Langley has estimated the quantity of heat from the moon that passed through the atmosphere (of mean composition) in his researches to be 38 per cent.^[1] As the mean atmosphere in Langley's observations corresponded with higher values of ${\text{K}}$ and ${\text{W}}$ than ${\text{K}}=1$ and ${\text{W}}=0.3$, it will be seen that he attributed to the atmosphere a greater transparence for opaque rays than I have done. In accordance with Langley's estimation, we should expect for ${\text{K}}=1$ and ${\text{W}}=0.3$ a value of about 44 instead of 37.2. How great an influence this difference may exert will be investigated in what follows.

The absorption-coefficients quoted in Table II. are valid for an interval of ${\text{K}}$ between about $1.1$ and $2.25$, and for ${\text{W}}$ between $0.3$ and $2.22$. In this interval one may, with the help of those coefficients and the values of ${\text{N}}$ given above, calculate the value of ${\text{N}}$ for another value of ${\text{K}}$ and ${\text{W}}$, and so in this way obtain by means of summation the total heat that passes through an atmosphere of given condition. For further calculations I have also computed values of ${\text{N}}$ for atmospheres that contain greater quantities of carbonic acid and aqueous vapour. These values must be considered as extrapolated. In the following table (Table III.) I have given these values of ${\text{N}}$, The numbers printed in italics are found directly in the manner

1. Langley, 'Temperature of the Moon,' p. 197.