824 Mr. C. Gr. Darwin on the Reflexion of 



9. Comparison with Experiment. 



There is not a great deal o£ material suitable for testing 

 these formulae, and the resalt of the test is not very satis- 

 factory. The first point of comparison is the curve in 

 B.J.B.ii. p. 12, which relates the modified absorption 

 coefficient to the integrated reflexion of a face. The ordi- 

 nate of the curve is given by (8'7) and its abscissa by (7*5). 

 The linear form of the curve means that 



is practically constant, and this it will be, if g^Q 1 , gzQ' are 

 negligible compared with g s fi. Neglecting these terms we find 



2 w , = 5-6-f-(5'41xl0- 4 ), 



whence </ 2 ~484. This may be best interpreted by assuming 

 an error law of distribution as in (5' 7). Then 



G(^)=Q^-^ 2 - 2 /v'2^rc7 and g 2 = Vw / 2a, 



which gives a = 6'. This is a good de;il smaller than would 

 be expected from the general description of the experiments ; 

 for it means that all the reflexion should take place within 

 less than half a degree, whereas the paper implies that the 

 band of reflexion was nearly a degree broad. A part of 

 the discrepancy may be due to the neglect of the further 

 terms in (9'1), for it is evident that the series is not very 

 rapidly convergent, when, as here, g 2 Q'/ jjl = 5' 6/ 10'7. 



A more detailed, but still less satisfactory, comparison 

 may be made with the reflexion curves of B.J.B.ii. p. 13. 

 The experiments dealt with the reflexion through two plates 

 of the same thickness, of which the surfaces had been dif- 

 ferently treated. The information about the curves is not 

 quite complete, but can be supplied indirectly. It is first 

 necessary to find the absolute values cf E tt /L The curves 

 are drawn in arbitrary units, and a constant multiplier must 

 be obtained for each from the observed value of its integrated 

 reflexion (which is the area of the curve), in terms of that of 

 a standard plate of the same thickness. The reflexion of the 

 standard was calculated (p. 7) from that of a face 7 on 

 the principle that for a surface the integrated reflexion is 

 Q'/2(fjL+g 2 Q!), while for a plate of thickness giving maxi- 

 mum reflexion it is QVK/^ + ^Q')- There is thus the 

 assumption that the plate has the same scatter as the face. 



