Diffuse Reflexion of Light on Matt Surfaces. 205 



on a plane perpendicular to the observed ray decreases with 

 increasing angle e as the cosine of this very angle e. 



2nd Method. — The length of the part of the plate which is 

 observed is not constant, but increases with increasing angle e 

 as the cosine of e. Or : the projection on a plane perpendi- 

 cular to the observed direction is constant. 



In case of homogeneous illumination the results of the 

 second method multiplied by cos e are the same as by the 

 first method. The reasons for using the second more com- 

 plicated method will easily be seen from the following : — ■ 

 For the sake of simplicity let us suppose Lambert's law is 

 true. Then the first method will vield for i = Q° and e = 0°, 

 the intensity of the reflected light L = 1000 ; for e = 80°, 

 L = 173. Such enormous differences cannot be measured 

 with exactitude by any existing photometer. The second 

 method, on the other hand, will yield for the same angles 

 6=0°, L = 1000, and e = 80°, also L = 1000. By multiplying 

 with cos e we get, of course, L = 1000 and L=173, as before. 

 Now, if Lambert's law is not strictly correct, we still are 

 forced to admit the superiority of the second method. A 

 further advantage is the exact knowledge of the extent of 

 the deviation, whilst by method I. it may very easily occur 

 that when the angles of emission are small one involunt- 

 arily uses method II. without noticing it. According to the 

 results of Messerschmitt there is little doubt that this mistake 

 was made by him. The values of the intensity of the reflected 

 light are nearly constant between e = 20° and 60°, and they 

 begin then suddenly to decrease very rapidly. By using 

 method I. it is evident that a certain limit length of the plate 

 may by no means be exceeded, whilst by the second method 

 the minimum dimensions may be exceeded to any extent. 

 Naturally this fact is made use of in the experiments so as to 

 be certain that no errors due to size can occur. 



It may be interesting to mention that Lambert elaborated 

 his famous law by means of method II. He noticed that a 

 whitewashed wall looks equally bright from any angle (e) 

 when the sun is shining on it. 



It is superfluous to say that the observations were made in 

 an absolutely dark room, with the head under a black cloth, 

 and that every possible precaution was taken. The measure- 

 ments were made in the first and third quadrant of the 

 nicol, which, according to Bakhuyzen *, is absolutely suf- 

 ficient. As far as possible the angles of emission (e) were 

 observed on both sides of the plate-normal. For coloured 



* H. G. van de Sande Bakhuyzen, Pogg. Ann. cxlv. p. 259 (1872). 



