C. C. Hutchins — Irregular Reflection. 375 



and opens the shutter daring the first swing of the needle. 

 The deflection being recorded, the arm is moved by intervals 

 of 10° and the deflection corresponding to each angle of reflec- 

 tion thus obtained. The numbers so obtained will be propor- 

 tional to the amounts of energy reflected at the various angles. 

 To make them comparable with the theoretical values these 

 numbers should be multiplied by such a factor as will reduce 

 the galvanometer reading for zero degrees reflection to one, or 

 one hundred. As it is impossible to obtain a reading at zero, 

 and as exterpolation is uncertain, it is better to employ such a 

 factor as will make the reading at ten degrees, the smallest 

 angle of observation, equal to the cosine of that angle. These 

 reduced readings may then be plotted for comparison along 

 with the curve whose equation is y = cosx. A glance will 

 then show to what extent a body in its reflection departs from 

 or approaches to Lambert's law. 



Among the bodies tested, those that approach most nearly 

 to a smooth surface without specular reflection are a carefully 

 prepared surface of plaster of Paris and a surface of magnesium 

 oxide, made by coating a zinc disc by holding it above burn 

 ing magnesium ribbon. 



The following table gives the galvanometer deflections for 

 these bodies, and the same reduced as above described. 



Plaster. 

 ADgles. Gal. Reduced. 



10° 



20 



30 



40 



50 



60 



70 71-7 -27'4 



80 24-0 9-16 21-0 109 



90 0-00 0-00 o-oo O'OO 



It will be seen that the curves plotted from these observations 

 (Figs. 1, 2) follow the sine curve very closely, and the direction 

 in which they depart is exactly what we should expect, assuming 

 the validity of the fundamental law. The amount of reflection 

 is a little too great, according to the observations, for small 

 angles of reflection. Now if there were any specular reflec- 

 tion it would be most manifest at the angle of reflection nearest 

 the angle of incidence, and, moreover, it will be immediately 

 shown that irregularities of surface also have the effect of 

 making the amount of reflection greater at small angles of 

 reflection than is demanded by the law. 



A disc of white filter paper and a plaster disc cut with a 

 graver into fine vertical furrows were substituted for the 

 smooth surfaces with the following results : 



258 



98-5 



249 



95-0 



224 



85-5 



197 



75-2 



170 



04'9 



119 



45-4 



Magnesia. 

 Gal. Reduced. 



190 



9S-5 



181 



93-6 



169 



87'6 



148 



76-4 



121 



62-7 



81-2 



42-0 



58-2 



30-1 



