Prof. Rood on measuring the average size of very fme Particles. 541 



that they varied in size from '000018 to '000012 of an inch. 

 Several months afterwards I made a calculation to ascertain 

 what the difference in the path of the interfering rays would be, 

 using these data, and what relation this difference bore to the 

 length of a wave of red light. 



Assuming the dimensions of the particles of lampblack to be 

 the same in all directions, wc have the annexed construction. B D 



will represent the diameter of a particle of lampblack, the ray 

 A B is reflected from its surface, the ray C B from the layer 

 next below ; X is the angle made by the light with the plate ; 

 and the difference in path of the two rays will evidently be equal 

 to CB— AB, a quantity readily found by calculation. 



Taking the size of the lampblack particles to be equal to 

 •000018 of an inch, the difference in path of the two rays for an 

 angle of incidence of 18° is "000011, while the wave-length of 

 the line C in the red space is nearly -000026 of an inch. This 

 shows that the difference in the path is not far from half a wave- 

 length of red light, if the larger of the two estimates of the size 

 of the particles of lampblack is employed. 



1 then made a new set of experiments relative to the angle at 

 which the red ray disappears, using, as before, lampblack from 

 paraffine. This was found to vary somewhat in different por- 

 tions of the same plate, as is seen in the Table below : — 

 21°, 20°-75, 18°»75, 20°, 20°; mean 20°'l. 



New microscopic measurements on the size of the lampblack 

 particles were made with a different microscope, the value of the 

 micrometer not being known ; it was estimated that the size of 

 the smaller and more numerous particles varied from 45^00 ^° 

 90000 °f an i nc h> Du t that there were more particles approach- 

 ing the first number than the second — a circumstance of wdiich I 

 have not taken any advantage in the following calculation. 



Taking the mean of these determinations and combining it 

 with the mean of the first determinations, we obtain for the mean 

 size of the particles qq^^ = '0000146 of an inch. 



The average angle of disappearance of the red ray being 20°, 

 there results a difference of path ='0000098; that is, the dif- 

 ference of path is to the wave-length of red light nearly as 10 

 to 26. 



