46 DR. JAMES BOTTOMLEY^S 



Some allowance must be made in the calculation for this 

 coloration of the disk. The formula qt = (^t' is applicable 

 to the case in which the surfaces are outside ; to adapt this 

 formula to the case when the disks are inside^ suppose x to 

 be the length of the column of fluid which would cause the 

 difi'erence in colour between an external and an internal 

 surface, then the formula would be q[t-{-x)=c^{t' +x). 



To find the value of x experimentally, I took a solution 

 containing 2400, and sunk a small disk in it until the inside 

 and outside colour seemed the same : for the outside the 

 length of column was 22'5_, for the inside 177, this being 

 the mean of eight trials. The difference is 4*8. With a 

 solution containing 1600, a white surface outside, with 

 length of column 21 •2, seemed to give the same colour as 

 white surface inside with length of column i6-2; the 

 difference is 5. I also tried to get the value by the follow- 

 ing combination : — A solution was taken containing 2400 

 with disk inside, and compared with a solution containing 

 1600 with a disk outside. Length of column in latter case 

 was 21*2 J in the former case a column 17*5 seemed to give 

 a similar colour. From the formula q{t-{-x) =§7' the re- 

 sulting value of x would be 5*2. I also tried the following 

 combination : — Solution containing 2400 and disk outside 

 was compared with solution containing 1600 with disk 

 inside. The mean of eight trials gave length of column 17 

 in the latter case, equivalent to 21 '2 in the former; from 

 the formula 1600 (17 + ic) =2400 x 21-2, the resulting value 

 of a; is 4" 3. Finally, we get for the approximate value of x, 

 taking the mean of the four determinations, a; =4* 8. The 

 experimental determination is not easy 3 but the value ob- 

 tained gives better results when we use it in the formula. 

 For instance, on a former occasion, with disks inside, when 

 a solution containing 1600 and length of column 21 '2 was 

 used as a standard, and there was compared with it a so- 



