Carbonic Acid on Smooth Glass Surfaces. 163 



The value of a was 0*002945 millim. The value of d from 

 Table I. deduced from the equation (1) is 



d= 0-015907 millim. 



In order to see whether the value already found for ft = 1000 

 can be taken as constant, 1000 threads out of fifteen other 

 bundles were measured. The following Table contains the 

 mean values of each ten of these measurements : — 



Table II. 



5-00 



5-84 



571 



6-96 



5-67 



5-95 



567 



531 



6-37 



4-97 



474 



529 



552 



5-82 



5-67 



504 



5-31 



603 



575 



5-65 



503 



602 



5-51 



6-68 



5-15 



5-68 



5-52 



4-60 



5-03 



5-55 



5*14 



5-97 



5-62 



5-88 



5-68 



515 



5-60 



4-97 



543 



5-29 



4-82 



6-14 



5*49 



5-86 



6-27 



5-27 



545 



4'90 



6-28 



4-92 



4-17 



611 



5-78 



5-96 



675 



5-17 



5-41 



4-93 



4-88 



5-19 



5-09 



7-12 



544 



5-43 



625 



5-32 



5-40 



5-07 



4-99 



5-15 



4-89 



5-58 



5-80 



5-49 



5-87 



4-87 



4-99 



553 



591 



4-78 



4-80 



6-45 



5-59 



527 



5-69 



4-97 



4-48 



5-14 



5-40 



5-09 



4-83 



647 



523 



5-47 



514 



5-83 



515 



4-93 



5-42 



5-98 



The numbers of this Table give for d, 



d=0*016136 millim., 



a value which varies little from that deduced from Table I. 

 The mean of both is 



d=0'0160215 millim., 



and may be taken as very near the true value. For n threads 

 of diameter d and length h the sum of the surface-areas M is 



M = nh7rd. 



This formula gives for 1000 threads of 1000 millim. long a 

 surface of 



0*050335 square metres. 



Where, as in the following observations, the surfaces of 

 hundreds of thousands of such threads is required, counting 

 them is impracticable. We take therefore, instead of the 

 number, the weight as the basis on which to calculate the 

 surface-area. To do this the measurements from which the 

 diameters in Tables I. and II. were derived are arranged in 

 the following Table in groups of like diameter. The column 

 d gives the diameter, the column n the number of threads of 

 this given diameter. 



* M2 



