496 Prof. Richards and Mr. Archibald : A Study of 



should of course be maintained if great accuracy is attempted. 

 Measurements with a fine millimetre-scale afford all the pre- 

 cision which it is worth while to attain under present 

 conditions. A t} r pical case (fig. 9, largest crystal) gave the 

 following measurements in millimetres for the successive 

 longest diameters: — 2*0; 2*6; 3*0; 3*2; 3*3: 3*5; 3*7; 

 3*9 ; 4*1 ; 4'2 : 4*4. The actual sizes of the crystals were 

 of course only a hundredth of these measurements, since the 

 enlargement was 100 diameters. 



In spite of the inexact nature of such measurements, it is 

 possible to use them as a means of denning approximately 

 the law regulating the changes in speed. The following table 

 details six series of corresponding diametric measurements 

 of six crystals taken at random. The measurements were 

 taken directly from the photographs, in millimetres. 



Diameters of Successive Images. 



First appearance . 

 Second appearance 

 Third appearance., 



1-0 

 16 

 17 



Crystal 

 2 m 



Crystal 

 3. 



Crystal 

 4. 



Crystal 

 5. 



Crystal 

 6. 



2-0 



30 



3-0 



4'0 



25 



26 



5-7 



6-0 



(5-7 



35 



3-0 



6-8 



70 



7-8 



4-1 



These all show greater growth in the first interval than in 

 the second. In order to reduce them to one standard, the 

 diameter of the third appearance was taken in each case as 

 unity. The table then becomes : — 



Diameters of Successive Images. 









Crystal 

 1. 



Crystal 

 2. 



Crystal 



Crystal 

 4. 



Crystal 

 5. 



Crystal 

 6. 



Average. 



First appearance ... 



0-59 



067 044 



0-43 



0-51 



0-61 



0-54 



Second appearance . 



0-94 



0-87 j 084 



0-86 



0-86 



085 



0-87 



Third appearance . . . 



100 



100 TOO 



1-00 



J -00 



1-00 



1-00 



At the time of the first appearance, the average age of the 

 crystal must be about half the time intervening between two 

 exposures ; for the crystal must have been formed since the 

 last exposure, and it is as likely to come near the beginning 

 as near the end of the interval. Thus in fig. 11 the crystals 



