Dr. L. Bieekrode. On the Determination of the 



sides ; it was therefore necessary to ascertain for each experiment 

 what reliance conld be placed upon it, the more so because, though the 

 glass plates themselves might have been very parallel, yet by a more 

 or less unequal compression of the intermediate leathern and leaden 

 disks, a somewhat prismatic form of cell could have ensued. Whether 

 this were the case, I always controlled with every new prepared 

 tube by trying to determine in it the index of refraction of sulphuric 

 ether, in the same way as had to be done afterwards with liquefied 

 gases. I compared the value obtained to that which has been found 

 with the more exact methods ; if it agreed within the degree of 

 exactitude that comports the use of the microscope, I was sure that 

 no error was to be feared from want of parallelism between the ends 

 of the cell ;* if there was discordance, I reconstructed the cell, till a 

 satisfactory result was got. 



To appreciate the influence of errors of observation on the obtained 

 value, a differentiation with respect to D and d of the relation 



D ... . 



= will give 

 D d 



Sn d 8n D 



3D (D-d) 3 ' d (D-d) 3 ' 



If a magnifying power of 30 were applied, I could adjust the test- 

 objects with a displacement to - 04 or 0'05 millim., calling the errors 

 made in the observation e and e lf the following expressions for the 

 errors in the values of D and d ensue 



In an experiment with sulphuric ether, for instance, D measured 

 15'92 millims., d=4'18 millims., e=0'04 millim., ^=0-04 millim. 

 therefore, 



EI= ( 



In the most unfavourable case, the total error may amount to 

 0'0058, and probably it may be expressed by + \/E 3 + K 2 = 0'0048. 



A higher magnifying power as, for instance, one of 200 times 

 would have allowed of reading a displacement to O'Ol millim. ; but 

 mechanical difficulties in the construction of a cell of very reduced 

 dimensions, required by the short focal distance, prevented the employ- 



* Sulphuric ether was chosen as controlling substance, because it could be easily 

 removed by evaporation, accelerated with the air-pump. 



