SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 121 



§ 50. Specimen Table indicating the Stages in the Calculations used in the Discussion 

 of the Values of v and c?A in the Case of Solutions of Different CoU' 

 centrations of KCl. 



n 



9 



8 



7 



6 



5 



4 



3 



2 



m 



1/4 



1/8 



1/16 



1/32 



1/64 



1/128 



1/256 



1/512 



V 



6-899 



3-416 



1-684 



0-841 



0-423 



0-217 



0-098 



0064 



1/1024 



Sub-table a. 



A -1000 = ^; 



dA -V 



7-102 



6-899 



+ 0-203 



3-483 



3-416 



+ 0-067 



1-732 



1-684 



+ 0048 



0843 



0-841 

 + 0-002 



0-418 



0-423 



-0005 



0-206 



0-217 



-0011 



0-119 



0-098 

 + 0-021 



0-034 



0-064 



- 0-030 



Sub-table b. 



'/„+i - v'„ = dA' 

 dA' -v' 





10-585 



5-215 



2-575 



1-261 



0-624 



0-325 



0153 





3-528 



1-738 



0-858 



0-420 



0-208 



0-108 



0-051 





3-522 



1-723 



0-856 



0-418 



0-219 



0091 



0-051 



6-944 



3-422 



1-699 



0-843 



0-425 



0-206 



0-115 



0-064 





+ 0-100 



+ 0-024 



+ 0-013 



-0-007 



+ 0-013 



-0-024 



-0-013 



Sub-table c. 



v"„+i-v"„ = dA" 



v +v „ 



2 ""^ 



dA" -v" 



7-080 



3-502 



1-728 



0-849 



0-416 



0-213 



0-105 



0-042 



6-921 



3-419 



1-691 



0-842 



0-424 



0-211 



0-106 



0-064 



+ 0-159 



+ 0-083 



+ 0-037 



+ 0-007 



-0-008 



+ 0-002 



-0-001 



-0-022 



Note. — The numbers in line w designate the columns of the table ; m is the concentra- 

 tion of the solution expressed in gram-molecules of salt dissolved in 1 000 grams of water. 



The significance of the symbols m, c?A, v, and c^A — v has been already explained. 



The differences (c?A - v) are accounted positive when dA is greater than v, and 

 negative when the reverse condition holds. 



From an inspection of the values of dA and v in sub-table a, as derived from con- 

 secutive values of A, it will be seen that there is a decrease in the positive values of 

 dA-v for diminishing values of w from 1/4 to 1/32, when change of sign occurs and 

 negative values are obtained for w=l/64 and 1/128, then a reversal to a positive 

 quantity of -1-0-021 for 1/256, and again a negative value for 1/512. 



There is thus a steady decrease in the positive values for dA — v from m ^ 1/4 to 

 m = 1/32. Between m = 1/32 and m = 1/64 there is change of sign, and from m = 1/64 to 

 m= 1/512 there are increasing negative values, with exception of -{- 0-021 at m= 1/256. 



The value -f 0-021 for dA-v at w= 1/256 is of appreciable magnitude, but the 

 concentration of the solution is low, and, as shown in the example for calculating the 

 effect of specific gravity changes on the displacement, its relative value would be con- 

 siderably affected by slight changes in the value of the specific gravity. 



If we now consider alternate values v^+i and v^_i instead of consecutive values 

 TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 16 



