226 Proceedings of the Royal Society of Edinburgh. [Sess. 
two waters cited above ; from which it follows that for the greatest 
possible difference both in density and temperature, the maximum error 
introduced by neglecting the temperature correction (± ’000006 per 1° C.) 
would be equal to dt '0002. It would, however, seldom happen that the 
two maximum differences would conspire to produce this effect ; and in 
such a case the observer could hardly fail to be aware of the fact, and 
would apply the necessary correction. 
(i b ) Abnormal Ocean Waters. 
To investigate the effects produced by fluctuations in the temperature 
of a water which is either exceptionally rich or poor in chloride, supple- 
mental experiments were made. Five waters marked K x . . . K 5 were 
chosen ; of these, two were diluted, two others were concentrated over 
a water-bath, whilst the fifth was kept in its natural condition. Their 
approximate chlorine values were respectively 10, 14, 20, 25, and 30 grms. 
per litre (the precise values are given in Table VIII.). The densities 
of all five waters were then determined at the temperatures of 10°, 20°, 
and 30° C. ; and in order to eliminate as far as possible slight incidental 
errors, all the measurements were made with the same pyknometer. In 
calculating densities, that of pure water at 4° C. was taken as unity. 
From the data thus obtained, the coefficient of expansion for each 
water within the above-named limits of temperature was found, and 
expressed in the form 
V* = V 0 {1 + at + f3t 2 }, 
V 0 being the volume at 10° C., and V^ the volume at t° C. above 10. 
The various values for the densities of the several waters, the corre- 
sponding values for the terms a and /3 in the above formula, and the 
weights of chlorine per litre, are set forth below : — 
Table VIII. — Data from which a and (3 in the Expression Vt = V 0 { l + at +/ 3 t 2 } 
were Obtained. 
Water. 
a X 1 0 6 . 
(3 X 10 8 . 
Grms. 
Cl per litre. 
K, 
k 2 
k 3 
k 4 
K, 
1-01359 
•01948 
•02712 
•03369 
•04031 
1-01170 
•01743 
•02489 
•03132 
•03777 
1-00889 
•01450 
•02187 
•02815 
•03450 
+ 134 
+ 153 
+ 179 
+ 193 
+ 212 
+ 500 
+ 465 
+ 390 
+ 380 
+ 343 
9-997 
14-322 
20-065 
24-957 
29-991 
f Natural 
\ water. 
