AQUEOUS SOLUTIONS.—M-KAY. 325 
weight of the substance (in this case 58.5), and D for the density 
of water at 18°C, we obtain :-— 
? 
W+aw _ ies kw , ,w 
D 13) a te l ae 
Then differentiating with respect to v, since w is a constant, 
0 a 
Gir JOX(ih== (jee = DA—lm?)> 
v2 
which becomes in the above particular case 
pommel li Th 
D(1+ .003im2) * 
Therefore when m is sufficiently small to make the quantity 
1m? neligible, the increase of the volume of the solution is equal 
to the volume of the water added, since in that ease 
1 du _ 
D dW 
Calibration of Flasks, Pipettes and Burettes. 
The flasks were calibrated by weighing them empty and 
again when filled with distilled water of known temperature up 
to the mark. The error in calibrating a 250 c.c. flask was deter- 
mined by a large number of measurements to be possibly .03 
per cent. No flasks of less volume than 200 ¢.c. were used in 
making up solutions. 
With the pipettes, the weight of water of known temperature 
which they delivered was found. In doing this the point was 
always held against the receiving vessel, and the liquid which 
remained in the point after the delivery was removed by blow- 
ing sharply into it once. The amount of water delivered in 
this way was determinable to about .005 «. ¢. 
The burettes used held 50 ¢. ec. and were graduated to tenths 
of lec. To calibrate them accurately it was found necessary 
to determine the volume of the tube for every 2 ¢.¢., and in 
some cases for smaller lengths. These determinations were 
checked a large number of times by weighing the volumes of 
water between very various points on the tube. Readings could 
be made to .01 ¢. c., and the calibrations were carried nearly, if 
