408 
MESSES. T. E. THOEPE AND A. W. EtiCKEE ON 
investigation of the physical condition of the ocean, the results of the'observations of the 
specific gravity of sea-water must be correct to one in the fourth decimal place. Of course 
we should have reason to expect that the variations in the rate of expansion of sea-water 
as it usually occurs, although doubtless appreciable, must be very small ; nevertheless 
we thought it desirable to attempt to determine the relation between the salinity of the 
water, as indicated by the specific gravity, and its thermal expansion. Accordingly we 
constructed dilatometers of greatly increased capacity ; and in order to expose a larger 
surface to the source of heat the bulbs were made in the form of elongated cylinders 
instead of being spherical, as in the case of the instrument we had hitherto employed. 
The new instruments were calibrated with great care, and the determination of the rates 
of expansion of the glass was made between the limits of temperature to which they 
were to be used. An additional set of thermometers was made for us by Casella ; they 
are denoted in the succeeding Tables by a and (3. Thermometer a was graduated for 
temperatures between —9° and 29°; the length of 1° was 13 millims. ; the range of (3 
was from 21° to 67°, and the length of 1° was about 11 millims. Both instruments 
could therefore be easily read to 0°-01. 
As it was desirable to obtain data to cover all possible cases of dilution and concen- 
tration in naturally occurring sea-water, we diluted quantities of our sea-water with 
distilled water so as to have samples of, approximately, the specific gravities 1-020 and 
1*025 ; and we concentrated a third quantity by evaporation until its specific gravity was 
increased to about 1-033. We also redetermined the expansion of the original sea-water 
by means of the new dilatometers. Two perfectly independent series of observations 
were made with each solution, different dilatometers and thermometers being used in 
each case. 
The details of the observations are exhibited in Tables II.-IX. ; the first column in 
each gives the reduced and corrected temperatures, and the second the reduced volume 
(uncorrected for expansion of glass) of the liquid in the dilatometer. Formulae expressing 
these results were obtained by the same method as that applied to the first set of obser- 
vations as described on p. 407 ; and as in some of the series of experiments more than 
twelve observations were made, while in no case was a larger number used in deducing 
the formulae, we have in the Tables marked the observations not employed for that 
purpose with an asterisk. The formulae are given at the head of the Tables containing 
the observations to which they refer ; the volumes calculated by their aid for the 
temperatures in the first columns are given in the third columns, the differences between 
the observed and calculated values being exhibited in the fourth columns. The specific 
gravities were taken at 0°, and are referred to distilled water of the same temperature. 
