160 Messrs. T. E. Thorpe and A. W. Riicker on [Jan. 6, 



The only attempt hitherto made to solve this problem which can lay- 

 any real claim to consideration is due to the late Professor Hubbard, of 

 the United States National Observatory. The results of his investiga- 

 tion are contained in Maury's ' Sailing Directions,' 1858, vol. i. p. 237. 



Muncke, nearly fifty years ago, determined the expansion of an artificial 

 sea-water at various temperatures between 0° and 100° C. • but our con- 

 fidence in the results as applicable to natural sea-water is affected by the 

 circumstance that the solution was prepared from data furnished by the 

 imperfect analyses of Vogel and Bouillon La Grange. 



The observations of Despretz were confined to temperatures below 

 13 0, 27, as the main object of his inquiry was the determination of the 

 point of maximum density of sea-water. The subsequent investigations 

 of Neumann and Eossetti were equally limited, as they were undertaken 

 with the same view. 



The water used in our observations was collected from the Atlantic, 

 in lat. 50° 48' N. and long. 31° 14' W.; and its specific gravity at 0° C, 

 compared with distilled water at the same temperature, was found by the 

 bottle to be 1-02867. 



The method of experiment was precisely the same as that already 

 employed by one of us in determining the expansion of the liquid chlorides 

 of phosphorus. It was essentially that already used by Kopp and 

 Pierre ; i. e. the expansion was observed in thermometer-shaped vessels 

 (so-called dilatometers), graduated and accurately calibrated. 



Three of these instruments and two sets of thermometers were 

 employed. The latter were made by Casella • the length of a degree in 

 different instruments varied between 9 and 13 millims. ; they had been 

 compared (the one set directly, the other indirectly) with Kew Standards. 



Three perfectly independent sets of observations were made with the 

 water in the state in which it was collected • and as Mr. Buchanan, of 

 H.M.S. \ Challeuger,' has found that the specific gravities of different 

 sea-waters lie between the extreme values 1-0278 and 1-0240, and since, in 

 order to be of value in the investigation of the physical condition of 

 the ocean, the observations on their values and the formulae of reduction 

 ought to be correct to the fourth decimal place, we diluted quantities of 

 our sea-water with distilled water, so as to have specimens of approxi- 

 mately the specific gravities of 1*020 and 1*025 • and we concentrated a 

 third quantity by evaporation until its specific gravity was increased to 

 1*033, and made two series of independent observations on the expansion 

 of each solution. 



As we wished to confine ourselves to circumstances to which sea-water 

 s naturally exposed, we did not carry on our experiments at temperatures 

 higher than 40° C. 



Empirical formulae were calculated to express the results of each series 

 of observations • and in the original paper full details of the observations 

 are given, together with Tables showing the agreement between the 



