1895.] Decimetre of Water at its Maximum Density. 147 



exceed more tlian decimilligrams of the weight of a cubic decimetre 

 of water. 



A detailed description of a great series of the determinations made 

 by Kupffer we find in vol. 2 of his memoir, ' Travaux de la Commis- 

 sion pour fixer les Mesures et les Poids de l'Empire de Russie ' (St. 

 Petersbourg, 1841). Kupffer used two brass cylinders, the volume 

 of which from a number of measurements as a mean was found to be 

 at t = 13^° R = 62° F. = 16f° C, 



For the small cylinder, V x = 24*17753 cubic inches (loc. cit., p. 133). 



large „ Y 2 = 49*89931 „ (loc. cit., p. 250), 



The coefficient of expansion of the brass used was not actually deter- 

 mined by Kupffer, and for the reduction of the volumes at temperatures 

 near 16f° C. I have, therefore, used the results of Fizeau. From the 

 coefficient of linear expansions (in degrees Celsius) we find for the 

 volumes, 



v t = v (l + O-0OOO5337 £ + 0-00000003 f~), (Ill) 



therefore for the coefficient of cubic expansion, 



(Z^j at 16|° C. = 0-00005437 for 1° C, 

 or = 0-00006796 for 1° R. 



The volumes of both cylinders at t° Reaumur will be, 



For the small cylinder, V,, = 24-17753 + 0-001643 (t— 13^). 



large „ Y 2( = 49*89931 + 0-003391 (£—13^). 



For the determinations of the diameters and heights of the small 

 cylinders we rarely find a maximum difference between the separate 

 measurements amounting to 0*00014 inch. From the mean results of 

 a large number of measurements, we must assume that the error in 

 volume determination was not greater than +0*00168 cubic inch, or 

 less than the 1/14391 part of the total volume, which for a cubic 

 decimetre corresponds to 0*069 gram. In the measurements of the 

 large cylinder having a diameter of about 4 inches, a greater accu- 

 racy has been obtained, so that the average error of the linear 

 measurements was smaller than 0-00005 inch ; therefore the error in 

 volume was smaller than 0*000190 cubic inch, corresponding to a 

 relative error of less than 1/26263, or for 1 cubic decimetre less than 

 0*038 gram. We must therefore expect a greater accuracy from the 

 determinations by means of the large cylinder than from those where 

 the small cylinder was used. 



Although I have made in similar detail a new reduction of all 

 Kupffer's data, in the further discussion I shall take into considera- 



