506 Mr. A. W. Warrington on 



are calculated from the formula 



V, A = Y + a A + b A 2 + xt +yt 2 , 



the values for V , a, b, x, and y being those given above. 



In the last column of the table under S are given the dif- 

 ferences between the observed and calculated volumes of the 

 hydrometer. The probable error of a single determination of 

 the volume of the hydrometer is + 0'000111 cub. centim. 



The table includes every experiment made ; none have 

 been rejected. 



The Temperature at which the Density of Water is at a 

 Maximum. 



Professor Schuster, for whose kindness I am very deeply 

 indebted, suggested that I might test the efficacy of the 

 method for the determination of temperatures of maximum 

 density. Experiments 24 to 32 inclusive were made with this 

 object more especially in view, and are discussed in the fol- 

 lowing note by Mr. G. A. Schott, B A., B.Sc, a colleague to 

 whom I owe much for his valuable advice. 



The data used by Mr. Schott are obtained from an earlier 

 and slightly less exact calculation than that given in this 

 paper. 



Note by Mr. G. A. Schott, B.A., B.Sc. 



The Determination of the Point of Maximum Density of a 

 Liquid by the Hydrometer of Tolat Immersion. 



The volume of the hydrometer is supposed given at the 

 temperature of the experiment, say V = A' + B'£ + C'£ 2 ; and 

 the probable errors of A', B', C are supposed known. 



The weight necessary to totally immerse the hydrometer in 

 the neighbourhood of the point of maximum density is deter- 

 mined by a number of experiments, and expressed in the form 

 A + Bt + Ct*. 



Then the density of the liquid is 



_ A + Bt + C t 2 _A + A + A 

 P ~ A' + B't+C't>~ A'\ B' 0' * 

 1+ A7 + Ai' 



The temperature t of maximum density is determined by the 



