PHYSICAL PROPERTIES OF WATER, ETC. 53 



The final result of these experiments, as assigned by the authors, was a probable 

 lowering of the maximum-density point of water ' by 5° C. for one ton pressure. To 

 this paper I added the following note (I.e. p. 813) : — 



"If we assume the lowering of the temperature of maximum-density to be 

 proportional to the pressure, which is the simplest and most natural hypothesis, we 

 may write 



where p is in tons weight per square inch. 



" Now Thomson's thermo-dynamic result is of the form 



Bt = A(t-t ')Sp. 

 " This becomes, with our assumption, 



8t=A(t-t +Bp)Sp. 



"As the left-hand member is always very small, no sensible error will result from 

 integrating on the assumption that t is constant on the right (except when the quantity 

 in brackets is very small, and then the error is of no consequence). Integrating, 

 therefore, on the approximate hypothesis that A and B may be treated as constants, 

 we have for the whole change of temperature produced by a finite pressure p — 



At = A(t-t )p + %ABp 2 . 

 " I have found that all the four lines in the diagram given [from Messrs. Marshall, 

 Smith, and Omond, on last page, where y is the heating effect of p tons at tem- 

 perature t] can be represented, with a fair approach to accuracy, by the formula 



y = 0-0095(< - i)p + 0-017p 2 , 

 where p has the values 1, 2, 3, 4 respectively. Hence, comparing with the theoretical 

 formula, we have the values 



A = 0-0095, B = 3°-6C. 



" B expresses the lowering of the maximum-density point for each ton weight of 

 pressure per square inch. 



" It seems, however, that all the observations give considerably too small a change 

 of temperature ; for the part due to the first power of the pressure is from 30 to 40 per 

 cent, less than that assigned by Thomson's formula and his numerical data. One 

 obvious cause of this is the small quantity of water in the compression apparatus, 

 compared with the large mass of metal in contact with it. This would tend to 

 diminish all the results, whether heating or cooling ; and the more so the more 

 deliberately the experiments were performed. Another cause is the heating (by com- 

 pression) of the external mercury in the pressure gauge. Thus the pressures are 

 always overestimated ; the more so the more rapidly the experiments are conducted. 

 A third cause, which may also have some effect, is the time required by the thermo- 

 electric junction to assume the exact temperature of the surrounding liquid. 



