56 THE VOYAGE OF H.M.S. CHALLENGER. 



To calculate the amount of this lowering, by the process indicated, we must know 

 the form of the curve abc. This, in its turn, can be calculated from a knowledge of 

 the form of ABC, and of the relation between compressibility' and temperature. Both 

 of the authors named took their data as to the latter matter from the experiments of 

 Grassi ; and, as was therefore to be expected, gave results wide of the truth. Puschl 

 calculates a lowering of 1° C. by 87 "6 atm., which is certainly too small; Van der 

 Waals, o, 78 C. by 10 - 5 atm., as certainly much too large. 



To obtain a good estimate in this way is by no means easy, for authorities are not 

 quite agreed as to the form of the curve ABC. If we calculate from the datum 

 of Despretz, which has been verified by Rossetti, 1 namely, — 



vol. at 0° C. _ 1 , nnm afi 

 vol. at 4° C. 



we obtain for the volume of water at 1 atm., in terms of temperature, 



l+0-OOOOOS5(<-4) 3 (1) 



[This refers only to the part A B of the curve, which is what we want. There seems 

 general agreement that the curve is not symmetrical about the ordinate at B.] Now, 

 by (A), the factor for reduction of volume by 1 ton of additional pressure is 



1- 0-007676 + 0-000055<-0-00000061< 2 (2) 



The product of these factors, (1) and (2), is a minimum when 



0-000017(; - 4) = - 0-000055 + 0-00000122/ ; 



or, ^4-^ = 4-3-17. 



' lob 



Thus, according to these data, the maximum-density point is lowered by 3° - 17 C. 

 per ton of pressure. It will be observed that this is not much less than the result I 

 calculated from the data of Professor Marshall and his comrades, but it agrees almost 

 exactly with that which I derived from my own. 



The following description of the results of my earlier attempts to solve this question 

 directly, is taken from the Proc. Boy. Soc. Edin., vol. xii. pp. 226-228, 1883 : — 



" I determined to try a direct process analogous to that of Hope, for the purpose 

 of ascertaining the maximum-density point at different pressures. The experiments 

 presented great difficulties, because (for Hope's" method) the vessel containing the 

 water must have a considerable cross section ; and thus I could not use my smaller 

 compression apparatus, which was constructed expressly to admit of measurements of 

 temperature by thermo-electric processes. I had therefore to work with the huge Fraser 

 gun employed for the Challenger work, and to use the protected thermometers (which 

 are very sluggish) for the measurement of temperatures. It was also necessary to work 



1 Pogg. Ann., Erganr.ungsband, v. p. SCO, 1871. 



