358 M. R. Riihlmann on the Alteration 'produced by Heat 



I add here the values of the same constants obtained from my 

 experiments, and employ the latest and most probably the most 

 trustworthy results obtained by Matthiessen on the expansion 

 of water. These numbers were got by weighing, in the liquid 

 to be examined, a solid body whose expansion was exactly knowu. 

 As all precautions were taken in these experiments, and this 

 method involves fewer constant sources of error than that em- 

 ployed by Kopp (determining by means of an instrument resem- 

 bling a thermometer — dilatometer), I think I am justified in con- 

 sidering Matthiessen/s data the- most correct. In order to in- 

 vestigate the influence of the maximum density of water upon 

 the relations under examination, I made use of the numbers 

 given by Kopp between 0° and 8° C, since Matthiessen has not 

 extended his observations to temperatures below 4° C. As the 

 data for the density of water given by different equally eminent 

 physicists differ from one another in the fourth decimal place*, 

 I content myself with giving the results to the fifth decimal 

 place. 



Matthiessen gives two formulae to express the expansion of 

 water between 0° and 100° C. ; the one is applied from 4° to 

 32°, and the other between 32° and 100° C. These formulae 

 are: — 



For £=4° to £=32°, 



^=l-0'00000253(/-4) + 0-00000389 (*-4) 2 

 -0-00000007173(*-4) 3 . 

 For* =32° to *=100°, 



^=0-999695 H-0-0000054724^-0-00000001126/ 3 . 



Kopp gives for water between 0° and 25° C, 



^=1~0-000061045* + 0-0000077184* 2 -0-00000003734* 3 . 



In order to reduce Matthiessen's numbers, which are referred 

 to the volume at 4° C. as unit, to the volume at 0° C. as unit, 

 they must be multiplied by 0-99988. 



* See Matthiessen' s collation of the results of various observers, Pogg. 

 Ann. vol. cxxviii. p. 534. 



