Specific Heat of Water. 303 



after observer has devoted himself to the question with every 

 appearance of the most thorough provision for refined accu- 

 racy ; but seems only to have made " confusion worse con- 

 founded." The latest research of any elaborateness is that 

 of Velten previously mentioned. He draws attention to ap- 

 parently great errors in Regnault' s calculations of the specific 

 heat of water from his data, giving a table in which are 

 compared the values given by Regnault and those calculated 

 correctly by himself from Regnault's data. In twenty-seven 

 of the experiments the two sets of values agree well enough ; 

 but in the remaining thirteen, while Regnault' s results are all 

 greater than unity, those of Yelten are all less than unity, the 

 difference between the corresponding values in the two series 

 amounting in one case to nearly four per cent. As the errors 

 could not be ascribed to misprints, Prof. Wiillner wrote to 

 the Paris Academy of Sciences to ask if any explanation 

 could be given for them ; but that body appeared to be able to 

 furnish none. 



Yet the explanation is simple enough. Regnault, in pre- 

 paring his table (M4m. de V Acad. xxi.) ,has, in the thirteen cases, 

 merely copied a wrong series of numbers into the column 

 headed " weight of hot water." I shall be able to show this 

 quite clearly, and to prove that in his calculations he must 

 have used the correct series of numbers. Yelten, using Reg- 

 nault's erroneously tabulated series, necessarily obtains erro- 

 neous results in the thirteen cases. 



Regnault employed a large calorimeter with a narrow 

 graduated neck. Its capacity, when filled to the zero-mark 

 on the neck, was carefully determined and, with the water- 

 equivalent of the calorimeter, was tabulated for temperatures 

 between 10° and 30°. The neck was also calibrated, so that 

 the water-equivalent of the calorimeter, when filled to any 

 mark on the neck, could be determined with great accuracy. 

 Let P be the water-equivalent of the calorimeter and the 

 water at t which fills it to the graduation n on the neck. A 

 weight, p, was then withdrawn and determined by weighing. 

 The hot water at T was then introduced, so that the calori- 

 meter was filled to the graduation n ; the water-equivalent at 

 the resulting temperature t of the calorimeter and its contents 

 was then obtainable from the table ; let it be P, then the 

 weight of hot water introduced was P — (P — p)> Let x be 

 the mean specific heat between T and t, supposing that between 

 t and t to be unity, then 



xrP-F +p) (T-t) = (P - P )(<-f ). 



