150 Royal Society : — Dr. A. Matthiessen on the 



To check, therefore, the method, I was led* to determine the coef- 

 ficient of expansion of mercury, and, basing my calculations on Kopp's 

 coefficients of expansion of water, I expected to obtain Regnault's coef- 

 ficient of expansion of mercury. The coefficient deduced from expe- 

 riments did not agree with Regnault's ; and being unable to discover 

 any source of error in the method of experimenting, I determined to 

 reinvestigate the matter. 



The memoir is divided into four parts. 



I. On the determination of the coefficients of the linear expansion 

 of certain glass rods. 



These rods (1825 millims. long and of 20 millims. diameter) were 

 kindly made for these experiments by Mr. F. Osier. The method 

 used for the determination of their increment in length was that of 

 measuring it with a micrometer-screw, with which a length could be 

 measured with accuracy to 0*001 millim. 



The rod was placed in a long trough, the one end of the rod 

 resting against a fixed glass tube capped with zinc, the other against 

 another glass tube the other end of which rested against the micro- 

 meter-screw. Water was allowed to flow through these glass tubes 

 during the time of observation. The trough being filled with water 

 at ordinary temperature and the position of the screw read off, the 

 water was heated to boiling and another reading taken. 



The mean of sixteen observations gave for the linear expansion of 

 these rods 



L,=L (1+0-000007290, 

 and therefore for the cubical expansion 



V*=V (1 +0-000021870. 



II. On the method employed for the determination of the cubical 

 expansion of water and mercury. 



This part of the paper contains a full description of the apparatus 

 employed, and the precautions taken. 



The method consists of weighing the substances in water at dif- 

 ferent temperatures, and from the loss of weight in water deducing 

 its volume. For this deduction, the expansion of water at differ- 

 ent temperatures is required. 



III. On the redeterminations of the coefficients of expansion of 

 water. 



To determine these, pieces of the glass rods (the linear expansion of 

 which had to be determined), ground to the shape of a double wedge, 

 were weighed in water of different temperatures. Three pieces of glass 

 were used (making three series), the weighings being made at tempera- 

 tures between 0° and 100°, the whole number of observations being 

 thirty-two. 



From these it was found that the expansion of water between 4° 

 and 100° may conveniently be expressed between 4° and 32° by the 

 formula 



V,= 1-0-0000025300 (t-4) + 0*0000083890 (t—4) 2 



-0*00000007173 (t-4) 3 , 



