8G2 



DB. A, MATTHIESSEN ON THE EXPANSION 



In Table I., T, T„ Tj, T3, T4 indicate the temperatures in the order in which the 

 observations were made ; a, b, c the increment in length in millims. of the rod between 

 T, and T,i T, and T„ T and T3 respectively ; the values in the three last columns are 

 the coefficients of expansion of the rod between the observed temperatures. The length 

 of the rod was 1804 millims. and its diameter about 15 millims. 



Table I. 



7-4 



7-0 

 8-4 

 7-5 



8-6 



50-7 

 61-2 

 61-9 

 50-9 



99*9 

 100-1 

 100-3 

 100-3 

 1006 



7-0 



104 

 7-0 



7-8 



7-2 



1-263 

 1-252 

 1-295 

 1-238 



i. 



2-807 

 2-808 

 2-807 

 2-805 

 2-775 



2-803 

 2-718 

 2-830 

 2-803 

 2-812 



Mean 0-02916 



0-02890 

 0-02925 

 0-02917 

 0-02927 



0-03026 



Or the mean coefficient between 0° and 50° may be taken =0-02915, and that between 

 0° and 100°= 0-03026. 



And taking the length of the rod at 0°=1804, it will be 



at 50°=1805-4575, 

 at 100°=1808-0260. 



From these values the linear expansion of the copper rod can be expressed by the 



formula 



L<=1804(l+0-00001555^+0-0000000122f''), 



or for any length of this sort of copper the formula for the coiTection of the linear 

 expansion for temperature will be 



L,=L„(1 +0-00601555^+0-0000000122)!=), 

 and that for the correction of the cubical expansion 



V,=V.(l+0-00004665if+0-0000000366!5=). 



Two series of weighings in water were made with the piece cut from the end of the 

 copper rod; the results are-given in Table II. 



