REPORT 1859. 



From these data the temperature of any one of the thermometers may be expressed 

 in the form 



«=A +A 1 cos27r-+B 1 sin27r- + A 2 cos4ff-+B 2 sin47r-+8rc. > . (l) 



■where v is the temperature at the time t reckoned from the middle of January, T is 

 the periodic time (a year), and the constants A , A 1( A 2 , B u B 2 are found in the 

 manner shown below : — 



A =mean of all the Nos. in I. and II. =46-27. 



The symbols S , S lt S 2 , S 3 denote the sines of 0°, 30°, 60°, and 90° respectively. 

 The following Table exhibits the values of the coefficients found as above : 



Expression (1) is now to be converted into the form 



t>=A +P 1 sinf27r^ + E 1 W 2 sinf47r^+E 2 V&c., ... (2) 



by applying the equations 

 A 



B„ 



il=tan E. 



i/A K 2 +B n 2 =P M ; 



