56 REPORTON 



The mean of the quantities in the column headed t is 75.8. Accordingly, 

 adding log. [ 1 + (t 75.8)2] to each log. m T , we obtain the values of log. m 

 given" in the table. Taking the mean of these values, and also the mean of the 

 numbers in the column "days," we find that at 134 days, which corresponds to 

 March 7th, 1866, the value of log. m was 9.83729 = log. i . Then, assuming 



Log. m = log. w ad 



we have 



= 9.83729 log. m ad 



and each value of log. m furnishes an equation of condition for the determination 

 of a, as follows. 



o = 260 +1340 



o = 261 + 128 a 

 o = 261 + 1140 



O = 326 +1110 



o = 165 + 99 

 o = 33 + 840 

 o= 139+ 74a 

 o = 117+ 7<* 

 o = 172 + 60 a 

 o = - 37+480 

 o = + 1+280 

 o = 49 + 50 



o = + 15 22 a 



o = 55 3 1 " 



o = + 29 35 o 



o = + 106 37 a 



o = + 73 50 a, 



O = + 50 61 a 

 o = + 225 68 o 

 o = + 49 840 

 o = + 161 940 

 o = + 278 100 a 

 o = + 292 ii i o 

 o = + 487 239 o 



O = + 107 12 o 



By the method of least squares we obtain the normal equation 



= 397497 + 203965 a 

 Solving, we get 



a = + 1.9488 

 Hence 



Log. m = 9.83729 0.0000195 d 0.000090 

 or 



m = 0.68753 0.0000310 d 0.000144 



From the first of these expressions the quantities in the column " concluded log. 

 j" were computed. 



If, in the expression for log. m, given above, we introduce the correction for 

 temperature, we obtain 



Log. m r = 9.83729 0.0000195 d 0.000087 (t 75.8) 

 by means of which the quantities in the column "concluded log. m" were com- 

 puted. 



The probable error of a single observed value of log. m is i 0.000452, and of a 

 single observed value of m it is -4- 0.000719. 



Observations of Inclination were all made with a dip circle by Henry Barrow 

 & Co., of London. It was provided with two needles, marked A 1 and A 2, each 

 3.5 inches long, and having axles 0.016 of an inch in diameter. The distance 

 between the agate planes on which they rested was 0.74 of an inch. By means 

 of two microscopes, one opposite each end of the needle each of which, assuming 

 distinct vision to be obtained at a distance of ten inches, magnified 18 diameters 

 the inclination of the needle was referred to, and read off upon a vertical circle six 

 inches in diameter, divided to half degrees, and reading by means of two verniers 

 to single minutes. The pointing of the microscopes to the ends of the needle was 



