of the Pendulum made by Capt. Kater, M. Biot, §e. 165 



with relation toy and to z. Since the coefficient of 2 is unity 

 in all the preceding equations, the condition of the minimum 

 with regard to that unknown quantity will be given by making 

 their sum equal to zero; thus 



274*05252 — 7 2— 4-64298023/=0 (10) 



This equation of the minimum can only take place in so far 

 as the sum of the errors shall be nothing. The new condi- 

 tion that it expresses, and which the errors ought to satisfy, 

 holds not with regard to the method of least squares, but to 

 the particular form of the equations above. 



If we multiply each equation of condition by the coefficient 

 of y in that equation, we shall have the following results : 



29-8237787-0-7613650 2-0-57967673/, 

 27-9692193-0-7142003 2-0-5100820 j/, 

 26-8978315-0-6869483 »— 0-471 8980y, 

 25-2707160— 0-6455504 2 — 0-41673543/, 

 24-4485230— 0-6246030 2— 0-39012903/, 

 23-9844238 — 0-6127966 2—0-37551983/, 

 23-3844933-0-5975161 z -0-3570262 y. 



The sum of all these quantities equalled to zero will give 

 181-7789856— 4-6429802 2— 3-1010671 3/=0 (11) 



From equation (10) we get 2=39-15036 — 0-66328293/, and 

 from equation (11) 2=39-1513592 — 0-66790453/. Equalling 

 these two values of z, we get y =0-2 162022. Hence 2 = 

 39-0069568 = the length of the seconds' pendulum at the 

 equator, and 39 in -0069568 + 0-2162022 = 39 in -2231590 = the 

 length of the pendulum at the pole. If in equation ( 1 ) we sub- 

 stitute the values of y and z determined above, we shall have 



^=39-0069568 + 0-2162022 sin 2 X (12) 



rom which we are enabled to find the length of the pendulum 

 by computation. 



The 



