ME. W. CEOOKES OX THE ATOMIC WEIGHT OF THALLIUM. 
289 
right side to supplement the three weights already in that pan. This was noted. The 
weights were then removed to the opposite sides, the 1000 grains being on the right 
and the three smaller weights on the left. It was now found that a small weight had 
to be subtracted from the side carrying the three weights in order to produce equili- 
brium. The weights were removed and interchanged in this manner ten times, so as to 
eliminate, as far as possible, the errors arising from observation, or the unequal expansion 
by heat of the arms of the balance ; and by applying the method of least squares to the 
results obtained, the following equation was arrived at : — 
(1000) =(600) -f (300) + (100) + 0-01000 . . . «, 
the figures within parentheses representing the nominal value of the actual pieces of 
platinum stamped 1000, 600, 100 grains, &c. 
In a similar manner the values of the remaining weights were ascertained ; thus, — 
(600)= (300) + (200) + (100) 
+ 
0-00777 . 
. . b. 
(300) = (200) + (100) 
+ 
0-00991 . 
. . c. 
(200) = (100)+ (60)+ (30)+ (10) 
T - 
0-01577 . 
. . a. 
(100)= (60)+ (30)+ (10) 
— 
0-00030 . 
. . e. 
(60)= (30)+ (20)+ (10) 
— 
0-00522 . 
• • /• 
(30)= (20)+ (10) 
+ 
0-00154 . 
• • 9- 
(20)= (10)+ (6)+ (3)+ (1) 
+ 
0-00355 . 
. . h. 
(10)= (6)+ (3)+ (1) 
+ 
0-00052 . 
. . i. 
(6)= (3)+ (2)+ (1) 
— 
0-00102 . 
• • J- 
(3)= (2)+ (1) 
+ 
0-00165 . 
. . Jc. 
(2)= (1)+ C6)+ ('3)+ Cl) 
— 
0-00312 . 
. . 1. 
(1)= (-6)+ (-3)+ (-1) 
— 
0-00508 . 
. . m. 
(-6)= (-3)+ (-2)+ (-1) 
— 
0-00260 . 
. . n. 
(•3)= (-2)+ (’I) 
+ 
0-00225 . 
. . 0. 
(-2)= (•l)+(-06)+(-03)+(-01) 
— 
0-00100 . 
• • JP- 
(•!)= C06)+ (-03)+ (-01) 
— 
0-00802 . 
• • 9- 
(-06)= (-03)+ (-02)+ (-01) 
— 
0-00607 . 
. . r. 
(-03)= (-02)+ (-01) 
— 
0-00642 . 
. . s. 
(-02)= (-01)+ (-01 r")* 
— 
O-OOllSr' . 
. . t. 
(-01)= (-01r") 
+ 
0-0041 3r' . 
. . u. 
(-01)= (-01/) 
+ 
0-00410r" . 
. . V. 
* r', r" represent riders, two of which were adjusted in this manner. 
