98 
Mr. Christie on the mutual action of 
The differences here, between some of the values of M and 
p , and their mean values, may appear more considerable than 
they ought to be, if the formula from which they are derived 
be correct ; but it is to be observed, that even very small 
errors in the observations are rendered very sensible by thus 
combining them. With regard to the differences in the 
values of e a , supposing the formula to be correct, and the 
observations to have been liable to no other errors than those 
in estimating the distances between the magnets and the ring, 
an error in this respect of y— inch would cause a greater 
difference than any here between the different values of e* and 
the mean. As I took every precaution to ensure accuracy, 
I consider that although I might be liable to an error to this 
amount, I was not liable to a greater. The best criterion of 
the correctness of the formula is, however, the agreement 
of the observed values of a with those deduced from it by 
employing these mean values of M, p , and e 2 , and likewise 
the agreement in the values of these quantities deduced from 
the separate observations. The comparison between the 
observed values of a. and those computed from the formula, 
_ f M ) 2 
* ~ i (P + c)*+ «*) 5 
assuming M == 23-314 ,p = -1052 and e 2 == 1504, is made in 
the following table. 
Table III. 
Values of c 
in the dif- 
ferent obser- 
vations. 
Observed 
values of 
a. 
Values of a. computed 
from 
«-( M y 
Difference 
between the 
observed & 
computed 
values of a. 
Quotient of 
this diff. di- 
vided by the 
computed 
value of or. 
Values of the constants 
deduced from the separate 
observations. 
M 
P 
£ 3 
inches. 
2’5 
20 
*‘5 
1-25 
1 00 
°75 
0-50 
”•375 
2575 
72-00 
I 39'00 
289-18 
706-25 
1982-5 
1 1 -293 
25-886 
73-086 
13768 
288-79 
600-03 
2035-9 
— 0-082 
+ 0136 
+ 1-086 
— 1-32 
— °'39 
— • 7-22 
+ 53*4 
— -00726 
+ -00525 
+ -01486 
— •00959 
— ■OO135 
— •OIO33 
4 -02623 
23-398 
2 3‘ 2 53 
23-140 
23-426 
23-330 
2 3434 
23-006 
•1005 
•1088 
•1115 
•1017 
• 1048 
• 1026 
•1109 
• I 5°4 
•*504 
.1504 
.1504 
• 1 5 c M- 
• I 5°4 
•* 5°4 
The mean values of M and p from the separate observations 
23-284 
*1058 
