loo Mr. Christie 07 i the mutual action of 
the mean value of M', deduced by combining all the observa¬ 
tions, I had previously found/) = *256, and M'= 5*1263 from 
the separate observations, but I afterwards discovered that the 
latter values were slightly affected by an error in one of the 
computations ; as however I had previously determined the 
values of u by means of them, and these are rather nearer to 
the observed values than those obtained from M' = 5-060 
and p = -240, I give the results of both to show the effects 
of such changes in the constants. 
Table IV. 
Values of c 
in the dif¬ 
ferent ob¬ 
servations. 
Observed 
values of 
a. 
Values of a, 
computed from 
M' 
Difference 
between the 
observed & 
computed 
values of 
a. 
Quotient of 
this diff. di¬ 
vided by the 
computed 
value of 
a. 
Values of 01 
computed from 
Difference 
between the 
observed & 
computed 
values of 
a. 
Quotient of 
this diff. di¬ 
vided by the 
computed 
value of 
a, 
t P cJ 
M' = 5 060 
p = O'240 
1. p 4. c J 
M'- = 5-1263 
p = 0-256. 
Inches. 
2-5 
20 
I '5 
I 25 
I -oo 
075 
0-50 
11-375 
2575 
72-00 
130-00 
289-18 
706-25 
1982-5 
11-631 
26-038 
71-516 
13300 
277-28 
682-43 
21861 
+ 0-255 
-f- 0-288 
— 0-484 
— 6-000 
— 11-90 
— 23-82 
203-6 
+ -02193 
-f- '01 106 
— -00677 
—-04511 
— -04292 
— -03490 
+ -09313 
11 -970 
26-659 
72629 
134-248 
277-490 
674-24 
2114-1 
+ 0-595 
+ 0-909 
-4 0-629 
— 4-752 
— 11-69 
— 32-01 
+ 131-6 
+ •04971 
+ -03410 
+ -00866 
— -03540 
— -04215 
—-04748 
+ -06226 
/ 
The quotients in the 5th and 8th columns are not in any 
case great, but are decidedly greater than the corresponding 
quotients in Table III. Considering these quotients as the 
errors arising from the respective formulas, and that the sum 
of the squares of the errors is the best criterion of correctness, 
it appears that the sum of the squares of these errors in the 
5th and Sth columns respectively, are *014417 and -012869, 
and that the sum of the squares of the errors in the ^th 
column of Table III. is only -001190, or not a tenth of the 
