of Edinburgh, Session 1883 — 84 . 
739 
common to both Methods I. and IL j we have — (a) templet 4 intro- 
duced involving two additional conditions from measurement^ and 
{h) templet 5 introduced, involving two additional conditions from 
measurement. So in respect to these two templets 4 and 5 we 
have four conditions introduced. 
And in the whole of Method I. there are the following known 
conditions unused 
That 
^ 1^-2 _ ^ 1^3 
A^Ag 
^ 1^2 _ ^ 1^4 
A1A2 A^A 
and that 
^1^2 
That is, in all, three known conditions unused. So instead of 
ascertaining 4 conditions by measurement and neglecting 3, we 
might get the result by 4 — 3, that is one new condition from 
measurement. Now in Method II. we do demand from measure- 
ment just one new condition, and we have no redundant informa- 
tion. The one new condition so introduced is the condition brought 
into use by the incomplete templet 4 ; videlicet, that when CA 
has a certain stated length CB has another certain ascertained 
length. 
So, on the vrhole, in Method I. we have from measurement 5 
templets supplying two conditions each, that is, we have 10 condi- 
tions from measurement; and, as shown already, we are thus 
supplied with 3 redundant conditions; and so 10-3 or 7 con- 
ditions from measurement, or independent data, must somehow be 
enough. 
Passing to Method II. we see that in it we have 3 complete tem- 
plets supplying 6 conditions, and 1 incomplete templet supplying 
1 condition; and we have got no redundant conditions; but we 
have just 7 conditions found necessary and brought into use. 
So the two methods agree in showing that the number of inde- 
pendent conditions from measurement necessary to be supplied is 
seven. 
