138 
CONTRIBUTIONS TO CHEMISTRY AND MINERALOGY. [bull. 167. 
Experiment Laving shown that tetrainetaphosphimic acid, PJS^OsHg, 
is vastly more stable than any other acid of the series, we may regard 
the angle 2 of the octagonal nucleus P 4 N 4 , which is 135°, as that 
which most nearly coincides with the angle ofleast tension in the sense 
of von Baeyer's theory, and as approximating to that which would be 
assumed in an open chain, and we may expect that the stability of each 
ring will be less the more the angle 2 differs from 135°. In the fol 
lowing table the mean angle and its difference from 135° are shown: 
King- 
Number of 
sides. 
Mean angle. 
Difference 
from 135°. 
PN 
2 
4 
6 
8 
10 
12 
14 
16 
Degrees. 

90 
120 
135 
144 
150 
154.3 
157.5 
Degrees. 
—135 
— 45 
— 15 

+ 9 
+ 15 
+ 19.3 
+ 22.5 
P. 2 No 
P { N 3 
P 4 N 4 
P 6 N 6 
P e N 6 
P 7 N 7 
P 8 N 8 
It is therefore to be expected that as we ascend in the series there 
will be a very rapid increase of stability to a maximum, followed by a 
gradual decrease. This coincides witli what we find. P 3 N 3 O g H g is 
vastly less stable than P 4 N 4 0;jH 8 ; the latter may be heated for hours 
with acids without complete decomposition, while the former is destroyed 
under the same conditions in a few minutes. P5N5O10H10 is much less 
stable than P 4 N 4 O i! H 8 , but markedly more stable than P 3 N 3 O g H g , cor 
responding to the difference of only 9° from 135° in one case against 
15° in the other. P^O^H^ is perceptibly less stable than P r) N 5 O 10 H 10 , 
and finally the ring P 7 N 7 of heptametaphosphimic acid is incapable of 
existence under the usual conditions, and as a result we get, instead 
of the ring acid P 7 N 7 14 H l4 , the open chain P 7 N 7 15 H 1G . 
When any of the acids above tetrainetaphosphimic acid is broken up, 
the latter is formed in considerable amount. This maybe explained in 
two ways: either the P 4 N 4 nucleus exists as such in the higher acid, or 
it is formed from the decomposition products. The former is highly 
improbable, for, considering its great stability, it should persist and be 
found in nearly theoretical amount, which is by no means the case. 
(P r> N 5 Oi„H 10 gave 12 per cent and P g N g O ]2 H 12 30 per cent of the theoret- 
ical.) Its formation from the decomposition products is easily explained 
on the tension hypothesis. If a ring of POOH and Nfl groups be 
broken up by the action of a stronger acid, the molecules resulting 
from its decomposition will tend to assume a configuration determined 
