stokes.] HIGHER METAPHOSPHIMIC ACIDS. 137 
close proximity, thus admitting of inner anhydride formation, while in 
other cases this is not possible, owing to their remoteness. Von 
Baeyer, 1 in his well-known " tension theory," has shown that the series 
of methylene-ring hydrocarbons, (CIT 2 ) n , may be expected to possess a 
maximumof stability in the pentamethylene ring, a ring in which there is 
the least "strain," because the attraction of the carbon atoms for each 
other acts very nearly in the direction which the valences naturally 
assume, a deduction which has been confirmed by recent work on the 
reduction of aromatic hydrocarbons, showing the tendency of these to 
form pentamethylene rings when reduced. 2 
The speculations of Wislicenus and von Baeyer admit of applica- 
tion to the series of acids derived from the phosphonitrilic chlorides, 
and as far as the subject has been worked out the analogy is a com- 
plete one. The acids in the open form are amides of imidophosphoric 
acids; those with from 3 to G phosphorus atoms have the open form 
in alkaline solution, from which they are thrown out by silver nitrate 
as salts of the general formula (PN0 2 Ag 2 ) n -+- H 2 G, but in acid solution 
they spontaneously form the inner anhydrides; i. e., the metaphos- 
phimic acids, which can be precipitated as silver salts of the general 
formula (PN0 2 HAg)„. The acid with 7 phosphorus atoms, on the con- 
trary, does not form the anhydride under any conditions. Not only 
does the series possess an extremely marked maximum of stability in 
tetrametaphosphimic acid, but the higher acids, on being subjected to 
energetic attack, break up, yielding this body. 
In previous chapters I have assumed that tri- and tetrametaphos- 
phimic acids contain phosphorus-nitrogen rings: 
PO OH N H 
"l^NH NH 
POOH 
NH 
POOHV yPOOH POOH 
NH NH POOH 
We know nothing of the steric relations of phosphorus and but little 
of those of nitrogen, and have therefore no definite theoretical grounds 
for assuming the magnitude of the angle a formed by the lines joining 
a POOH group with two NH groups, nor of the angle b formed by lines 
connecting a NH group with two POOH groups, in the case when these 
are free to assume a relation of greatest stability or least tension, as in 
an open chain. Neither can we assert that in a 6-sided ring, P 3 N : „ 
with alternate phosphorus and nitrogen, the angles a and b must each 
be 120°. We are, however, justified in assuming that the mean of a 
and b is 120°. Similarly in an 8-sided ring, P 4 N,, the mean angle is 
135°, even though a may be 180° and b 90°. 
'Ber.Deutsch.chem.C^sc-U.. Berlin, Vol. Will. p. 2277. 
2 Zelinsky, Ber. Deutach. chein. Gesell., Berlin, Vol. XXX, pp. .'587, L539. 
