Assuming five simple and reasonable rules concerning the formation of atomic groups in borosilicate glasses, the author was able to interpret satisfactorily, by the way different from those used by others in their attempts, not only the boric oxide anomaly in the glasses of the ternary system Na₂O-B₂O₃-SiO₂ but also various properties of borosilicate glasses in general, and further succeeded in improving the properties of these glasses by the method based on these considerations.
In the first place, by representing, for simplicity, the BO₄ tetrahedron by x and the BO₃ triangle by y, the following two rules were assumed concerning the atomic arrangement in the glass of the composition corresponding to the maximum number of x in Na₂O-B₂O₃ system: Rule 1. One x is bonded to four y's. Rule 2. One y is bonded to two y's and one x. By satisfying these two rules, x's and y's must be bonded to each other forming the unit group xy₄ in the network of glass, i.e., to one BO₄ tetrahedron four BO₃ triangles are bonded each of which sharing only one corner with the tetrahedron.
Then the large network of glass should be built up of these unit groups by the following rule: Rule 3. “xy₄-groups” share corners with each other not edges or faces. These “xy₄-groups” may exist in all glasses of Na₂O-B₂O₃ system, Na₂O-B₂O₃-SiO₂ system, and even in borosilicate glasses in general by the following rule: Rule 4. “xy₄-groups” and BO₃ triangles or SiO₄ tetrabedra share only corers with each other. These rules, however, prescribe only the manner in which several unit groups are bonded, and the selection of the associate group should be considered by other rules based on various experimental facts. One of them may be as follows: Rule 5. “xy₄-groups” are formed only in a certain specific temperature range between the softening temperature, and are decomposed to y's at higher temperatures.
By these assumptions concerning “xy₄-group” formation, the manner of the variation of the expansion coefficient of the glasses in the ternary system Na₂O-B₂O₃-SiO₂ determined by Gooding and Turner as well as the limit of glass formation tn this system was very satisfactorily interpreted, and it was also deduced that for the domain of composition where the mol ratio of SiO₂ to B₂O₃ is more than 3/2, the “xy₄-group” formation is accompanied by the separation of the glass into two phases, one is rich in SiO₂ and the other in B₂O₃ and Na₂O.

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