This will be understood by looking at Fig. 12, showing _S_{1}_ and neighbours on each side of it in the rows of _S_{1}S_{2}_, _S_{1}S_{3}_, and in a row parallel to that of _S_{2}S_{3}_. The plane of the diagram is parallel to the planes of corresponding points of these seven bodies, and the diagram is a projection of these bodies by lines parallel to the intersections of the tangent planes through _p_ and _r_. If the three tangent planes through _p_, _q_, and _r_, intersected in parallel lines, _q_ would be seen like _p_ and _r_ as a point of contact between the outlines of two of the bodies; but this is only a particular case, and in general _q_ must, as indicated in the diagram, be concealed by one or other of the two bodies of which it is the point of contact. Now imagining, to fix our ideas and facilitate brevity of expression, that the planes of corresponding points of the seven bodies are horizontal, we see clearly that _S_{4}_ may be brought into proper position to touch _S_{1}_, _S_{2}_, and _S_{3}_ either from above or from below; and that there is one determinate place for it if we bring it into position from above, and another determinate place for it if we bring it from below. § 26. If we look from above at the solids of which Fig. 12 shows the outline, we see essentially a hollow leading down to a perforation between _S_{1}_, _S_{2}_, _S_{3}_, and if we look from below we see a hollow leading upwards to the same perforation: this for brevity we shall call the perforation _pqr_. The diagram shows around _S_{1}_ six hollows leading down to perforations, of which two are similar to _pqr_, and the other three, of which _p′q′r′_ indicates one, are similar one to another but are dissimilar to _pqr_. If we bring _S_{4}_ from above into position to touch _S_{1}_, _S_{2}_, and _S_{3}_, its place thus found is in the hollow _pqr_, and the places of all the solids in the layer above that of the diagram are necessarily in the hollows similar to _pqr_. In this case the solids in the layer below that of the diagram must lie in the hollows below the perforations dissimilar to _pqr_, in order to make a single homogeneous assemblage. In the other case, _S_{4}_ brought up from below finds its place on the under side of the hollow _pqr_, and all solids of the lower layer find similar places: while solids in the layer above that of the diagram find their places in the hollows similar to _p´q´r´_. In the first case there are no bodies of the upper layer in the hollows above the perforations _similar_ to _p´q´r´_, and no bodies of the lower layer in the hollows below the perforations _similar_ to _pqr_. In the second case there are no bodies of the upper layer in the hollows above the perforations _similar_ to _pqr_, and none of the under layer in the hollows below the perforations _similar_ to _p´q´r´_.