Next let us take the Pluvium presentation. We again mark with an asterisk in Table C the possibilities inferred from the Mala-Vesper solution, and take the projections those possibilities would produce. The additional projections are again marked (†). There are twelve Pluvium projections altogether, viz. Bidens, Ostrum, Cudo, Cardo, Luctus, Verbum, Urna, Moles, Vitta, Thyrsus, Securis, Cervix. Again we compare these with the given Pluvium projections, and find three are absent, viz. Ostrum, Cardo, Thyrsus. Hence the tessaracts implied by Ostrum and Cardo and Thyrsus cannot be in our shape, viz. Uncus, Ocrea, Crates, nor Thyrsus itself. Excluding these four from the seventeen possibilities of the Mala-Vesper solution we have left the thirteen tessaracts: Orcus, Pallor, Tessera, Lacerta, Cudo, Frenum, Polus, Plebs, Cura, Penates, Moles, Vitta, Urna. This we call the Mala-Vesper-Pluvium solution. Lastly, we have to consider whether these thirteen tessaracts are consistent with the given Lar projections. We mark them again on Table D with an asterisk, and we find that the projections are exactly those given, viz. Frenum, Plebs, Moles, Urna, Cura, Vitta, Polus, Penates. Therefore, we have not to exclude any of the thirteen, and can infer that they constitute the shape, which produces the four different given views or projections. In fine, any shape in space consists of the possibilities common to the projections of its parts upon the boundaries of that space, whatever be the number of its dimensions. Hence the simple rule for the determination of the shape would be to write down all the possibilities of the sets of projections, and then cancel all those possibilities which are not common to all. But the process adopted above is much preferable, as through it we may realize the gradual delimitation of the shape view by view. For once more we must remind ourselves that our great object is, not to arrive at results by symbolical operations, but to realize those results piece by piece through realized processes. APPENDICES. APPENDIX A. This set of 100 names is useful for studying Plane Space, and forms a square 10 × 10. Aiōn Bios Hupar Neas Kairos Enos Thlipsis Cheimas Theion Epei Itea Hagios Phaino Geras Tholos Ergon Pachūs Kiōn Eris Cleos Loma Etēs Trochos Klazo Lutron Hēdūs Ischūs Paigma Hedna Demas Numphe Bathus Pauo Euthu Holos Para Thuos Karē Pylē Spareis Ania Eōn Seranx Mesoi Dramo Thallos Aktē Ozo Onos Magos Notos Mēnis Lampas Ornis Thama Eni Pholis Mala Strizo Rudon Labo Helor Rupa Rabdos Doru Epos Theos Idris Ēdē Hepo Sophos Ichor Kaneōn Ephthra Oxis Lukē Blue Helos Peri Thelus Eunis Limos Keedo Igde Matē Lukos Pteris Holmos Oulo Dokos Aeido Ias Assa Muzo Hippeus Eōs Atē Akme Ōrē Gua APPENDIX B.