The solution of this case, in a manner a little different, I have given some time since, in another place; where the principles of the general method, here extended and illustrated, are pointed out. I shall put an end to this paper with observing, that if, in the series given, the even powers of x, or any other terms whatever, be wanting, their places must be supplied with cyphers; which, in the order of numbering off, must be reckoned as real terms.
CIV. Observatio Eclipsis Lunæ Die 30 Julii 1757. habita Olissipone à Joanne Chevalier, Congregationis Oratorii Presbytero, é Regia Londinensi Societate. Communicated by Jacob de Castro Sarmiento, M.D. F.R.S.
Tubo optico 8 pedum.
Read Nov. 16, 1758.
| h | ´ | ´´ | |
| INitium penumbræ | 9 | 15 | 18 |
| INitium dubium eclipsis | 9 | 22 | 24 |
| Certo jam incœperat | 9 | 23 | 34 |
| Umbra ad mare humorum observata vitro plano cæruleo | 9 | 31 | 2 |
| Solo tubo optico observata | 9 | 31 | 29 |
| Vitro flavo observata | 9 | 31 | 48 |
| Umbra tangit Grimaldum observata vitro plano cæruleo | 9 | 31 | 20 |
| Solo tubo optico | 9 | 31 | 50 |
| Vitro plano flavo | 9 | 32 | 8 |
| Totus Grimaldus tegitur observatus vitro plano cæruleo | 9 | 34 | 4 |
| Solo tubo optico | 9 | 34 | 28 |
| Vitro flavo | 9 | 34 | 47 |
| Umbra ad Tychonem observata vitro plano cæruleo | 9 | 38 | 25 |
| Solo tubo optico | 9 | 38 | 42 |
| Vitro flavo | 9 | 38 | 59 |
| Umbra ad Harpalum vitro cæruleo observata | 9 | 55 | 6 |
| Solo tubo optico | 9 | 55 | 35 |
| Umbra ad Fracastorium | 9 | 59 | 57 |
| Umbra ad Mare Nectaris | 10 | 00 | 50 |
| Observata vitro flavo | 10 | 1 | 8 |
| Umbra ad Dionysium | 10 | 5 | 2 |
| Umbra tangit Mare Tranquillitatis | 10 | 5 | 50 |
| Umbra ad Mare Serenitatis | 10 | 10 | 16 |
| Umbra tegit Menelaum observata vitro cæruleo | 10 | 11 | 4 |
| Solo tubo optico | 10 | 11 | 29 |
| Vitro flavo | 10 | 11 | 50 |
| Totum Mare Fœcunditatis tegitur | 10 | 18 | 39 |
| Umbra tangit Mare Crisium vitro cæruleo observata | 10 | 22 | 52 |
| Solo tubo optico | 10 | 23 | 12 |
| Vitro flavo | 10 | 23 | 29 |
| Umbra ad Proclum | 10 | 23 | 33 |
| Possidonius totus tegitur | 10 | 23 | 50 |
| Totum Mare Serenitatis tegitur | 10 | 24 | 36 |
| Totum Mare Crisium ab umbra tegitur | 10 | 30 | 27 |
| Plato tegitur vitro cæruleo observatus | 10 | 31 | 26 |
| Solo tubo optico | 10 | 31 | 48 |
| Vitro flavo | 10 | 32 | 4 |
| Obscuratio maxima | 10 | 55 | 40 |
Emersiones.
| h | ´ | ´´ | |
| Plato emergit observatus vitro flavo | 11 | 19 | 5 |
| Solo tubo optico | 11 | 19 | 31 |
| Vitro cæruleo | 11 | 19 | 50 |
| Aristarchus emergit | 11 | 21 | 3 |
| Gassendus incepit emergere observatus vitro flavo | 11 | 25 | 36 |
| Observatus solo tubo optico | 11 | 25 | 52 |
| Observatus vitro cæruleo | 11 | 26 | 11 |
| Gassendus totus extra umbram | 11 | 28 | 2 |
| Schicardus incipit emergere | 11 | 45 | 44 |
| Totus extra umbram | 11 | 47 | 10 |
| Totum Mare Humorum extra umbram | 11 | 46 | 50 |
| Menelaus extra umbram | 11 | 55 | 36 |
| Mare Serenitatis extra umbram | 11 | 59 | 46 |
| Tycho extra umbra observatus vitro flavo | 12 | 00 | 33 |
| Solo tubo optico | 12 | 00 | 52 |
| Vitro cæruleo | 12 | 1 | 14 |
| Incipit emergere Mare Crisium | 12 | 8 | 31 |
| Totum Mare Crisium extra umbram | 12 | 16 | 28 |
| Finis eclipsis | 12 | 28 | 26 |
Observatio hæc peracta é cœlo claro; umbra autem terræ ita diluta erat, ut maculæ in ea conditæ satis dignoscerentur.