# Philosophical Transactions of the Royal Society (1665-1886)/Volume 3/Number 41

Contents:
* Contents
* An Account from Bristol of some observations made in Hong-road this present year, by way of Answer to some of the Queries concerning the Tydes, recommended No. 17. & No. 18.⁠
* An Extract of a Narrative communicated from Sevill, of 0bservations made in a late Voyage from Spain to Mexico, concerning the Minerals of Mexico, and particularly the exact and perfect way of separating the Silver from its ore by Mercury, together with divers other Curiosities, Natural and Chymical.⁠
* Continuation of Dr. Wallis's second Letter on the printed Paper of Franciscus Du Laurens.⁠
* An Account of two Books:
** ⁠I. Tractatus duo, prior de RESPIRATIONE; alter de RACHITIDE, A. JOH. MAYOW, &c. Oxon. 1668; in 8°.⁠
** II. A Discourse concerning PHYSICK, and the many Abuses thereof by APOTHECARIES. London, 1668, in 8°.
PHILOSOPHICAL
TRANSACTIONS.
Monday, Novemb. 16. 1668.
The Contents.
I Have observed, that our Annual Spring-Tydes do happen in March and September, either at the Tyde next bcfore the Suns Ingress into the Æquinoctial points of Aries and ​Libra, of the next Tyde after, according as the Moon is near her Full or Change, when the Sun thus enters into the said Signes: And then it flows in height about 7½ fathoms, or 45. foot; the lowest Neap-tydes flowing in height 27. foot.
2. We observe also, that the lowest Neap makes the highest Spring, if the North-East Winds hinder not by blowing hard, and so keep back the Tydes; as usually they do when they blow: whose contrary winds (South-west) if they blow hard, make here the highest Tydes.
3. Concerning our Diurnal Tydes, we observe, that from about the latter end of March till the latter end of September, they are about 1. foot and 3. inches higher perpendicularly in the Evening than in the Morning, that is, if high water happen after the Sun is past the Meridian, or in the Tydes betwixt Noon and Midnight. But from Michael-mas till our Lady-day we find the contrary, the Day-tydes being in that season higher by 15. inches than the Night tydes, or the Tydes between Midnight and Noon. And this proportion holds in both, after the gradual increase of the Tydes rising from the Neap to the highest Spring, and the like Decrease of their Height till Neap again.
4. As for the higest Menstrual Spring-tyde, that is always the third after the Full Moon or Change-day, if it be not kept back by North-East winds, as it hath been, by my own Observations.
5. I have observed several times, that it flows here on the Change-day, when the Moon is East-South-East the Tyde flowing in for the space of 5. hours, and ebbing 7. hours; so that there is an hour and an half difference from the Old Tables, which say, it flowes but to the Moons being East and West: An Error so great, that by all means it ought to be rectified.
6. There is some difference in reckoning the Tydes by the Moons Bearing on such a point of the Compass on the Full or Change day. Fort-hen about that time only will the Rule hold to be exactly true. But from the Change to the Quarters, and from the Full to the Quarters again in the Neap-Tydes, I have observed, it does not flow here by two points of the Compass so long. But concerning the difference betwixt the New and ​Full Moon, and the Quarters, Mr. Henry Philipps hath framed a Table for the rectification of this Error in the River of Thames; to be found in Number 34, p, 656, 657, of the Phil. Transactions.
7. The water flows nor ebbs equal spaces in equal times, but its Velocity is strongest at the first both of the Flood and Ebb, and so gradually decreaseth until Fu1l Sea or Low water. This is observ'd in Spring-Tydes only, as you may see by the following Table, which I have made from my Observations of our Tydes here. To make them always so near as to half inches, is neither easie, nor material, or usefull. But this hath been likewise observed, that it hath flowed or ebbed at the first of the Tyde one foot in 6. minutes, or that then the Tyde ran out afoot in 6. minutes, or did rise so much in height.
The Tyde-Table by Hour-quarters.
| | | | Hours | | | | | | | Hours |
| | | | & quart. | Feet | Inch | | | | & | quart. | Feet. | Inch. |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 1—— | 2—— | 7½ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 1—— | 2—— | 7½ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 2—— | 2—— | 6. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 2—— | 2—— | 6. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 3—— | 1—— | 6. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 3—— | 2—— | 6. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | ——— | 2—— | 6. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | ——— | 2—— | 6. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 1—— | 2—— | 6. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 2—— | 2—— | 5½ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | 3—— | 2—— | 5. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1… | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 2… | ——— | 2—— | 5. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 2… | ——— | 9—— | 0 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | 1—— | 2—— | 3. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | ——— | ——— | ——— | | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | 2—— | 2—— | 3. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | 3—— | 2—— | 3. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | ——— | 2—— | 3. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | ——— | 8—— | 0 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | 1—— | 2—— | 2. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 4… | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | 2—— | 2—— | 1. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 4… | ——— | 6—— | 9. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3… | 3—— | 2—— | 1. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 4… | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 4… | ——— | 2—— | 1. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 5… | ——— | 5—— | 0 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | 1—— | 1—— | 9. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 6… | ——— | ——— | ——— | | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | 2—— | 1—— | 8. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 6… | ——— | 4—— | 0 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | 3—— | 1—— | 8. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 6… | ——— | ——— | ——— | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | |
| For the flowing of 5. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 5… | ——— | 1—— | 8. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | For the Ebbing of 7. hours. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 7… | ——— | 3—— | 0 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ |
| | | 45. feet circiter. | 45. feet circiter. | 45. feet circiter. | 45. feet circiter. | | | | 45. feet circiter. | 45. feet circiter. | 45. feet circiter. | 45. feet circiter. |
[The Observer did not think it necessary to make everywhere in the Ebbing the like Division, he doth in the flowing hours, all edging for that omission the easiness of such a division, soon made by any body, because of the near agreement betwixt the divisions of both.]
8. The usual number of Tydes from New Moon to New Moon, or from the Full to the Full, is Fifty nine.
9. In the River of Severn. 20. miles above Bristol near Newnham, 160. miles from the Rivers mouth (Lundy,) the head of the Floud, at its coming in in Spring-tydes, ariseth in height, like a Wall near nine foot high, and so runs for many miles together, covering at once all the Shoales, which were dry before; at which time all Vessels, that lye in the way of the said Head-tydes, or (as it is vulgarly called) Boar, are commonly overset or carried upon the Banks, and the head of the Tyde being past, such Vessels are left dry again. It flows there but two hours, and eighteen foot in height, and it ebbs ten hours. The reason of the said Boar is doubtless the straightening and shoaling of the River in that place, it being there but half a mile broad; as it is but 20. pearches over, three miles higher; running tapering to Glocester.
So far this Observer; To whom as there are due particular acknowledgements for his care of observing hitherto, and for his frankness of communicating, so he is further desir'd to continue his Observations with as much exactness as may he, according to the directions set, down in the above mentioned Numb. 18. especially to rake particular notice, whether the Annual High-tydes, which he seems to fix on those (be it at New or Full) which happen nearest the Equinox, (be it before or after it) be not always before the Vernal Æquinox in March, and upon the New Moon; and always after the Autumnal in September, and upon the Ful-moon Spring-tydes: For as much as by a former relation, imparted by a curious Gentleman, we have been informed, that the Annual highest Tydes about Chepstow-bridge, were at St. Davids and Michaelmas-Stream, that is, the one a little before the Vernal, and the other somewhat after the Autumnal Æquinox, which agrees also with the Conjecture of at very intelligent Mathematician, who is withal of opinion, that because both are not fat from the Æquinoxes, ( though the one ​before, the other after) it might well give occasion to think it was depending on the Æquinox.
Moreover, the curious Reader may be pleased to compare this Account with that, which was given concerning the Tydes observed at Plymouth, Numb. 33. p. 633, and to take notice, that the difference of the Day-tyde from the Night-tyde, agrees in both, (of which the reason may be considered;) but, as to the difference of the increase and decrease of the-Water about Bristol from what Mr. Colepress observed at Plymouth, that may much depend upon the position of the places; that of Plymouth being out to the Sea, this near Bristol being on the Severn far within Land.
Whilst the Reader is comparing this Information; with that of the lately cited N°. 33. he will meet there pag. 633. in the last line, with the word perpetual, which he is defied to change: into proportional; which indeed should have been intimated much sooner.
En Extract
TO, pass by many curious Observations touching the Vegatable and Animal Sphere, (which I reserve for another occasion) I shall now entertain you only with some of the Observables, I meet with about Minerals in the kingdom of Mexico whither I travell'd A. 1664, under the Character of a Biscaner, by the recommendation of a friend in the same Ship; that carried thither a New Vice-roy of Mexico, remaining in that Country almost two years in continual studies and researches, especially about Minerals and their Generation, Separation, &c.
And indeed Nature hath so prodigally enriched this Country with all sorts of Minerals, both perfect, imperfect and mixt that the almost overwhelms the Observation of the most diligent and most curious Naturalists, I have dealt with the skilfullest Minemen in those parts, but I found them to know of, and care for little in the matter of Minerals, but Gold and Silver. Some of them ​shew'd me certain Stones, gathered in great abundance in the Mines of Tasco, which they would have to, be Amethysts, by which they said that certain Flemings had got much money.
I was once desired to visit a famous Cave there, some Leagues from Mexico on the North-west side of the City beyond the Lake. This was said to be guarded all over with a kind of leaf-gold, which had deluded many Spaniards with its profiling Colour, they never having been able to reduce it into a body, neither by Quick-silver nor Fusion; though the fame ran, that. the antient Indians knew how to make use of it, and that the great Montezuma had borrowed thence a considerable part of his Treasure. I rid thither one morning, taking with me one Indian only for my guide, with a Tinder-box and a Candle, and some other instruments for my design. I found it situated somewhat high, in a place very convenient for generation of Mettals; but the mouth so barricaded with stones, that both my Indian and I had work enough to clear the passage for my entrance, which being open'd, I went in with my Candle lightned, but could not make the Indian follow me, being afraid of Spirits and Hobgoblins. The light of the Candle soon discover'd to me on all sides, but especially above my head, a glittering Canopy of the said Mineral Leaves; at which I greedily stretching forth my hand to reach some parcels of it, there fell down presently so great a lump of clotted sand on my head and shoulders, that not only it put out my Candle, but my eyes also, And calling out with a loud voice to my Indian, who remain'd at the mouth of the Entry, there rebounded within those hollow Caverns such thnndring and redoubled Eccho's, that I admired it, and the Indian imagining by those Tumultuous voices, that I was wrestling with some infernal Ghosts, soon quitted his station, and thereby left a free passage for some rayes of light to enter, and to serve me for a better Guide: My sight mean while being not a little indangercd by the corrosive acrimony of that Mineral dust, Having got my Candle lighted again, I proceeded in the Cave, and heaped together quantity of the mineral mixt with sand, and scraped also from the superficies of the Earth, a quantity of the same kind of glittering leaves; none of which exceed the bredth of a mans' nail, and with the least handling ​they divide themselves into many lesser spangles, as with a little rubbing they leave one's hand all guilded over like gold.
I knew well enough, that the ordinary Tryals made by the Indians, had proved fruitless upon this Mineral; for it could neither be reduced into a massy form by the violence of fire, nor separated from its heterogeneous substances by the mild tryal of Quick-silver, yet on the Touch-stone it equalized the most refined gold; so that there wanted nothing but to reduce it to at fusible and malleable metallick Form; which soon would be accomplished, if it could be made to take Quick-silver.
Considering with my self, what might be the reasons of its refusing Mercury, and being not ignorant, that some of the choicest Mines of Silver and Gold, are almost of the like nature, till the impediments are remov'd, which are certain mineral viscosities, that sometinres by their oleaginous fatness, and at other times by a fretting acrimony, hinder the ingress of the Mercury; I conceiv'd, the like might happen in this case. Whereupon, to find a cure for this disease, I began first to make experiment on the sand, which had been the matrix of the Mineral; and there I tryed first the ordinary way used in the Indies on such occasions, which was, to observe the colour of the fumes, yielded from the spang1ed sand in a strong reverberating fire; but here could little be observed, by reason of the adust drying of the sand, not able to afford any visible fumes; fit for such a discovery Likewise I proceeded to another way, to boyl it in water, and having powred that off, to observe the Alcali, left after the waters evaporation, I by this means dis'cover'd, that it abounded rather in sulphureous unctuousness, than saline acrimony; or else I think, my eyes in the Cave had run a greater hazard. Finding this, I applyed first the Quick-silver, mingled with the ordinary Magislrals (as they call them) used in that Country, to curb and break the force of these sulphureous impediments. But perceiving these to be of no effect, I encouraged the Quick-silver with the Caput mortuum of Vitriol and Salt-peter, (kept as a secret among the chiefest Mine-men) but with as little signs of the Mercury's operation as before. Then I boyled my mixture over the ​fire, a way found out in Peru in such difficult cases; but all to no purpose; so froward a matter it was, that it could not be brought to receive Mercury, neither-by fair means, nor by foul. Then I devised a way to torment it with a Corrosive of ordinary separating water, impregnated with common salt, and it made a dissolution, like that of Gold; which, thus dissolved, I shew'd to a Mineralist, who had been versed all his life time in the separatory Art of Gold and Silver; and he would not believe but that it was true gold. But having steam'd away the Aqua fortis, I found my hopes turn'd into a dirt something yellow, out of which, with distill'd vineger, enforc'd with its own tartareous Salt, I extracted a Tincture more curious, than useful.
The said Mineralist would not despair yet, but taking a quantity of the golden dull, he cemented it with the powder of vulgar sulphur, stratum super stratum, and this in a moderate fire for three days together, hoping, the Sulphur would consume all the impediments, which kept the Mercury from entring. But (as I told him before-hand) it only serv'd to clog the matter with more sulphureous unctuosity, than it had before.
I brought for a curiosity some of this Mineral from the Indies into Spain, where some of our friends had a view of it; but have not been able hitherto, to do any good upon it. What I learnt by these Tryals, was not only Caution, but several secrets of extracting Mettals by Quick-silver; in which there are so many Cautions and observations, that it would require much writing to rehearse them.
Having reduc'd the Ore into small stones, they calcine it first in a reverberating Oven, yet with a moderate fire, for fear of fusion, and driving away into the air part of the treasure, the volatile parts being by nature not perfectly mixt per minima with the fixt, as they afterwards come to be by industry and Art. And I have heard some of the more intelligent Mineralists say, that they judge their metallick labors and operations, to be many times not so much a reaping of silver ready made, as a kind of artificial compounding, and bettering of that, which nature had left dispers'd and imperfect. This Calcination serves chiefly to free the Mineral from many infirmities, that hinder the operation of the Quick-silver, and it serves also to discover, by the color of the fumes it yields, what corrosive mixture chiefly abounds in it, besides that it renders the one more tractable and plyant under the Mill-stone, which is to reduce it to a smal flower before the application of the Mercury. This is chiefly observed in those Silver-veins, that are of so hard and dry complexion, yet those which are usually more soft, abounding in oleaginous Sulphures, before burning are first ground into powder in such Mills as I have often seen in Glass-houses: and then they receive a gentle calcination, the Mineralist mingling therewith Ingredients sutable to the peccant humour, if l may so speak, of the Ore. As if, (e.g.) the mettal be sulphureous and antimonial, Rust and dross of Iron is found to be an excellent cure of this distemper: if Martial, and abounding in iron, then Sulphur and Antimony reduced to powder, is used as a convenient remedy for that disease. Sulphur hath a particular force, as I have found by experiment, to soften and dissolve Iron. But not only in this operation of Calcining, but also in applying the Quick-silver, there are so many different cases, in which different remedies are to be used, as there are Silver veins of several constitutions; of which elsewhere.
The Ore being ground, calcin'd, and curiously sifted, they divide it in several heaps, and then by lesser Essays, they find out how much silver is contained in every heap, where 'tis very ordinary to find only 6 ounces in 100. Pounds; sometimes 12; but if it yield 18. 'tis esteem'd a very rich vein: yet sometimes there are great Masses found all of pure silver, which is call'd Virgin-mettal.
Having discovered the quantity of silver contain'd in each heap, then proportionably they besprinkle them with quick-silver, and that not all at once, but at several times, stirring the Ore up and down. Then according to the diseases already discovered in the Vein by the fumes in the calcination, or according to any new symptoms, appearing in the operation of the quick-silver, convenient remedies are apply'd, if (e.g.) the Mercury give signes of being tocado (as they call it) i.e. if it appear ​mortified, not in small and clear spherical figures (which is a good prognostick) but in the form of long worms of a wan, pale, dark and leadish colour, then sick Mercury is easily cur'd of the worms (as they speak) by certain Magistrals, so called, that are diversly compounded, but have for their basis or master ingredient calcin'd Copper mingled with Salt. These worms indicate, that the Mineral abounds with Lead and Pewter, which overcharging the stomack (thus they carry on the Metaphor) of Mercury, hinder his appetite to the silver; in which case, those Copper-Magistrals with their vitriolick force consume and destroy this impediment.
The heaps of the Ore being thus mingled with Quick-silver, they are often stirr'd about, the better to incorporate it with the silver. I find, they have none but conjectural signes to know, when the Mercury hath intirely perform'd its office in separating all the silver from those heterogenial substances, the uncertainty whereof occasions often very great losses, especially when they work about Gold: for in passing the right time, the greatest part of the Gold dyes away in a fume, because, to borrow the reason of Chymists, Summa volatilis superat summam fixi; or rather because Nature hath not yet accomplisht the perfect composition and proportionate mixture of the volatile Elements with the fixt: which defect is supply'd by Art in this extraction by Mercury, in whose bosom the parts are combin'd together in small Atoms, and also by gentle fires, succeeded by violent ones, whose activity is assisted by Ingredients, fit for a sutable and easie fusion, and so curbing the volatile parts, that by air exquisite proportion they enter a perpetual amity with the fixt.
When by the colour of the Mercury, coagulated by the silver in clear massy lumps, they conjecture the work done, they wash it by means of three vessels, standing in order one under the other; so that the matter in the first and highest vessel being washed and stirred about with a Molinet, all the dust of the heterogeneous Minerals, that imbody not with the Mercury, is carried away together with the water into the other Vessels, and from thence quite thrown out by the continual current of the water; whereas in the mean while the silver in clotted lumps, called pella's, is by the weight of the Mercury depressed downto the bottom of the said tubbs.
This lavatory work being ended, the Mercury with the silver is taken out of the Vessels, and diligently squeezed in course and strong linnen, and even with stroaks of a beetle, the Quick-silver is separated, as much as may be, from the Silver. And this mass is afterwards reduced in molds of the shape of the Indian Pine-apple, into a pyramidal or conical figure, which they call Pineas de plata, thus fashion'd for the easier placing them round about the ridges of a great earthen vessel, of the form of a blind Alembeck; round about the top of which, a fire being made, all the rest ​of the Mercury forthwith abandons the siiver, and falls to the bottom, from whence it is recover'd, and kept for the like use.
Lastly, The siiver is melted down with the Liga, (as 'tis call'd) which the King of Spain allows, by which He returns to the people in Copper that fifth part, which they allow him of all the silver.
Having described this whole operation, you will perhaps expect, I should somewhat enlarge here upon the generation of Mettals, and my speculations and theory concerning it. But, though this was indeed one of the chief motives of my undertaking this long and tedious Voyage, yet considering the subject to be of such a nature, that it requires very many things to be supposed and premised, and more experience, than I yet dare pretend to, and l dare not at present engulf my self in this Ocean. I shall only say this; first, that my opinion of this matter is something different from the ordinary, though I will not deny, that for the substance, I differ not much from the opinion of the famous Sendivogius, in librode 12. Tractatibus. And then that I think it observable, that there is a very strong offensive smell, ranker then that of Sepulchers, which I have observed in some Mines, the Work-men telling me, that that is one of the chief signes of a rich Mine.
To conclude, I shall presume to give you some of my thoughts concerning the so much discoursed of Transmutation of Mettals; concerning which, I am of opinion, that that Change is erroneousiy apprehended by many, imagining that the whole imperfect mettal is totally transform'd into the more perfect by the substance mixed with it; whereas the mixture added to the melted mettal, joyns it self, (as I conceive) to those parts, which being homogeneal, symbolize together with the nature of the more perfect, whereby the pure metalline parts are separated from the other heterogeneal impure Sulphures, which together, with other causes, did hinder nature in the Mine from concocting that substance into the perfecter Mettal.
That which contributed not a little to make me a Proselyte to the Art of Chymistry, was, among others, a very pretty experiment, a friend shew'd me, more curious than gain-full; It was a continual budding forth of silver in the form of a branch in a glass over an indifferent strong fire of Coals, which sprouts being clipp'd off with Scissers, and a small supply of crude Mercury added to the matter, in a small time there arose another branch of true siiver, which had sucked and converted into metallick sprigs a considerable portion of the Quick-silver. This motion, and the increment of new silver-branches ceased not, as long as the fire continued, and fresh Mercury applyed for the due nutriment of this mineral Vegetation. This ingenious Knack made me reflect on the golden Tree of Virgil. 6. Æneid.
— —Primo avulso non deficit alter Aurem, & simili frondescit virga metallo.
The whole complex of Ingredients is known to consist only of vulgar Aqua fortis (abstracted from two parts of Vitriol, and one of Salt-peter) and Quick-silver, and a small quantity of Silver, far less than you may reap in a small time from those Silver-sprigs, yet gain there is none, there being more expences blown away into smoak by continuance of fire in one month, than can be recover'd from this Silver-harvest in a longer time. And though this seem but a toy, yet 'tis very Philosophical, much informing the understanding, however it enrich not the purse. For here we see crude Mercury manifestly turn'd into Silver, notwithstanding 'tis deny'd by so many.
So far this generous Observer for this time; with the last part of whose relations may be compared Numb. 39. p. 779, 780. 'Tis hop'd, that hereafter more particulars of this Curious Traveller, concerning both the Subject, he hath here begun to discourse of, and others of a Philosophical nature, will be further communicated by him.
An Account
ALlegators are shap'd like Lizzards, being four footed they walk with their Belly at distance from the ground, like Lizzards. Those of a full growth, have Teeth like a Mastiff and a Mouth of 1⁠1/2⁠ foot wide. They are of so strong a scent, that you may smell them at a pretty distance, when they lie on the land. They may be master'd and kill'd by any, dextrous and skill'd in the way of doing it, which is, that a Man be arm'd with a good long Tronchion, and fall upon them side-wayes; for doing it front-wayes, they are too nimble for the assailant, and may, by leaping upon him, (which they can do the length of their whole Body) spoil him: but if he lay his Club on them against their shoulder, and behind their fore-feet, and lame them there, the beast being thereby rendred unable to move, is easily subdued.
2. Tortoises, if their blood be heated, they dye, and if they shall live, their blood must not be hotter, than the Element, they live in.
3. The Chego's, described by Ligon, are not felt to have got into the body, till a week after. They will breed in great numbers, and shut ​themselves up in a bagg, which when you feel, there are certain skilfull Men who with little pain will take them out; having great care to take out the bagg entirely, that none of the brood (which are like Nits) may be left behind, for fear of giving rise to a new generation.
4. The shining Flyes are a kind of Cantharides, looking green in the day time, but glowing and shining in the night even when they are dead; this relator affirming that he hath applyed them dead to a Printed and Written paper in the dark, and read it.
5. The Manchinel-Apple is one of the beautifullest fruits to the Eye, of the agreeablest to the smell, and of the pleasantest to the taste (being thence call'd by many the Eve-Apple). but if eaten, certain death. The wood of it yet green, if rubb'd against the hand, wilt fetch off the skin, or raise blisters; and if any drops of rain, falling from this Tree, light upon one's hand, or other naked part of the Body, it will also have the aforesaid effect.
This other part of Dr. Wallis's second Letter to Mr. Du Laurens, though written and sent to the Publisher at the same time, when the first part was, yet came not then abroad, upon a consideration intimated, in Numb. 38. p. 750. and the same could not find room in these Tracts, till this Month, when 'tis publish't, rather from a desire, further to comply with the said Du Laurens, demanding the reasons of the Animadverter's Censure, than from any propension to disputes. The Publisher can bona fide assure the Author of the Paper, here further animadverted upon, of the reality of what is here affirm'd and profess'd by him, and in particular, that the original of this, what follows, came ​to his hands but a day or two after its Date, which was July 18, 1668. the same, which was mention'd, Numb. 38. p. 750.
The Letter it self is thus continued.
——— ——— Porro (ut minutiora quædam præteream, ne nimius sim, quæ tamen ipsa reprehensionem merentur) inter alia, quibus Æqualitatem ob Moderationis virtutem laudat, inæqualitati interim vitio vertens, quod Exessu & Defectu laborert; hæc occurrunr Sect. 18. Tanta est æqualitatis moderatio, ut eas non solum, quas afficit quantitates, augeat, minuat, multiplicet atq, dividat, nulla facta in ipsis quoad æqualitatem mutatione, sed etiam, ut quantitats ab inæqualitate affectas per similes operationes tractando intactam in illis inæqualitatis notam relinquat.
Id credo vult, (nisi velit rhetoricando fucum facere,) eandem, quæ prius erat vel æqualitatem vel inæqualitatem, manere immutatem; quæcumque facta fuerit utrinque vel æqualium additio auy subductio, vel per æqualia multiplicatio aut divisio, Missis autem Æqualibus, de inæqualibus dispiciamus. Inæqualitatis nota quam vuly, (ni fallor,) est ipsa inæqualium Differentia; &, hanc intactam relinqui, est, eandem manere quæ prius fuerat. (Quippe hoc tum ipsa verba spectare videntur, tum argumentum ejus.) Quod quidem in Additione & Subductione, verum est; Pura, si expositis 10 & 6, addantur utrinque 2, ut fiant 12 & 8; vcl subducantur 2, & fiant 8 & 4; eadem intacta manet inæqualitatis nota, seu Differentia (4.) Non autem in Multiplicatione & Divisione; Quippe si per 2 vel multiplicentur ut fiant 20 & 12; vel dividantur, ut fiant 5 & 3; Differentia fit illic 8, hic 2; neutrobique (qua prius erat) 4. Argumentum ejus est merum sophisma, (quod plus habet in conclusione quam in Præmissis: Hoc (inquit) facile celligitur ex inæqualitatis ad æqualitatem revocandi ratione: ut enim inæquales quantitates ad æqualitatem perveniant, necesse est addi minori, vel a majori detrahi, ipsarum quantitatum Differentiam: seà, per communem æqualium Additionem vel Subductionem, (vides de multiplicatione & Divisione nihil dici,) neque minor quantitas, majoris differentiâ angetur, neque major eadem differentiâ contratur; cum idem utrique inaequalitatis parti adjiciatur vel dematur; (quod in multiplicatione & Divisione non fit:) Hæc sunt præmissa; videamus conclusionem: Ergo (inquit) sive æqualium additione, aut Multiplicatione, sive æqualium detractione vel Divisione, inæquales quantitates augeantur minuanturve, (vides quomodo in conclusione se insinuant Multiplicatio & Divisio, quæ in permissis non erant;) nunquam hac ratione in æqualitatem incident, hoc est, manebit semper in ipsis inæqaulitas; (vides quomodo jam languet illud, manere intactam, in nudum manere; sed mox resumes vires: Verum hoc non est quod erat probandum, inæqualitatem manere aliquam, sed manere intactam; & præmissa, quatenus quicquam probant, hoc probant, propter idem utrique parti adjectum vel demptum: Sed pergit rhetoricando; Sic ergo, inquit, Æqualitas seipsam primo, deinde inæqualitatem, per quælibet ​augmenta vel decrementa, modo æqualia, (quod interim per æqualia multiplicando, vel dividend non obtinetur, ut ipse putaverat,) decuere valet, nullo vel æqualitatis vel inæqualitatis detrimento: (vides, resumptis viribus, languidum illud manere, in cum nullo detrimento manere, jam erigi: quod per rhetoricum variationem phraseos, idem significet, quod prius, intactam relinqui, &c. nulla facta mutatione.) Hæc autem fusius aliquanto deduxi, ut videas, quam, in Demonstrando vacillet hic Mathematicius Rhetoricaster.
Mox autem Sect. 19. quoniam Inæqualium quantitatum una Major, sive Excedens; altera minor, sive Deficiens dicitur; hæec autem Excessus atque Defectus nomina, aberrationes a medio significant, (quod vitiorum est;) hoc est, ab Æquali, (cujus itaque modo laudata Moderatio, virtus erit:) quo tandem in vituperatæ Inæqualitatis favorem se insinuet; mistis his (quæ imperfectam Inæqualitatis naturam respiciunt) nominibus; alia (inquit) bi termini nomina sortiuntur; nam qui Major est, Totum dicitur; qui Minor, Pars: (quasi quidem Partis nomen, non pariter imperfectam naturam insinuet, atque Minoris:) Adeoque (novis definitionibus) Totum definit esse quantitatem majorem ad minorem & homogeneam collatam; Partem vero, minorem esse quantitatem ad majorem & homogeneam comparatam. Sed omnino fallitur hic novus Definitor, qui Totum et 'Pertem, tantundem significare autumat, atque Majus & Minus, Verum quidem est Totum sua Parte majus esse, (& Partem Toto minorem:) Sed non vice versi, omne Minus cujusquc Majoris Partem esse; quod hic insinuat. Lunam ego selluri Minorem existimo; sed non existimo selluris Partem esse. Hoc illum forte decepit, quod videret apud Euclidem, 1 def. 5, Partis nomen, peculiari significatione prout Multiplo opponitur, pro eodem atque Submultiplo, seu aliquota parte, (uti nonc loquimur,) usurpari. Sed aliud significat Pars, prout, peculiari sensu, est correlatum Multipli: (1 def. 5.) aliud, prout, vulgata significatione, opponitur Toti', 9. ax'. 1. (nempem illud quod, cum reliquo, componit Totum) Atq; exhis, inquit, manifestum fit, Totum majus esse sua parte; (quod est Euclidis Axioma Nonum:) Omnino quidem; nempe si Totum & Pars, idem significant atque Majus & Minus. Sed & inde pariter manifestum est, Euclidem fuisse Afinum, Nempe si in illo Axiomate, hoc solum dictum velit, Majus, Majus est Minore. Quod si forte pro Definitione, ferri posset, saltem Axioma esset plane ridiculum.
Deinde Sect. 21. Commensurabilitatis & Incommensurabilitatis sontem aperire satagit, (eadem felicitate, qua multitudinis, & Æqualitatis sive Inæqualitatis originem quæsivit:) Nempe, Quando pars aliquoties sumpta totum suum præcise constituit, Aliquota dicitur: Atqye hæc pars est toti suo commensurabilis. Belle quidem.
Annon vero est hic egregius Definitor, qui Partem commensurabilem, eandem esse Definit, atq; Partem aliquotam? Verum quod si pars ​qua non possit aliquoties sumpta totum suum præcise constituere?) puta si sit ut 4. ad 6.) An propterea non erit commensurabilis? Quid item, si duæ sumantur quantitates quarum altera alterius non sit pars? Num propterea non possunt esse commensurabiles? vel etiam duæ quantitates invicem æquales; (quarum itaq; altera alterius pars esse non possit, cum non sir minor) Annon erunt commensurabiles? Dic tu potius; Duas pluresve quaslibet quantitates (sive altera alterius pars aliquota sit, sive non aliquota, sive ne pars quidem,) commensurabiles esse; si ulla quantitas assumi possit (ut ut ab eis omnibus diversa) quæ singulas possit aliquoties repetita adæquare. Noli autem commensurabilitatem coercere ad eam solam, quæ est inter Partem aliquam aliquotam, Totumq; illud cujus ea pars sit, Quippe hoc non est commensurabilitatis fontem aperire, sed obturare.
Mox autem Sect. 24; Partem Aliquantam (quæ ab Aliquota distinguitur) sic definit. Quando vero Pars, aut quantumlibet exigua hujus partis portio aliquoties sumpta, toti suo æqualis fieri nequit, sed vel ipsum semper excedit, vel ab eo semper deficit, tunc Aliquanta vocatur. Atq; hæc pars, inquit, est Toti suo Incommensurabilis. Si ego cum singulis, quæ passim occurrunt, verbis imperite positis, litem movere vellem; infinitus essem. Hæc autem Definitio ita multis scatet mendis, ut ea prius amovenda sint, quam id dicat, quod ille dictum vellet. 1. Perperam dicitur, Sed vel ipsum semper excedit, vel ab ipso semper deficit; & satis absurde. Impossibile enim estt pars ea, ejuse portio sic sumpta vel semper excedat, vel semper deficiat. Verbi gratia. 1, ad ${\sqrt {5}}$. talis est, qualem ille vellet, sed non vel semper excedit, aliquoties sumpta, (nam 1, semel vel bis sumpta, minor est quam ${\sqrt {5}}$,) vel semper deficit, (nam ter vel pluries sumpta, major erit; est enim ${\sqrt {5}}>$. major quam 2. & minor quam 3.) sed aliquando excedit, aliquando deficit, semper autem vel excedut vel deficit, nunquam æqualis est; atq, hoc ipsum est quod ille dictum vellet. Pro his icaq; verbis, vel semper excedit vel semper deficit, reponendum erit, semper vel excedit vel deficit. 2. Perperam etiam, disjunctive, dicitur, Quando pars, aut hujus partis portio, nequit, &c. Quippe hoc semper contingit, ut vel ipsa Pars, vel saltem hujus aliqua Portio, nequeat aliquoties sumpta toti æqualis fieri: Adeoq; per hanc definitionem, pars omnis dicenda esset tum Aliquanta, tum Incommensurabilis cum toto suo: Verbi gratia, si Pars sit ad Totum suum, ut 4. ad 6. non posset ea toties sumi ut tori sit æqualis; nam semel sumpta, minor erit; bis sumpta, major: Si sit ut 4. ad 8; pars quidem ea bis sumpta, toti æquabitur, sed ejus portio, 3, nequit ita sumi ut æqualis fiat; nam bis sumpta, minor erit; ter sumpta, major quam 8: & quidem semper, vel pairs ipsa, vel ejus aliqua portio, (saltem in quantitate continua) ita se habebit. Itaq; pro eo quod disjunctive ​dicitur, Pars, aut hujus partis portio, nequit; dicendum erat copulative, neque pars ipsa, neque hujus partis portio, potest. 3. Neque hoc sufficit, fieri enim potest, ut tum ipsa pars, tum ipsius aliqua portio, (nedum aliquammultæ portiones,) ita se habeant, nec tamen ea pars sit incommensurabilis. Verbi gratia, si pars sit ad totum, ut 4 ad 5, non poteil ipsa pars sic furni (nam semel sumpta, minor est; bis sumpta, major illo Toto;) sed neque ipsius portio 3 vel 2; (nam portio 3 semel sumpta, minor eest quam 5; bis sumpta, major: Et 2, bis sumpta minor; ter sumpta, major:) potest tamen ejus alia portio, nempe 1, sic sumi; (nam portio 1 quiaquies sumpta, toti 5 æquatur.) Neque hic opem feret, inferta clausula quantumlibet exigua; certum enim est, in parte, quæ vel maxime commensurabilis sit, sumi posse portiones quantumlibet exiguas, quæ non modo totum non metiantur, sed ne commensurabiles sint. Dicendum igitur, neque pars ipsa, neque ulla hujus partis portio, &c. (Quod ita limitandum erit ut mox dicetur,) 4. Superest adhuc aliud mendum, quod majoris est momenti, & imperitiam arguit. Quippe si hæc conster definitio, omnino nulla pars erit cum toto suo incommensurabilis. Nam in ea quæ vel maxime sit incommensurabilis, sumo poterit portio aliqua (nedum innumeræ) quæ Totum mensurant. Verbi gratia, Latus Quadrati ad Diagonium suum, est incommensurabile; vel (ut hic loquitur) est pars ejus incommensurabilis: Sumi tamen porest Lateris aliqua portio, quae Diagonii Dimdio, vel Quadranti æquetur: quæ itaque bis aut quater sumpta, Toti æquabitur. Quod videtur hic Definitor non animadvertisse; cui vel maxime prospiciendum erat. Non enim sufficit ad commensurabilitatem ut partis aliqua Portio mensuret Totum, (quod semper fiet,) sed ut partis aliqua Pars aliquota totum mensuret. Pro Portio itaque reponendum erit Pars aliquota. Suntque hæc quatuor menda, tanti momenti singula, ut eorum nullum non evertat totam definitionem: & quartum omnium maxime; quod ego non Incuriæ, sed Inscitiæ (prout ipse distinguit) imputandum existimo.
Sed esto Definitio, vel maxime ad mentem suam sic reformata; Quand Pars ad Totum suum ita se habeat, ut neque pars ipsa, neque ulla hujus partis pars aliquota, quantumlibet exigua, possit, aliquoties sumpta, Toti suo æqualis fieri, sed semper vel ipsum excedit vel ab eo deficit, tunc Aliquanta vocatur. Atque hæc pars est toti suo Incommensurabilis. Hæc inquam, Definitio sic reformata (quæ apud ipsum erat misere deformis) amitti potest pro Partis Incommensurabilis definitione. Si vero sit etiam definitio Partis Aliquantæ; Dic tu mihi, quæso, (modo Oedipus sis,) Qualem ego partem dicam, numerum 4. numeri 6? Pars Aliquota non est, per Sect. 21, quia non aliquoties sumpta totum præcise constituit, (nam semel sumpta, minor est; bis sumpta, major:) Neque est Aliquanta Pars, per jam definirt; quamquam enim non possit ispa, potest tamen ipsius aliquota pars, ut 2 vel 1, aliquotes sumpta, toti æqualls fieri; (nam 2 ter sumpta, vel 1 sexies, æquantur toti 6.) Cum itaque neque Pars Aloquota sit, nec Aliquanta, (partem autem omnem vel Aliquotam vel Aliquantam dicendam, ​hactenus censuerint homines,) Dic mihi, Quam dicam? Sed neque Pars Commensurabilis est, per Sect. 21, (Quippe commensurabilem non aliam definit ille, quam Aliquotam;) Nec Incommensurabilis, per jam definita. Ecqua igitur? At inrerim hic Definitor; qui Partem Commensurabilem, ideme esse facit cum Aliquota: & partem Aliquantam, idem cum Incommensurabili; male se habitum conqueritur, quod apud eum nonnulla reperiri parum sana dixerim.
Statim vero, Sect. 26, (ne sibi non, ut solet, contradiceret,) Numeros omnes, invicem esse commensurabiles, affirmat; quoniam omnes mensurat Unitas. Quæ quidem vera sunt; sed prius traditis contraria. Quippe ille non alias definiverat commensurabiles quantiates, quam quorum altera sit alterim aliquota pars: multi autem numeri ita se non habent; puta 4 & 6. Neque illas commensurabiles dixerat, quas aliqua tertia commensurat. (quod definivisse oportuit,) Sed quaram altera mensurat reliquam, Sitque ejus aliquota pars. Adeoque ut ut 1 sit ad 4 & ad 6, commensu abilis, (quoniam utrumq; metitur) non tamen erit (perillius tradita) numerus 4 ad 6. commensurabilis quorum neuter metitur reliquum, sitve ipsius aliquota pars. Eandemenim ille, & Partis Aliquotæ, & partis Commensurabilis, definitionem fecerat, Sect. 21; Sicut & (illi contradistinctam) Partem Aliquantam, eandem esse definit atque Incommensurabilem, Sect. 26. Quæ quidem ego inter ipsius Nova Principia, hucusque nondum tradita (necdum recipienda,) annumeranda censeo.
Sed & Sect. 25, Commensurabilitatis & Incommensurabilitatis fontes, porro investigatum it. Omnis, inquit, numerus juxta possibiles quae sunt in eo Sectiones divisus, tandem relinquit unitatem, seu particilam sui minimam. Docuimus enim, inquit, omnem numerum divisibilitatis suæ terminos habere, ultra quos. Sectio non procedit. Fateor hæc dixisse, (docuisse, non dico: Ecquis enim ante nescivit.) Sed & contraria docuit, (nempe, si quis Discere velit,) Ait enim, Sect. 7, Multitudo nunquam ita divisa est, ut pluribus aliis modis secari non possit. Veluti numerus Duodenarius non ita divisus est in partes duodecimas, ut in tertias, quartas, sextas, & adhuc alias quasdam sine nomine divie nequeat. Sed esto; ea jam dicit. Quid postea? Ergo (infert) Ex naturali numerorum structura commensurabilitas exurgit. Commensurabilitas, inquam, Numerorum, ex sua numerorum natura exsurgit, (non minus quam ex sua Linearum natura, Commensurabilitas Linearum;) Hoc est, ex numerorum natura fit, quod illis (quæ & aliis quantitatibus convenit) conveniat commensurabilitas, (sicut & ex omnium omnino rerum natura oritur, quod eas, quas habent, habeant affectiones;) & quidem omnibus, (quoniam omnes mensurat unitas.) Sed Commensurabilitatis simpliciter (quæ & aliis quantitatibus cum numero communis est) non minus ex sua. cujusque quantitatis natura, vel ipsa Quantitatis, quæ est omnibus communis, petenda est ratio. Sed ait, ex naturali magnitudinis constitutione Incommensurabilitas exoritur. Recte quidem. Sed & Commensurabilitas. Sed & pariter ea quæ in Sonis est, & quæ in Ponderibus, vel Durationibus, tum Commensurabilitas tum Incommensurabilitas, ex ipsa Sonorum, Ponderum, Durationum, ​&c. constitutione exoritur. Quippe omnium horum naturæ ita sunt comparatæ, ut Soni, Pondera, Tempora, &c. sint Incommensurabilitatis capacia: sed & Commensurabilitatis non minus. Quod vero ille persuasum iret, Incommensurabilitatis quæ in magnitudinibus est, rationem ex magnitudinum natura petendam; illius autem quæ in eisdem est Commensurabilitatis, non ex ipsa Magnitudinis, sed ex Numerorum natura oriri: omnino est ridiculum. Non minus enim est ex magnitudinis natura, ut possit in partes Commensurabiles dividi, quam ut possit in Incommensurabiles. Quod & eo magis absurdum est, quod ea quae jam est numerorum constitutio, ex humano instituto oritur. Sed et, si ipsi adhibenda fides, ipsa numerorum natura, (adeoq; & horum Commensurabilitas) ex continui divisione oriri putanda erat. Sect. 10. Sed, cæteris missis, videamus quam hic Demonstrator probet, (non quidem Incommensurabilitatem ex magnitudinis natura ortam, sed) omnino ullas esse posse magnitudines Incommensurabiles. (Quamquam enim ego illud non negem, sed aliunde probari posse sciam: Nego tamen eum, esti hoc probandum suscipiat, omnino probasse.) Omnis, inquit, Magnitudo in infinitum divisa no relinquit particulam, quæ propterea quod parva sit secari non possit, quin illa in infinitum secta infinitas efficit particulas, quarum singulæ in infinitas minores sectiles sunt, ut res finem habitura non fit, fi quis minutias omnes conectari velit. (Quippe hoc est, quod aliter dici solet, continuum esse divisibile in semper divisibilia.) Nunquam igitur, inquit, ex infinita magnitudinis divisione, ad aliquam particulam devenietur, quæ minima dici debeat: quæ pro communi omnium mensura sumi queat. Esto, Hallucinatur autem omnino si hinc oriri sentiat Incommensurabilitatem: Non enim ex sectione interminabili, sed ex modo sectionis, probasse oportuit Incommensurabilitatem. Certum enim est sectionem in infinitum continuari posse, sine ulla Incommensurabilitate, (Crassamq; arguit naturæ Incommensurabilitatis ignorationem, hoc nescire.) Verbi gratia. Si exposita recta (aliave magnitudo) intelligatur continua bi-sectione dividi quousq; libet: Certum est, Commensurabiiem illam esse dimidiis fuis, & dimidiorum dimidiis, & sic deinceps in infinitum, utut ad minimum nunquam pervenitur, (quod Tyro quilibet in Mathematicis facile demonstrabit; tantusq: Magister hon debuit ignorare.)
Nam aliquoutæ partis aliquota pars (quantumlibet continuetur sectio) erit & Totius aiquota pars; &. omnes invixem commensurabiles. (Quodq; de Bi-sectione dicitur; de aliis sectionibus in partes commensurabiles, pariter ostendi potest, etiam in infinitum continuatis) Nunquam igitur, hac ratione, ad Incommensurabilitatem pervenietur. Adeoq; argumentum ejus, ab interminabili divisibilitate continui, ad partium Incommensurabilitatem; non modo non probat quod susceperat probandum; sed probat eum Commensurabilitatis & Incommensurabilitatis ​naturam non satis intelligere. Quod ex proxime dicendis confirmabitur.
Nam, Sect. 29. Utrum fortuito oblata Problemata sive Theoremata, in quibus Commensurabilitas vel Incommensurabilitas ex ipsis terminis non statim apparet, Geometrica solum an vero Numerica simul sint, idest, utrum solis magnitudinibus, an & numeris etiam accommadari possint, hac (inquit) ratione dignosces. Si ad illorum constructionem arbitraria tantum requiratur quantitatum Divisio, vel Multiplicatio, indubitabile signum est, ipsa de utraq; quantitatum specie simul exponi: Si vero per appositam in quæstione conditionem determinatæ vel multiplicationes vel divisiones necessariæ sint ad quæsitum efficiendum, tunc generales Commensurabilitatis vel Incommensurabilitatis regulæ docebunt, utrum numerorum essentiæ talibus multiplicationibus ferendis idonæ sint. Quippe nullæ vel Additiones, vel Subductiones, vel etiam Multiplicationes, vel Divisiones, (inter terminos invicem commensurabiles peractæ,) ullam unquam Incommensurabilitatem inducent. Oritur utiq; hæc ex Radicum extractionibus; (quoties nempe faciendæ requirantur, nec absolvi possunt.) Adeoq; si nulla requiritur Radicum extractio, (seu quod huic tantundem est;) sed Additionibus, Subductionibus, Multiplicationibus, & Divisionibus, (inter terminos Commensurabiles peragendis,) quæcumq; demum illæ, vel qualescunq; fuerint, peragenda sint omnia; nullus erit Incommensurabilitatis metus. Admodum igitur imperite, & absurde satis, de Multiplicationibus Divisionibus, hac in re, præcepta tradit. Quod & Indubitabile signum est, (ut cum ipfo loquar) Commensurabilitatis atq; Incommensurabilitatis naturam, huic minime perspectam eesse.
Porro, Sect. 31. Rationem definit esse, Determinatem quandam æqualitatis, inæqualitatisve, speciem. Cujus contrarium verum est. Sunt enim Æqualitas & Inæqualitas, species rationis.
Mox Sect. 32. Cum Rationem in Arithmeticam & Geometricam divideret; De Ratione indiscriminatim pronunciat Rationis terminos, in infinitum augeri posse, manente semper eadam ratione: quasi idem in Arithmetica ratione, (quæ Differentiis, æstimatur, non Quotientibus,) paritur verum effet atq; in Geometrica.
Sed tædet plura commemorare. Hæc interim eorum aliqua sunt (nec tamen omnia) quæ in ipsius Libri primi Capite primo, vetanda censui. Ex quibus possis de reliquis conjecturam facere. Totum vero librum ita recensere atq; ad Examen vocare, mihi neq; vacat, neq; animus est: sed neq; operæ pretium fore autumo. Hæc autem sunt de quibus gloriatur; quæ adhuc, observavit nemo; quæ huc usq; nondum tradita. Tu vero boni consulas; Vale.
​An Account of two Books.
THe Author in the former of these Tracts, having first given an account, how the Air by its Elastick force is inspired, and upon the dilatation of the Chest, caused by the intercostal Muscles, drawn upwards, rushes into the Lungs, which are thereby expanded, being nothing else but a Body made up of very thin little Membranes, in the form of innumerable small bladders, delivers his thoughts of the Use of Respiration, waving those opinions, that would have Respiration serve either to cool the heart, or to make the Bloud pass through the Lungs out of the right ventricle of the heart into the left, or to reduce the thicker venal blood into thinner and finer parts; and affirming, That there is something in the Air, absolutely necessary to life, which is conveyed into the Blood; which, whatever it be, being exhausted, the rest of the Air is made useless, and no more fit for Respiration. Where yet he doth not exclude this Life, That with the expelled Air, the vapors also, steaming out of the Blond, are thrown out together.
And inquiring, what that may be in the Air, so necessary to life, he conjectures, that 'tis the more subtile and nitrous particles, the Air abounds with, that are through the Lungs communicated to the Blond: And this Aereal Niter he makes so necessary to all life, that even the Plants themselves do not grow in that Earth, that is deprived thereof, which yet, being exposed to the Air, and afresh impregnated by that fertilizing salt, becomes fit again to nourish those Plants.
And considering futher, what part this Nitrous Air acts, and what operation it performs in the Animal Life, he is of opinion, that this Niter, mixt with the sulphureous parts of the Blond, causeth a due fermentation, which he will have raised, not only in the Heart alone, but immediately in the Pulmonary vessels, and afterwards in the Arteries no less than in the heart. Examining also the reason, why Death so suddenly ensues upon Respiration suppressed, the Blond being then not yet unfit for motion, he inquires yet after another Use of Respiration, which maketh it so very necessary to Life. And considering with himself, that the Life of Animals conflicts in the Distribution of the Animal spirits, for the supply of which is required the Pulsation of the heart, and the Afflux of the Blond to the Brain, it seems to him, that Respiration is highly necessary to the motion of the heart, forasmuch as the heart is one of the Muscles, the motion of every one of which absolutely requires this Aereal Niter, so that without the same, even the beating of the Heart cannot be performed.
​But here he declareth, that he seeth not, how that Explosion, by which the Muscles are so suddenly inflated and contracted, should proceed from the Arterious Bloud and the Nervous juyce. He esteems rather, that the nitrous particles proceeding from the inspired Air, do by the Afflux of the Arterious bloud everywhere flow between the fibres of the Muscles, and lodge therein, and that the animal spirits, made up of at very volatile salt, and not much differing from the distilled spirit of bloud, highly rectifi'd, do, as often as they are tent from the Nerves for motion, meet with the former nitrous and differing particles; by which mixture of a kind of Volatile Spirit of bloud, and a Salin liquor, united together, is caused that sudden explosion, and consequently the inflation and contraction of the Muscles. To which Ebullition, he saith, may perhaps something also conduce the Bloud, forasmuch as its sulphureous particles, conjoyn'd with the Niter inspired, may render that juyce Nitro-sulphureous, and yet more explosive. And thus he thinks the motion made in the heart, (a musculous substance) to be done no otherwise, than that in other Muscles. Whence he concludeth, that upon the suppressing of Respiration, when that darting Niter, so requisite to all motion,is deficient, the Cardiaque Nerves convey their inHu; in vain, so that the pulhition of the heart cealing, and consequently the afflux of the Blood to the Brain, Death must needs follow; but yet that the Animal may live a while without; Respiration, forasmuch as the Blond contained in the vessels of the Lungs, and impregnated with Air enough, may suffice to maintain for some few moments the motion of the heart.
And thus much of the first Tract, the other treating of the Rickets, examins in the first place, wherein Nutrition consists, and finds, That the Nervous Juyce performs not alone the whole office of that operation, in regard that besides it, the Blond diffused through the Arteries, hath no small share in that work, seeing that the nervous liquor mixt with the blond, causeth a certain effervescence, whereby the matter, fit for nutrition, is precipitated, and that for want of this nervous liquor, the Bloud in this distemper of the Rickets, though it be laudable enouih, yet being destitute of its one ferment, is not able to excite Heat in the parts, nor to execute the office of Nutrition. So that the Rickets, in the opinion of this Author, are a disease, caused by an unequal distribution of the Nervous juyce, from whose either defect or superabundance, some parts defrauded of nourishment, are emaciated others, being surcharged, grow into a disproportionate bigness. Proceeding to assigne the Cause of this inequality in the distribution of the Aliment, he finds it not in the influx of the Brain, but in the obstruction of the spinal Marrow, whence it happens, that, that high way of the passage of the spirits being damm'd up, the parts, to be sustain'd and cherish'd by that nutritious Juyce, must needs languish, and fall into an Atrophy and the highest Consumption.
​Having assign'd this cause, he endeavours from thence to deduce all the Appearances and Symptomes peculiar to this Disease, and suggests that upon their ground it ought to be the main intention of the Physitian, to remove such Qbstructions, and to strengthen the Nerves: subjoining a general method for curing this Infirmity, and specifying the principal remedies, both Internal and External, to be used therein, among which he chiefly recommends the spirits of Sal Armoniack, Harts-horne, Blood, Urine, Soot, as such, that by the high volatility and subtleness of their parts are able to dislodge those Obstructions, which cause this Disease.
IN this Discourse are chiefly perform'd these Two things. First, The Interest of the Patient, in reference to Physick and Physitians, is soberly debated. And here, the Patient: being they, who are most highly injur'd by the unwarrantable practises of those, that are in this Tract accused, the Author represents, that, although many intelligent persons among the People are sufficiently sensible of the Abuses, here manifested, and that it is of absolute necessity, some reformation be made; yet all are not thus perswaded, since we may daily observe, that many, who are lets discerning, being deceiv'd by an Imaginary good, covet unawares their own ruine; and unless they be given to understand, which is the Evil and which the Good, by persons in whom they have reason to confide, they must necessarily run much hazard. The Author therefore hath here endeavour'd to undeceive them, discovering both the many inconveniences, they are lyable to, and the many things, whereof most Aapothecaries are highly guilty, as Carelessness, Unskilfulness, Unfaithfullnes son the one hand, and Intrusion into the Physitians Imployment (the Practise of Physick) on the other: on all which accounts, he thinks, he hath demonstrated they are exceedingly injurious to the Publick.
In order to the Prevention of such intolerable Abuses of the People he makes this Proposal, That Physicians prepare and dispence their own Medicins, and shews at large, that the Advantages of such a Constitution will be many and great: As, that it will much abate the Expence of Physick; and the Medicins themselves will be more sate and effectual, than now they are, Interest obliging Physitians to have their Physick as good, as they can contrive or prepare; and that such a state of Physick of all other cannot but be most definable, wherein No Man having the Interest, can have the Power, nor any having the Power, can have the Interest to prepare Medicins unfaithfully; wherein had men shall ne made good, and the good never be tempted to become dishonest: So that, if the Sick have regard either to profit or safety, they will address themselves to those Persons, who supply them with the best of Remedies, and at cheapest rates.
Secondly, As to Physitians, the Author tells them, that they must necessarily put their Affairs into some such method, as is here commended, if they ​have any concern for their Patients, or intend to improve Pharmacy it self Here he considers, that if Physitians depend onely upon what they read in Books, they shall never promote this Art beyond its present limits; and that, if Physitians in former times had not been knowing in Simples, examin'd their Vertues and Tempers, inquired into their effects, and mix'd them with their own hands, there had been no such Science as Physick; and therefore those things, which gave a being to this noble Faculty, ought to help to make it compleat; towards which as nothing can contribute more than the Improvement of Pharmacy; so neither can anything promote that more, than Physitians taking it into their management. Besides all which, he thinks, it most fit, that they, who exercise themselves in the Practise of Physick, be satisify'd, their Medicins are good; whereby their mind will be free and without any clog: which would add more difficulties and dangers to at thing, by it self hard and dangerous enough.
These and other Considerations, insisted on in this Discourse, will, in the Author's perswasion, induce all Physitians, who have respect to the Good of their Patients, Honour of their Profession, or own Reputation, to put Pharmacy into other hands, and better methods (for which he intimates, that a strong revolution is already taken) than those, wherein now it is; whereby they, who dishonour it (meaning the Apothecaries) will either be reduced to a sense and performance of their Duty, or sufficiently punished.
Besides all this, there are interspersed in this Discourse not a few particulars, both Philosophical and Physical; such as concerne the Improvement of Natural Philosophy by the exercise of Chymistry in the hands of discreet and able Physitians: the Discovery and use of abundance of Generous Remedies, hitherto industriously concealed by their Possessors from the Apothecaries and Common Chymists, upon the consideration, that they would make a preposterous use of them; such as are the Essences of Plant; made by the Union of their Volatile Spirits, Essential Oyles, and fixed Salts, Volatile Salt or Spirit of Tartar, Tincture of Corals, Essences of Pearls and Crabs Eyes, Valentinus's Tincture of Antimony, his Mineral Bezoar, Helmonts Elixir Proprietatis, his Laudanum, the Volatil Spirit of Vitriol, the Anodine Sulphur of Vitriol, its Essential Oyle, the Tincture of Gold, &c. All which the Author assures to have seen himself, and declares himself ready to witness, that they have had extraordinary Effects. And he omits not particularly to insinuate, how much Diet can contribute to the cure or moderation of Distempers; and he affirms boldly, That there is scarce any Chronical Disease, that is cured by the Shop-medicines, which may not be cured with more certainty, ease and pleasure by Drinks, (joyn'd with a regular Dyet) as Wine, Ale, Beer, Cider, &c. impregnated in the time of their Fermentation, with the Vertues of Simples, Animal, Vegetable or Mineral, or their Preparations &c.
In the SAVOY Printed by T.N. for John Martyn, Printer to the Royal Society, and are to be sold at the Bell a little without Temple-Bar, 1668.