IV. The semi-diameter of the Earth’s shadow. V. The Moon’s semi-diameter. VI. The Moon’s Latitude. VII. The Moon’s true hourly motion from the Sun. VIII. The Angle of the Moon’s visible path with the Ecliptic. These Elements are easily found from the following Tables and Precepts, by the common Rules of Arithmetic. _Note_, 60 minutes make a Degree, 30 degrees a Sign, and 12 Signs a Circle. A Sign is marked thus ^s, a Degree thus °, and a Minute thus ʹ. When you exceed 12 Signs, always reject them and set down the remainder. When the number of Signs to be subtracted is greater than the number you subtract from, add 12 Signs to that which you subtract from; and then you will have a remainder to set down. [Sidenote: How the Signs are reckoned.] 354. As we fix arbitrarily upon the beginning of the Sign _Aries_ to reckon from, when we speak of the places of the Sun, Moon, and Nodes; we call _Aries_ 0 Signs, _Taurus_ 1 Sign, _Gemini_ 2 Signs, _Cancer_ 3 Signs, _&c._ So, when the Sun is in the 10th degree of Aries, we say his Place or Longitude is 0 Signs 10 Degrees, because he is only 10 Degrees from the beginning of Aries: if he is in the 5th, 10th, _&c._ Degree of Taurus, we say his Place or Longitude is 1 Sign, 5, 10, _&c._ Degrees: and so on, till he comes quite round again. But in reckoning the Anomalies of the Sun and Moon, and their distance from the Nodes, we only consider the number of Signs and Degrees the Luminaries are gone past their Apogee or Nodes; not how far they have to go to these points, were the distance ever so little. The Sun, Moon, and Apogee move according to the order of Signs, but the Nodes contrary. We shall now give the Precepts and Examples for the above Requisites in their due order. _To calculate the time of New and Full Moon._ [Sidenote: First Element or Requisite.] 355. PRECEPT I. For any proposed year in the 18th Century, take out the mean time of the New Moon in _March_ from Table I., and the mean time of Full Moon from Table III., for the _Old Stile_; or from Tables II and IV for _New Stile_; with the mean Anomalies of the Sun and Moon for these times, and set them by themselves. Then, from Table VI, take out as many Lunations as the proposed Month is after _March_, with the days, hours, and minutes belonging to them; and also the mean Anomalies of the Sun and Moon for these Lunations. II. Add the days, hours, and minutes of these Lunations to the time of New or Full Moon in _March_, and the Anomalies for the Lunations to the Anomalies for _March_: the sums give the hours and minutes of the mean New or Full Moon required, and the mean Anomalies of the Sun and Moon for that time. III. Then, with the number of days enter Table VII, under the given Month, and right against this number, in the left hand column you have the day of New or Full Moon; which set before the hours and minutes above-mentioned.