78 



EQUATION OF PAYMENTS EQUESTRIAN ORDER. 



at any given time. Thus we have the equation 

 of the centre, a quantity to I < added to or subtracted 

 from the anomaly, in order to determine the true 

 position of a heavenly 

 body, thus ; let the curve 

 E C F represent the earth's 

 orbit (which is an ellipse) 

 E F the line of the apsides, 

 and A i lie position of the 

 sun. When the earth is in 

 any position as C, the line A C drawn from the sun to 

 the planet is the radius vector, then will the angle 

 C A F be the anomaly, or the angular distance from 

 the perihelion. Were the earth's motion uniform, the 

 increase or decrease of this angle would be equal in 

 equal times, and the mean anomaly would be the true 

 anomaly ; but the earth's motion is retarded, as it 

 advances from F to C, is slowest at E, and is accele- 

 rated from that point, the aphelion, through the other 

 half of its orbit till it arrives at F, the perihelion. The 

 quantity to be added to the mean angular motion, 

 during one portion of the orbit, or subtracted from 

 it in the other, in order to find the true anomaly, is 

 called the equation of the centre. 



EQUATION OF PAYMENTS, in arithmetic, is 

 the finding the time to pay at once several debts due 

 at different times, and bearing no interest till after 

 the time of payment, so that no loss shall be sustain- 

 ed by either party. The rule commonly given for 

 this purpose is as follows ; Multiply each sum by 

 the time at which it is due ; then divide the sum 

 of the products by the sum of the payments, and the 

 q uotient will be the time required. Thus, for example, 

 A owes B 190, to be paid as follows ; viz. .50 at 

 six months, .60 at seven months, and 80 at ten 

 months : what is the equated time at which the whole 

 ought to be paid, that no loss may arise, either to 

 debtor or creditor ? By the rule, 



60 X 6 = 30C 

 69 X 7 = 420 

 80 X 10 = 800 



190 ) 1520 (8 months, equated time. 



1580 



This rule, however, is founded on a supposition, that 

 the interest of the several debts which are payable 

 before the equated time, from their terms to that 

 time, ought to be equal to the sum of the interest of 

 the debts payable after the equated time, from that 

 time to their terms respectively, which, however, is 

 not correct, as it is the discount that is to be con- 

 sidered, and not the interest, in the latter sums. In 

 most cases, however, that occur in bussiness, the 

 error is so trifling, that the popular rule will probably 

 always be made use of, as being by far the most 

 eligible and expeditious method that we could 

 suggest. 



EQUATION OF TIME, in astronomy, denotes 

 the difference between mean and apparent time, or 

 the reduction of the apparent unequal time, or mo- 

 tion of the sun or a planet, to equable and mean time 

 or motion. If the earth had only a diurnal motion, 

 without an annual, any given meridian would revolve 

 from the sun to the sun again in the same space of 

 time as from any star to the same star again, because 

 the sun would never change his place with respect 

 to the stars. But as the earth advances almost a 

 degree eastward in its orbit in the time that it turns 

 eastward round its axis, whatever star passes over 

 the meridian on any day with the sun, will pass over 

 the same meridian on the next day, when the sun is 

 almost a degree short of it, that is, 3 minutes 56 

 seconds soouer. If the year contained only 360 

 days, as the ecliptic does 360 degrees, the sun's 

 apparent place, so far as his motion is equable, would 

 change a degree every day, and then the sidereal 



days would be 4 minutes shorter than the solar. 

 The mean and apparent solar days are never equal, 

 except when the sun's daily motion in right ascension 

 is 59'' ; which is nearly the case about the 15th of 

 April, the 15th of June, the 1st of September, and 

 24th of December, when the equator is 0', or nearly 

 so ; and it is at its greatest about the 1st of Novem- 

 ber, when it is 16' 14". 



EQUATOR. By the celestial equator is under- 

 stood that imaginary great circle in the heavens, the 

 plane of which is perpendicular to the axis of the 

 earth ; it is everywhere 90 distant from the poles of 

 the earth, which are therefore its poles, and its axis 

 is the axis of the earth. It divides the celestial 

 sphere into the northern and southern hemispheres. 

 During his apparent yearly course the sun is twice 

 in the equator, at the beginning of spring and of 

 autumn. (See Equinox, and Day). Then the day 

 and night are equal,' whence the name of equator. 

 The situation of the stars, with respect to the 

 equator, is determined by their declension and right 

 ascension (q. v.). The equator, or equinoctial, 

 called by mariners simply the line, is that great 

 circle of our globe, every point of which is 90 de- 

 grees from the poles, which are also its poles, and 

 its axis is the axis of the earth. It is in the plane 

 of the celestial equator. All places which are on 

 it, have invariably equal days and nights. (See 

 Day.) Our earth is divided by it into the northern 

 and southern hemispheres. The diurnal revolution 

 of the earth is in the direction of it. It crosses the 

 centre of Africa, the islands of Sumatra, Borneo, 

 Celebes, &c., in Asia, then traverses the Pacific 

 ocean, and crosses South America, in Columbia, 

 thence proceeds through the Atlantic back to Africa. 

 To cross the line, in navigation, is to pass over the 

 equator. The equatorial regions are subject to long 

 calms, alternating with frightful hurricanes. As 

 equal or mean time is estimated by the passage of 

 arcs of the equator over the meridian, it frequently 

 becomes necessary to convert parts of the equator 

 into time, and the converse, which is performed by 

 the following analogy, viz. as 15 : cne hour : : any 

 arc of the equator : the time it has been in passing. 

 Or, conversely, one hour : 15 : : any given time : 

 to the arc of the equator.' From this circle is reckoned 

 the latitude of places, both north and south, in degrees 

 of the meridian. See Latitude and Longitude. 



EQUATORIAL, UNIVERSAL, or PORTABLE 

 OBSERVATORY is an instrument intended to 

 answer a number of useful purposes in practical 

 astronomy, independent of any particular observatory. 

 It may be employed in any steady room or place, for 

 performing many useful problems. 



EQUER Y, an officer of state, under the master of 

 the horse. There are five equeries, who ride abroad 

 with his majesty ; for which purpose, they give their 

 attendance monthly, one at a time, and are allowed 

 a table. 



EQUESTRIAN ORDER, in Roman antiquities 

 (ordo equestris.) The equites did not at first form a 

 distinct order, but were merely selected, one hundred 

 from each tribe, as the body-guard of the king and 

 were called celeres, because they were mounted. 

 Their number was afterwards increased ; but when 

 the equites became a distinct order, or class, is not 

 known with certainty ; it was probably soon after the 

 expulsion of the kings. None but those who were 

 named by the censor belonged to the order of equites; 

 they were taken from plebeian or patrician families, 

 and those'who were of illustrious descent were called 

 illustres, speciosi, &c. Their number was not fixed. 

 In the latter periods of the republic, property of the 

 value of 400 sestertia was required for admission 

 into it. The privileges of a knight or eques were, I. 



