132 



THE POPULAR EDUCATOR 



(5tn (tin, cine, rin), 



grott, 



tret, 



vter, 



fiinf, 



\ttyt, 



fteben, 



a$t, 



ncun, 



je^n, 



elf, 



fiinfjefyn, 

 fec^efjn, 

 fiebenje^n or fte&jetyn, 



jnxinjig, 



ein unb j'ajanjig, 



jwct unb jwanjig, K., 



1. 



2. 



3. 



4. 



5. 



6. 



7. 



8. 



9. 

 10. 

 11. 

 12. 

 13. 

 14. 

 15. 

 16. 

 17. 

 18. 

 19. 

 20. 

 21. 

 22, etc. 



treifug, 



tin unb brdjjtcj, K., 



sieqicj, 



fiinfitg, 



fccf^jig (not fecf^tg), 



fictcnjiij or ficbjuj, 



acfjtjig, 



neunjig, 



Ijuntcvt, 



Ijuntcrt unb ein, 



^untcrt unb yon, 



tyuntcrt unb tret, ic., 



jmct fyuntert, 



tret fyunbert, 



taufcnb, 



jttict taufenb, 



tret taufeitb, 



jefyn taufcnb, 



l;untert tiufenb, 



30. 



31, etc. 

 40. 

 50. 

 60. 

 70. 

 80. 

 90. 

 100. 

 101. 

 102. 



103, etc. 

 200. 

 300. 

 1,000. 

 2,000. 

 3,000. 

 10,000. 

 100,000. 



eine million, 1,000,000. 

 jiuci fflitUioiten, 2,000,000. 



(1.) Observe that the cardinals are, for the most part, inde- 

 clinable. 



(2.) in (one), however, is declined throughout like the inde- 

 finite article. It is, in fact, the samo word with a different use, 

 and is distinguished from it in speaking and writing only by a 

 stronger emphasis, and by being usually written with a capital 

 initial. This is the form which it has when immediately before 

 a noun, or before an adjective qualifying a noun. Thus : 



Masculine. 



f (Sin QJJann, one man. 



\ (Sin gttter DJann, one good man. 



( (StncS 3Ranne3, of one man. 



^ S'tncS guten 2)ianne3, of one good man. 



(3.) In other situations, ein follows the ordinary rules of 

 declension ; thus in the 



Nom. 

 Gen. 



Nom. (finer, 

 Gen. (SincS, 



Nom. Der etne, 

 Gea. >c3 ctnett, 



(a.) OLD FORM. 



etne, cineS, one. 



ctner, cine3, of one, etc. 



(6.) NEW FORM. 

 tie cine, ta3 cine, the one. 



tcr einen, 



einen, of the one, etc. 



(C.) MIXED FORM. 



Nom. OTlcm cuter, metne eine, mcin einc?, my one. 



Gen. SDicincS etncn, meiner einen, meineS einen, of my one, etc. 



In relation to the numeral ein, note, further, these three 

 things : 



(1.) That in merely counting, it has the termination of the 

 neuter, with e, however, omitted; as: StnS, jtuet, bret, one, 

 two, three, etc. 



(2.) That ein maybe used in the plural when the design is 

 to distinguish classes of individuals ; as : TUe (Sinen, the ones ; 

 ter (Stiten, of the ones, etc. ; just as, in English, we say, the ones, 

 the others. 



(3.) That ein, unlike the English one, cannot be employed so 

 as to fill the place of a noun ; thua, we cannot say in German, a 

 new one, a good one, etc. In such cases, the adjective stands 

 alone. 



(4.) 3roet (two) and brct (three), when the cases are not suffi- 

 ciently pointed out by other words in the context, are declined 

 thus : 



Nom. 3ftet, two. 

 Gen. Sroetcr, of two. 

 Dat. 3rc>cten, to or for two. 

 Ace. 3n)et, two. 



3)ret, three. 

 5)rcter, of three. 

 JDreten, to or for three. 

 2?rci, three. 



In place of 3rcet, Betbe (both), which is declined like an adjec- 

 tive in the plural, is often employed; as : IMtc 2Iugen, both eyes ; 

 bie beiten JBriiber, both the brothers. The neuter bcibeg never 

 refers to persons. (Sect. XXXII. 1.) 



(5.) All the rest of the cardinals, when employed substan- 



tively, take en in the dative, except such as already end in thesfl 

 letters ; as : 3d; fyabe c3 Siinfen gefagt, I have told it to five (per- 

 sons). 



(6.) unbert and Xaufenb are often employed as collective 

 (neuter) nouns, and regularly inflected ; as, singular nom. ba* 

 ijuntert, the hundred, gen. te8 -untcrt3, of the hundred, etc. ; plural 

 nom. tie Sunterte, the hundreds, etc. 2JZHlion, million, is, in like 

 manner, made a noun (feminine), and is in the singular always 

 preceded by the article ; as : Sine SDiidtun, a million. 



(7.) In speaking of the cardinals merely as figures or charac- 

 ters, they are all regarded as being in the feminine gender ; 

 aa : >te in?, the one ; tie 3met, the two ; tie iDrei, the three ; 

 where, in each case, the word 3al;t (number) is supposed to be 

 understood ; thus, tie (3<il?0 brei, the (number) three. 



LESSONS IN ASTRONOMY. XI. 



THE MOON : ITS MOTIONS. 



THE earth differs from the planets we have hitherto con- 

 sidered in this important particular, that in its journey round 

 the sun it is accompanied by a secondary planet or satellite 

 the moon. This may almost be considered as a part of the 

 earth, for in its revolution round the sun it is not the earth's 

 centre that travels along the orbit, but the centre of gravity of 

 the earth and moon taken together. 



Some of the superior planets are, as we shall shortly learn, 

 accompanied by several of these companions ; but the inferior 

 ones are all destitute of them. As the moon is our nearest 

 neighbour in space, and exerts a greater influence on us than any 

 other of the heavenly bodies, with the exception of the sun, it 

 has naturally at all times demanded a large share of attention. 

 Its great apparent size, and the phases it presents, increase 

 this interest. 



To the eye, the moon appears very nearly as large as the 

 sun. This, however, entirely results from its greater proximity 

 to us ; in reality, it is the smallest of all the heavenly bodies 

 which can be discerned by the unaided eye. Its distance from us 

 is easily learnt from its horizontal parallax, which is sufficiently 

 great to be accurately measured. This varies in different 

 parts of the orbit ; but its mean value is about 57 seconds, 

 and thus the mean distance is found to be 238,833 miles. 

 Knowing this distance, and also the angle which the moon's 

 disc subtends to an observer, we easily ascertain its real 

 diameter to be 2,153 miles. 



This body, then, revolves in its orbit round the earth, and 

 completes its circuit, reckoning from the time it passes any star 

 till its return to the same star, in 27 days, 7 hours, 43 minutes, 

 11'5 seconds, which period is known as a sidereal revolution. The 

 more usual plan of reckoning its period, is to count from the 

 time of one full moon to the next. This is, as has been stated, 

 greater ; the reason of the difference being, that the moon is 

 full when it is in the part of the heavens diametrically opposite 

 to the sun. Now, if the earth remained stationary, this would 

 always occur in the same part of the sky ; but as the earth is 

 moving in its orbit round the sun, carrying the moon with it, 

 by the time, therefore, that the moon has completed its circuit, 

 the earth has travelled round nearly one-thirteenth of its orbit, 

 and the moon must travel so much the farther before it again 

 comes opposite to the sun. The average length of this period, 

 which is called a sy nodical revolution, is 29 days, 12 hours.. 

 44 minutes, 3 seconds : this interval is, therefore, termed a. 

 lunar month, and during it the moon passes in succession 

 through all its phases. 



As these changes in its appearance must have often excited 

 the attention of all observers, we must carefully explain tho 

 reason of them. The moon, it must be remembered, unlike the 

 sun, is a non-luminous body, that is, it does not -shine by its own 

 light, but only by that of the sun reflected from its surface. 

 When the moon is between the sun and the earth, it is clear that 

 the side towards the earth will be in darkness, and then it will be 

 called new moon. Fig. 22 will render this more clear. In it the 

 sun must be supposed to be situated considerably to the right 

 of the engraving, consequently the illuminated hemisphere of 

 the moon will always face that way. E represents the earth, 

 and the moon is represented in eight different parts of its orbit, 

 the outer row of discs showing the appearance the moon presents 

 to us when in each of these positions. When at A, as already 



