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follows. The distances ed, ac, cb, are each equal to one-fourth
EXAMPLES OF THE SEVERAL CASES. of an inch, and da to three-sixteenths of an inch.
Nominative. By following the above instructions, the learner will be enabled
The camel is strong. to rule his paper in sets of five horizontal and parallel lines, five Das Kameel ist stark.
The dog is faithful and watchful. lines being required in each set, in this case, to determine the Der Hund ist treu und wachsam.
The horse is beautiful and useful. height of the letters and their relative proportions one to another, Das Pferd ist schön und nüglich. *To rule the diagonal lines (No.5), set off e x along the topinost line
Nominative and Genitive. ee, equal to thirteen-sixteenths of an inch, and draw a straight Das Wasser des Meeres ist salzig. The water of the sea is salt. line through the points br. This will serve as your guide Der Baum des Waltes ist groß. The tree of the forest is large. line for regulating the remainder of the sloping lines, and all Des Kindes Ball ist weich.
The child's ball is soft. that remains to complete them is to set off spaces along the lines ee, b b, equal to ry or bz, and rule straight lines passing
Whether in cases of this kind, where the genitive is used to through every succeeding pair of points, commencing from the denote possession, we should say, Der Wall tes Kindes (the ball of first pair z b, through which the guide line for regulating the the child), or, Des Kindes Bal (the child's ball), is a point regulated inclined lines was drawn.
by no certain rule. The former mode is the more common in
Nominative and Dative.
Der Brief ist von dem Vater. The letter is from the father. SECTION V.-THE NOUN. OLD DECLENSION.
Der Bauer ist in dem Felte. The peasant is in the field. THERE are in German four cases, namely: the Nominativ, Er schidt es dem Freunde.
He sends it to the friend. answering to the English nominative; the Genitiv, answering to
Nominative and Accusative. the English possessive; the Dativ, which has no corresponding Der Hund beißt den Dieb. case in English; and the Accusativ, which answers to the English Der Schmied hämmert tas Gisen.
The dog bites the thief.
The smith hammers the iron. objectire.
The child loves and praises the of the four cases, the dative, withont a preposition, generally Das sind liebt und lobt ten Vater.
father. corresponds to our objective governed by to or for, as :35 gebe tem Manne tas Olas. I give (to) the man the glass.
Nominative, Dative, Genitive, and Accusative. Er matt tom Manne einen Hut. He makes (for) the man a hat. Der Vater des Kindes giebt dem The father of the child gives Often, however, the dative in German is construed with a
Bruder ten Vogel.
(to) the brother the bird. preposition, where, as above, the objective is of course employed Der Herrscher des Staates schict dem The ruler of the state sends (to) in English, as :
Krieger tas Shwert.
the warrior the sword. Das Kind ist in tem Hause, The child is in the house.
VOCABULARY. Da hunt ist unter dem Baumc. The dog is under the tree. An, at.
Soun, m. son. Der Jäger geht nach dem Walbe. The hunter goes to the forest.
Korb, m, basket. Stall, m, stable. Der Mann ist auf tem Schiffe. The man is on the ship.
Ball, m. ball.
Loben, to praise. Stuhl, m. chair. De Kop ist an dem Tische. The cook is at the table. Vruter, m. brother. Pfert, n. horse. • Tischler, m. joiner.
Durstig, thirsty. Sad, m. bag.
Unter, under. DECLENSION OF THE DEFINITE ARTICLE MASCULINE AND
Freund, m. friend. Schläfrig, sleepy. Wo ? where? NEUTER IN THE SINGULAR.
Hund, m. dog. Süler, m. scholar. Zimmer, n. room.
Zimmermann, m, car-
penter. Genitio. Dee, of tho; dell, of the ; Datis. Dom, to or for the; bem, to or for the;
RÉSUMÉ OF EXAMPLES.
The child loves the brother. German nouns have two forms of declension, called the oia Das Kind liebt ten Vruter. and the New. In the old declension, the genitive, like the cor
Der Schrer lobt res Schülers Fleiß. The teacher praises the scholar's responding case in English, is formed by affixing $ to the
industry. nominative, as :
Der Schnee liegt auf tem Verge. The snow lies on the mountain. Nom. Der Bater, the father. Gen. Des Waters, the father's.
Das Mitchen hat des Vaters Hut. The girl has the father's hat.
Der Sohn des Baders hat Brod in The son of the baker has bread Noans ending in 8, 5, 3, or two consonants, generally add cs in tem Sorbe; er giebt es tem Bet. in the basket; he gives it to the genitive, thus, like our words which end with the sound of tler.
the beggar. $, 2, 7, soft c or s, forming an additional syllable.
EXERCISE 6. Nom. Das Rob, the horse. Gen. Des Rosses, the horse's.
1. Sind Sie der Freund des Bäders? 2. Nein, ich bin der Freund tes EULES FOR FORMING THE CASES OF NOUNS ACCORDING TO Tischlers. 3. Was hat der Freund tes Fleischers? 4. Er hat den Hund THE OLD DECLENSION.
und das Pferd tes Bauers. 5. Wo ist das Mehl ? 6. Es ist in dem RULE I. The genitive adds & or cs to the nominative.
Sade des Müllers. 7. Wo ist tad Kort 8. Es ist in dem Korbe tes ROLE II. The dative drops the 8 of the genitive (§ 13. Note). Vauers. 9. Wer licbt den Lehrer ? 10. Der Schüler liebt den Lehrer. RULE III. The accusative is like the nominative.
11. Siis Sie schläfrig? 12. Nein, ich bin durstig. 13. Wo ist ter DECLENSION OF NOUNS ADDING & IN THE GENITIVE.
Vall tes Bruters? 14. Das Kind hat den Ball des Bruders in dem Hute
des Vaters. 15. Wo ist das Pferd tes Lehrers ? 16. Es ist in dem Masculine.
Neuter. N. Der Bater, the father ;
Stalle. 17. lobt der Tischler ten Zimmermann? 18. Nein, der Sohn das Märchen, the girl ;
des Zimmermanns lobt den Sohn des Lehrer8. 19. Wo ist der Stuhl tes 6. Der Baters, the father's ; tes Märchens, the girl's ;
Tischlers? 20. Gr (Sect. XVIII. 3) ist in dem Zimmer tes Lehrers. D. Dem Bater, to, for the father; dem Märchen, to, for the girl ;
21. Liebt ter Zimmermann ten Lehrer? 22. Ja, er liebt und lobt ten A. Den Water, the father ; tad Mädchen, the girl.
Lebrer. 23. Der Mann ist an dem Tische, bas Buch ist auf dem Tisde, DECLENSION OF NOUNS ADDING ($ IN THE GENITIVE. und der Hund ist unter dem Tische. Masculine.
Neuter. N. Der Mann, the man;
SECTION VI.-DEMONSTRATIVE PRONOUNS. das Kint, the child. G. DEMannes, tho man's; 108 Rintes, the child's;
„Dieser“ is declined, in the masculine, precisely like the defiD. Dem Manne, to, for the man; tem Kinte, to, for the child; nite article ; while in the neuter, as will be seen in the follow1. Den Mann, the man; Das Kind, the child.
ing declension, all its endings, except the dative, are alike CONJUGATION OF THE PRESENT SINGULAR OF Soin AND Loben.
[$ 62. (2)]. * Ich bin, I am; ich lobe, I praise ;
By the references in Roman numerals, thus (Sect. XVIII. 3), as Sie fint, you arc ;
Sie loben, you praise ; above, the learner is directed to Sections in Part I. of theso Lessons. Gr ift, he is ;
er lobt, he praises.
References thus [$ 62 (2)] refer to the Sections in Part II.
DECLENSION OF Dieser : MASCULINE AND NEUTER SINGULAR Er sagt ihm nichts.
He says nothing to him.
W.8 geben Sie dem Capitain ? What do you give the captain?
Who praises the servant ?
Whom does the servant praise? O. (1-c0) ties-c6, of this ; (0-6) ties-es, of this;
EXERCISE 8. D. (t-cm) ticf-em, to, for this; (6-cm) bicí-em, to, for this ;
1. Wo ist ter Bruter des Steuermanns ? 2. Er ist bei bem Caritain A. (t-en) ties-en, this; (t-as) tiej-es, this.
in tem Schiste. 3. Ist der Sohn tes Gtelmanns auch bei ihm? 4. Nein,
cr ist in Deutschland. 5. Wo ist ter Vater ? 6. Er ist bei dem Capitain DECLENSION OF TYE INTEPROGATIVE 200X AND THE PERSONAL
in tem Zollhause, 7. Pobt ter Capitain den Sohn tes Otelmanns? 8. Ja, PRONOUN er AND ($ IN THE SINGULAR.
und er lobt auch den Vater. 9. Ciebt der Gtelmann ten Capitain ? Masculine.
10. Ja, er liebt und lobt ihn sehr. 11. Iit dieser Mann ter Sohn tes N. Wer? who?
Garitains ? 12. Nein, er ist der Sohn tes Steuermanns. 13. 3it rieser O. wenien ? whose ? seiner, of him ; sciner, of it;
Matrose reich? 14. Noin, er ist arm und fröhlich 15. Wie alt ist ricer D. wem? to, for whom? ism, to, or for him ? ilm, to, or for it; Mann? 16. Er ist nicht sehr alt. 17. Ist er Frant? 18. Nein, er ist A. wen? whom? ibu, him;
hungrig. 19. Was gibt ticsco Mädchen dem Kinde? 20. És ($ 134. 2) VOCABULARY.
gibt ibant nur Zuder. 21. Was geben Sie tem Knechte? 22. Jó gebe Arfel, m. apple. Golb, n. gold. Sattler, m. saddler.
ihm Gelt. 23. Was gibt der Knecht tem Pferte? 24. Er gibt ihm Heu. Bür'germeister, m., bur-Maus, n. houso. Sdneiter, m. tailor.
25. liebt dieses Sint ten Lehrer ? 26. Ja, und ter lehrer lebt das Kind. gomaster, mayor. Hut'madyer
, m. hatter. Scub'maciyer, m. shoe - 27. Ist ter Jäger noch in tem Walte? 28. Ja, und der Sohn des Dieser, ticses, this. Surfer, n. copper.
Grelmauns ist bei ihm. 29. Der Jäger geht nach dem Walde zu dem Für, for ($ 113). Cercr, n. leather. Silber, n, silver.
Vater, und ich gehe zu tein Bruter.
THE UNIT OF FORCE.-FORCES APPLIED TO A POINT.
HAVING in our first lesson explained the meaning of the word Dieses Jünglinge Hut ist neu. Dieses This youth's hat is new. This
"force," and shown how a force is applied and measured, we shall Matchens Band ist schön.
girl's ribbon is beautiful.
next consider the simplest kind of mechanical problem, that of Geben Sie diesem Bettler und diesem Do you give this beggar and several applied to a single point. Before I proceed, however, it Kinte Geld?
this child money ?
is advisable to fix clearly your notions of the "unit of force." Lieben Sie diesen Irländer? Loben Do you love this Irishman ? I have already laid down the rule, that a force may be measured Sie dieses Mädchen ?
Do you praise this girl ?
i by the number of feet it would cause the unit ivory ball, equal Weisen Federmesser hat dieses Kind? Whose penknife has this child ? in weight to a cubic inch of pure water, to move over in one Des Schrers.
second, when applied to it suddenly by a blow. If the ball
over seven feet, the number 7 should be written for EXERCISE 7.
the force; if over a furlong, the number is 660, the feet in a 1. Wer hat das Papier dieses Matchens ? 2. Dieses Kind hat ex. furlong. But suppose it moves over exactly one foot, then it is 3. Wessen Buch hat dieser Schüler? 4. Er hat das Buch tes Lehrere. clear that the numeral 1 should be written; and that particular 5. Bon wem haben Sie dieses Lerer ? 6. Ich habe es von tem Schuß. foroe is the "one" of forces. And the conclusion to which inacher. 7. Für wen ist dieser Apfel ? 8. Er (Sect. XVIII. 3) ist für we thus are led is that, das Kind des Sattlers. 9. Wessen Rock hat ter Sohn des Schneiters?! THE UNIT OF FORCE is the force which would, if applied 10. Er hat den Rod dieses Freundes. 11. Von wem hat der Sohn dieses instantaneously to the unit of mass, make it move over one foot Hutmachers Geld ? 12. Er hat Geld von dem Bater. 13. Wo ist ter in one second. Wagen des Bauers? 14. Der Freund des Lehrers hat ihn. 15. Wessen! But you can clearly see that the force which could produce Haus und Garten hat ter Lehrer ? 16. Er hat das Haus und ten Garten no greater velocity than this in the ball—which, instead of being tes Bürgermeisters. 17. Von wem haben Sie diesen Aut? 18. Ich ivory, we may take to be a ball of frozen water, a cubic inch habe ihn (Sect. XVIII. 3) vor dem Hutmacher. 19. für wen ist er in volume-cannot be a very strong force. In fact, it is equal 20. Gr ist für den Sohn des Schneiters. 21. Haben Sie Gold, Silber, to a little less than eight grains of weight, that is, this unit of oter Kupfer für den Lehrer ? 22. Ich habe Silber für ihn. 23. Wen force could be balanced by that with which an eight-grain liebt das Kind ? 24. Es liebt den Bruter des Lehrere.
weight pulls downwards. How this is ascertained I cannot
here explain to you, as you would require some little knowledge SECTION VII.
of dynamics to understand the proof. For the present, thereCONJUGATION OF THE PRESENT SINGULAR, gehen and geben. fore, you must take my statement on credit.
But this unit is evidently too small for practical purposes. Ich gehe, I go. Ich gebe, I give.
The strains in the mechanical powers, the lever, the wheel and Sie gehen, yon go. Sie geben, you give.
axle, the pulley, etc., and in roofs and bridges, cannot be Er geht, he goes.
Gr gibt (Sect. XIX. 1), ho gives. 'calculated in grains, on account of the large numbers we should The learner should mark the irregularity in the conjugation have to operate on. A larger unit is therefore necessary, and of geben.
the pound weight exactly answers the purpose. We can calVOCABULARY.
culate and measure forces in pounds; or, if the figures in Ait, old. Seu, n. hay. Schiff, n. ship.
that case be too large, we can calculate them in hundred. Hungrig, hungry. Schr (with verb), weights, or even in tons. All that is necessary is to keep clearly Bei, with. 3åger, hunter,
in mind what your unit is in your calculation, and to know how Caritain', m. captain. ranger.
Sehr (with adj. or to pass from one unit to another. If, in the same calculation, Deutschland, R. Ger- Knecht, m, servant. adv.), very,
you were to use different units in different places-a pound for many. Krant, sick.
Steu'ermann, m. mate. instance, in one, and a hundred-weight in another-without Grelmann, m. noble Matroʻsc, m. sailor. Walt, m. forest. reducing the one to the other, the result could be nothing but Nach, to ($ 112. 8, 9). Wie, how, as.
confusion and error. Fröhlich, merry. Nicht, not.
Zolthaus, n. custom. But how are you to pass from one unit to another ? This is a Geben, to give. Nah, still, yet.
nice point in practice, as we shall see in due time; but this much Geben, to go. Reid, rich. Zu, to (S 112. 13).
l is clear, that, if your unit be a hundred-weight, you should RÉSUMÉ Op EXAMPLES.
multiply all the numbers which represent your forces by 112
(the number of pounds in a hundred-weight), and then these Der Baum ist sehr groß. The tree is very large.
forces will be expressed in pounds. If they are already esEr liebt ihn sebr.
He loves him very much. pressed in pounds, then divide by 112, and you will have them + Fieser Mann tem lehrer? What says this man to the in hundreds and fractions of a hundred-weight. And so, from teacher?
hundred-weights you can pass to tons by dividing by 20, and
reverzo the operation by multiplying by that number. Thus, forces applied to the rope along its length is the difference we see that “ton," "hundred-weight,” and “pound," are only between tho united powers of tho fifteen and of the eleven, So many different expressions for the game unit--namely, the whatevor be tho particular strength of each man, and its pound-either singly or collectively, and that, therefore, for direction is that in which the fifteen pull. practical purposes, we may say that a pound weight is the “unit But supposo now that two forces only are employed, and that of force."
they are cual and in opposite directions; what will be tho But we cannot leave this subject without determining the result? They will balance, or be in equilibrium. Now it is somc. relation between this unit and the very small one of which I times said that the body to which two such forces are applied first made mention. I have asked you to take it on credit that at one of its points is in the same condition as if no force had the latter is nearly eight grains. The more correct value been applied to it. This is not true, strictly. It is in the same involves decimals, and is 7.85 grains nearly, that is, seven condition so far as equilibrium is concerned, but not otherwise. grains and eighty-five parts out of a hundred of one grain. It is not in the same condition as to pressure or strain. The Hence, since there are 7,000 grains in an avoirdupois pound, if rope, which at one moment is lying stretched on the ground, i3 ve divide this number by 785, wo shall have the number of not in the same condition it was in a few minntes before, when these small units (which henceforth we shall call the dynamical two strong men were pulling at opposite ends of it with balanced init), to which one pound weight is equal. The division gives strength. In the latter case it is strained along its whole 892 nearly for the quotient; and thus we learn how we may length-every thread on the stretch, ready to snap. Its condi. pass from dynamical units to pounds, or from pounds to these tion is very different on the two occasions—different in every units. The result may be summed up in the following table :- circumstance, except that of there being no motion. So, also, 7.85 Grains make nearly one Dynamical Unit.
if two equal and opposite pressures are applied to a round ball, 892 Dynamical Units make nearly one Pound.
it will be an equilibrium, but the condition of its substance will 112 Pounds make one Hundred-weight.
be changed. Its particles will be pressed towards one another 20 Hundreds make one Ton.
inwards; and, if it be made of soft or elastic material, its form Forces applied to a Point.-When a single force is applied will be altered by the flattening effect of the opposing forces. to any point of a body, if the latter be free, motion will And this is true, whatever be the magnitude of the ball. It ensue, and the question belongs to Dynamics. If it be not free, may be as small as we please, even so small as an atom, or bat fastened in any way to fixed objects, the force will be what is called a “material particle," and yet there will be this communicated through its substance to the points of support or internal compression or straining. Thus we see that even the connection, which will resist, and by resisting cause the body to “matorial particle," acted on by two equal and opposite forces, sustain strain. For example, suppose a beam of wood is fixed cannot be said to be in the same condition before and after their at one point, round which, as on a pivot, it can turn in any application. direction, and that a force is applied to it at some other point. The case of equal and opposite forces presonts some other It is clear that this force will pall the beam round towards points of interest, which may well occupy your attention in this itself so far as it can go, that is, until the line of direction of lesson. Suppose, for example, two men pull against each other the force passes through the fixed point. Then this point will with equal strength at the opposite ends of a rope. What will resist, and equilibrium will be produced. The case thus becomes be the strain on the rope? What will be its amount, considering one of two forces-namely, that applied and the resistance pro- that both are pulling? Most persons at first incline to say that daced ; and we see thus that a single force can never in Statics it is strained by the united strength of both, or by double the be the subject of study, without involving the consideration of strength of either man. Such is not the case; the strain is other forces which it calls into existence. A statical problem only equal to the strength of one of tho men. What is the must be concerned about at least two forces.
reason of this ? A moment's reflection makes it evident. If two forces be applied to a point in the same direction, we Suppose one man only to pull; the rope follows him, and there assume in Mechanics, as a self-evident truth, the result of is no strain on it. But the instant the other soizes his end and experience, that their joint effect is the same as that which pulls, strain begins, caused by his resistance. If he gives i would be produced by a single force equal to their sum. If two strong pull, it is great; if a weak, it is slight. But, to put this men of unequal strength pull on a rope against another man in another way, suppose the first man leads, pulling with all his stronger than either, who succeeds in balancing their united might, while the other, holding on with less strength, is dragged strength, we say, without hesitation, that his force is equal to after. The rope is strained in this case also. By how much ? the sum of those pat forth by the two. When two forces thus By the loss of the two forces. The stronger pull becomes act separately at a point, the single force to which their joint divided into two parts, one putting both the rope and th3 power is equal is called the “resultant" of these forces. We second man in motion, and the other balancing the latter's pull. therefore say, if two forces act on a point in the same direction, It is this second portion which strains the rope, and must be their resultant is the sum of these forces. If three act on it, equal to the strength of the hinder man, while the other, which since two of them are equivalent to one equal to their sum, this causes motion, is the difference of the two pulls or forces. Sapone with the third must be equivalent to a single force equal to pose, lastly, that the two pulls become equal, their difference the sum of the three. And so on, as to more than three, we becomes nothing, motion ceases, and the men come to a standmay lay it down as a general rule that
still. But the strain remains, as before, equal to the hinder The resultant of any number of forces acting on a point in force, which, being equal to that of the leading man, we can the same direction, is 4 single force equal to the sum of the say it is equal to either of the forces. Separate forces.
Let us next suppose that for one of the men an iron ring, When two forces act in opposite directions on a point, for the fastened on a wall, is substituted, to which one end of the rope same reason as in the former case, we assume that the resultant is attached. So long as the rope hangs loosely from the ring is the difference of the two. And this leads us the most there is no strain on it. Let the other man now pull at the far general case that can occur of such forces-namely, that in end, the rope at once is strained, evidently not by the wall, but which any number of them are applied to a body along the by the man's pull. The wall puts forth no more effort to strain same line, some in one direction and others in the opposite it than it did before ; but simply resists the force communicated direction. To determine the resultant of all, it is evident that to it through the rope. It is, in fact, a case of a force applied it is sufficient to take the separate resultants of the opposing to the wall through the rope, every point of which may be consets, then take the difference of these resultants, and that this sidered a point of its application. difference will be the required resultant of all, and its direction Again, take two equal weights attached to the ends of a that of the greater of the two separate resultants. Hence the cord which passes over a pulloy. The strain on the cord which following rale :
hangs down at either side is evidently equal to the weight on If any number of forces be applied to a body along the same that side; and, since the weights are equal, the strains on both lire, their resultant is the difference between the sums of those sides, and therefore all through the cord, are equal to that which act in the opposite direction, and its direction is the same weight. as that of the greater sum.
If two bullocks raise water from a pond in a large bucket by For example, if fifteen men pull on a rope against eleven, a rope which passos over a pulley, as the bucket ascends two and drag them along a road, the resultant of the twenty-six forces are acting at the ends of the rope. The stronger pall of
the bullocks overcomes the weight of the water and bucket, and other, and therefore could not make equilibrium. In the case an amount of motion results, due to the difference of the two of the ring on the table, to which the three strings are attached, forces. The rope, however, is strained only by the weaker if the direction of the effect of the pulls on two of the strings were force, evidently so in the part which descends from the pulley not opposite to that of the third pull, the three would make the to the bucket, and therefore also in the remainder, since the 'ring move to the side of the table, towards which these two strain must be uniform along its whole length.
directions incline. And, furthermore, even if the directions In all these cases the forces wero of the nature of a pull, were opposite, the ring would move, if the effect of the two, or causing a stretching strain. But the conclusions hold equally their resultant, were not equal to the third force. These two good of pushing forces. If two such, equal to each other, bo principles may be definitely stated as follows :applied to a ball at opposite sides in opposite directions, the 1. When three forces applied to a point are in equilibrium, compressing strain within the ball will be equal to only they are in the same plane. one of the forces. Or if the ball be pushed against a 2. The resultant of any two of three forces in equilibrium at wall by only one of them, thongh the wall resists, the strain a point is equal and opposite to the third force. will still be the same equal to the single force.
The re- From these principles it is evident that in order to ascersistance counts for no
tain when three forces thing. Also, when the
applied to a point are two forces are unequal,
in equilibrium, it is and motion ensues,
necessary first to disthere is a compressing
cover what the result. strain equal to the
ant of any two of them smaller force, while the
is. If you find that motion produced is due
the resultant is oppoto the difference of the
site to and equal to forces. When a man
the third force, then ascends a ladder with
you are certain of equi. a hod of mortar, there
librium. The question are two such compress
then is, how may the reing forces acting on
sultant of two forces be his shoulder at the
found? This we shall spot on which the hod
defer to the next lesrests—namely, his own
son, closing this with muscular power push
the single instance in ing his shoulder up
which, without looking wards, and the weight
for a resultant, we can of the hod and mortar
say that three forces pushing it down. His
in equilibrium ; ascent is effected by
that is, when three the difference of these
forces are all equal, forces, the muscular
and make equal angles being the greater;
with each other, the while the compressing
first with the second, strain is evidently the
the second with the weight of the loaded
third, the third with hod. These examples
the first, in order all will make clear to
round. you the principle I
Take, for instance, have been explaining;
three equal weights, atand you will find no
tached to three strings, difficulty in multiplying
two of them much them by thinking of
longer than the third, others yourselves.
which are tied togeWe now pass to the
ther in a knot at their case of three foroes,
other ends. If the
ALATAN MUNT whose directions are all NOT
two longer strings with different, applied to a
their attached weights point, and producing
are now thrown over equilibrium. Now it is
two pulleys in the same evident, first of all, that
plane, one of the pal. the three must pull or
leys being even higher push in the same plane
up than the other, HODMAN ASCENDING LADDER. or flat, such as, for in
and the third string stance, the flat surface
and weight is allowed of a table; for if two of them pulled along that surface, while to hang down in the middle, we shall have a case of three the third pulled in a slanting direction upwards, this latter force equal forces applied to a point. There are the two outside should lift the body off the table. Try the experiment with weights acting over the pulley, and drawing the knot obthree strings attached to a ring which lies flat on a table, two of liquely to either side, and the middle weight pulling it down. which are pulled horizontally along the table, and the third in wards. What position will the strings settle themselves into ? any direction upwards. The ring will be lifted, and soon the Evidently so that the angles all round between the strings may three strings will come into one plane. I am not here taking be equal; for no reason in the world can be given why they into account the weight of the ring and strings, which are a should be unequal. Whatever reason could be assigned for fourth force applied to the body. For the sake of simplification, supposing one of these angles greater than the other, since the to enable you to understand the principle, I suppose these to be forces are equal all round and all the other circumstances the so small in comparison to the others as to count for nothing. same, that same reason should make that other angle greater
Secondly, when three forces applied to a point are in equili- than the first. The angles, therefore, must be eqnal. Let any brium, the resultant of an
hem is equal and opposite one of you make the experiment, and measure the angles, and to the third force. Th
for, if it were not, the he will find the result to be as I have stated. But you will find resultant of the two
o which the three are this same conclusion arrived at in the next lesson in another equivalent, would
Land opposite to each and more satisfactory manner, by the Parallelogram of Forces.
place in the chorcid of pigment of metallic brilliancy. This
may be well seen at the bottom of the eye of the ox inside; in THE EYE (Continued).
others, the sclerotic is coloured, as any visitor at the Zoological THROUGHOUT those classes of animals which are called verte Gardens may see to be the case in the eye of the chimpanzee. brate, because they have an internal skeleton, the main central
These diversities, with many others, such as the contraction portion of which consists of a back-bone of pieces jointed to one of the iris of the cat, so as to leave a slit instead of a circular another in a long row stretching from one end of the body to opening, are interesting, but by no means so functionally imthe other, the eye is essentially of the same structure as in man. portant as others to be mentioned hereafter, when we describe It is true there are differences in the proportion and shape of eyes suited to conditions altogether different, such, for instance, the parts, and in some cases additional parts are found, while as the fish's eye, which is constructed to see in water. in others the eye is so reduced and degraded as to be of little Birds, some of which are almost exclusively denizens of the
air, and most of which have the power of betaking themselves to flight occasionally to escape pursuit, to hunt active prey, to search for new feeding-grounds, or to select a more genial climate at the change of the seasons, must have eyes suited to distant vision. Hence the lens is of a very flattened form, and does not increase in density from the outside to the inside as it does in mammalia, and more strikingly in fish. The distance from the lens to the back part of the eye is small, and to the cornea large relatively; in other words, they have a larger amount of aqueous and a smaller amount of vitreous humour
than brutes have. The back part of the eye too is flatter, and 22
is a portion of a larger sphere in relation to the rest of the eye than in animals. The shape will be best seen by the aid of the diagram of the vertical section of the eye of a soaring bird.
When the eye is spherical and distended with fluid, as in man, there is no tendency of the pressure within to alter the shape of the ball; but when, as in the case of birds, it has any other form, the internal pressure would strain the elastic capsule of the eye in some parts more than in others. This strain can
only be prevented by rendering those parts of the capsule which VERTICAL SECTION OF THE EYE OF A SOARING BIP.D.
are exposed to the extra pressure more solid. In the case of 1, Sclerotic; 2, Choroid; 3, Retina ; b, Picten; 4, Vitreous humour; the bird, this is effected by means of a series of bony plates
3, Bony support of sclerotic or hard coat; 6, Iris ; 7. Cornea ; which encircle the sclerotic, bedded in its substance, and 8, Lens; 9, Aqueous humour; 10, Lens ligament; 11, Ciliary pro stretching from the rim of the cornea to the circumference of cesses; 12, Optic nerve.
the large segment of the eye, on the inside of which the retina or no rise; but in the majority of cases in brutes, reptiles, and is spread out. fishes, and in all birds, the eye is well developed, and even where The structures described above, conducive to long sight in a it can be of no use, still indications of it are found.
thin medium, are more especially to be remarked in soaring, Our English mole is an instance of an animal with a degraded raptorial birds, like the eagles, vultures, and hawks. These, as condition of eye. It is in this animal smaller than a pin's head, they wheel round at a great height, survey a large extent of and has to be looked for carefully in the midst of the velvet fur. Of course, to an animal which lives underground, burrowing continually in soft earth, an eye would be useless, and even inconvenient; yet the rudiment of an eye is found.
5 Besides man, only apes (and some lizards, such as the clameleon, and perhaps some fish) have the yellow spot of distinct vision. Vision in some apes must be very powerful, for it is suid a gentleman who owned a baboon used to ride away across the plain until he could only just see his dog-ape with the naked eye; then using his telescope, he made a number of gestures, which were immediately mimicked with precision by the animal.
In looking into the open eye the white is part of the opaque sclerotic. The coloured part is the iris seen through the transparent cornea and vitreous humour, while the pupil is the hole through the middle of this, which seems black because of the
11 dark non-reflecting choroid at the back of the eye.
The iris gives the colour to the eye. When there is only a layer of pigment on the back part of this, the eye is blue; but when, in addition, specks or sheets of pigment are distributed through the substance of the iris, eyes of various colours are
VERTICAL SECTION OF THE EYE OF A FISH. produced. Thus, fair people have usually blue eyes, and black eyes accompany an olive complexion and dark hair. In other 1, Sclerotic ; 2, Choroid , 2, Inner layer of Choroid; 3, Retina ; 4, words, people that have a surplus of internal paint elsewhere Choroid gland; 4, Vitreous humour; 5, Bony support of sclerotic have it in the iris too.
or hard coat; 6, Iris ; 7. Cornea; 8, Lens; 9, Aqueous humour;
10, Lens ligament; 11, Ciliary processes ; 12, Optio nerve. Again, the lack of pigment is sometimes so great that even the choroid has none, and then the pupil looks red because the country; yet their sight is so keen at that elevation that no blood vessels of the choroid can be seen through its front layer. young unprotected animal, or maimed and disabled prey, escapes Albinos, as individuals with the last peculiarity are called, are their sight. So keen is the sight of the condor of the Andes, found among rabbits, mice, cats, and many other species, and that if a carcase be exposed where the naked eye can detect are especially prone to occur under domestication. These none of these creatures in the horizon, yet in a few minutes creatures present an appearance which is very ethereal and they are seen streaming in from all directions straight towards fairy-like, so that artists have often introduced them into their their hoped-for meal. fanciful pictures, as in Landseer's “Bottom and Titania.” But But though birds be long-sighted, it is also highly necessary however they may grace the ideal creation of the painter, they that they should see minute objects at a short distance. No are less suited to this working-day world than their coarser entomologist will deny that an insectivorous bird must have brothers.
keen eyes for short distances, if it is to get its living with On the other hand, in some species a further deposit takes ease A microscopic sight is scarcely less requisite for a grain.
5 VOL. L.