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each half an inch
long, marked 1, 2, 3, &c., to 10, from right to as, d the smaller divisions from E to F, are each a quarter of an anch long, marked 1, 2, 3, &c., to 19, from left to right. The mode of constructing this scale is the following: Draw eleven equidistant and parallel lines, such as those between c D and E F inclusive ; divide the upper of these lines C D, into as many equal parts as the scale is intended to contain, with one additional part of the same, size as the rest ; from each of these divisions draw perpen:dicular lines across the eleven parallel lines, that is, from C D to E P; subdivide the additional part on cI ad E Flinto 10 equal parts, and draw a line from the left extremity of the additional part on CD, to the first divtsion of the additional part on EF to the left; a line from the first division on the left of the same part on C D, to the second division on the left of the same part on E F; a line from the second division on the left of the same part on CD, to the third division on the left of the same part on E F, and so on, until the rectangle be filled up with oblique or diagonal lines, and presents the appearance of an oblique chequer, the last oblique line being drawn from the ninth division of the additional part on c D, to the right extremity of the same part on E. F. In regard to these oblique lines, it is to be very particularly remarked that each of them in passing from the additional part on cI, to that on EF, crosses the parallel lines between & D and E F at a point which is one-tenth more of each of the subdivisions of that part, in proportion as it descends from the line cD, viz., at the points where they intersect each succeeding parallel ; and as each of the subdivisions of the additional part is one-tenth of each of the larger divisions, so the intersection
of each of the succeeding parallels with each of the diagonal lines gives an additional one-tenth of each of the preceding
tenths, or an additional one-hundredth of each of the larger divisions of the scale. If, therefore, the larger divisions of the scale be reckoned units, the first subdivisions of the additional part will be tenths of these inits, and the second subdivisions, marked by the intersections of the diagonals and the parallels, hundredth parts of the same units. Again, if the larger divisions of the scale be reckoned tens, the first subdivisions of the additional part will be units, and the second tenths; or if the larger divisions of the scale be reckoned hundreds, then will the first subdivisions be tens, and the second units, and so on, the value of the subdivisions always depending on that of the larger divisions of the scale.
The reason why each of the subdivisions of the additional part on c D, which are marked at every second division 2, 4, 6, 8, from left to right, is one-tenth of each of the larger divisions marked 1, 2, 3, 4, &c., to 10, from right to left, is plainly this, that one-tenth of any part is also one-tenth of each of the parts that are equal to that part ; but the reason that each of the diagonal lines intersects every successive parallel, at one-tenth part more of one of these tenth parts, according as it des: cends from c D, must be sought for in Prop. IV. Book VI. Cassell's Euclid. Thus let A B C, fig. 3, be a triangle, such as is formed by the perpendicular drawn through the right hand extremity of the larger division of the scale marked 1, the diagonal line drawn from the same extremity to the first subdivision on the Heft of the additional part on E F, and the first equal part on the left of the same 3: F, where A B represents the first of these limes, A C the - - **, second, and B C the third ; then supposing B C that D E is that part of the first line below cl which is intercepted by the perpendicular and the diagonal above mentioned, (scarcely perceptible on the scale, fig. 1) we have by the proposition of Euclid referred to, this proportion, A.B.: B C ; ; AB :#D, and alternately A B : A E : : B D : E D ; but A E is by construction one-tenth of AB; therefore E D is, by Prop. D. Book W. Cassell's Euclid, one-tenth of B c. Whence, it follows, that if the point c be one-tenth of a certain distance from the point B, the point D will be one-tenth of that one-tenth, or one-hundredth of that distance from the point E. This shows why at every successive parallel lower than G D, the distance of each diagojval is an additional hundredth part of the unit or of each larger division, farther remote from the perpendicular drawn through the left extremity of the additional part. By this decimal diagonal scale, therefore, we can lay down or measure lines whose jengths are given in numbers consisting of hundreds, tens, and
units; or of units, tenths, and hundredths of units. Hence, the numbers 478 47-8, and 4.78 may all be expressed by the same extent of the compasses upon the Diagonal Scale; thus, setting one foot of the compasses on the line marked 4 of the larger divisions, at its intersection with the 8th parallel below c D, and extending the other foot till it reaches the diagonal marked (or understood to be) the 7th at the top, viz., on c D, that distance in the compasses will be the length of the line which is 478 equal parts, 47-8 equal parts, or 478 equal parts, accord‘ing as the unit is considered to be one-hundredth of half an inch, one-tenth of half an inch, or one-half of an inch; for if the four larger divisions be taken for 400, seven of the first subdivisions will be 70, and this, taken upon the 8th parallel below CD, which takes in 8 of the second subdivisions for units, gives the whole number 478; or, if the four larger divisions be taken for 40, seven of the first subdivisions will be 7 units, and the 8 subdivisions of the second kind upon the 8th parallel will be 8 tenths of a unit; or, lastly, if the four larger divisions be reckoned as only 4 units, then will the first subdivisions be 7 tenths, and the 8 second subdivisions 8 hundredths of a unit. Finally, in reference to fig. 1, in order to construct the Diagonal Scale, with the larger divisions equal to only a quarter of an inch, we have only to bisect each of the larger divisions of the former scale, on E F, and from the points of bisection to raise perpendiculars to C D ; we shall then, omitting the additional part of the former scale, have 20 equal parts along E. F. Now, keeping for the additional part of this scale the first division on the left, and marking 1, 2, 3, &c., to 19, we have the larger divisions of the quarter-inch scale; then, subdividing as before the additional part on E F and C D into 10 equal parts, we have the first subdivisions of this scale; and drawing diagonal lines as before in the additional part between E F and C D, but reckoning them upwards, instead of dowrawards as in the former scale, we have the second subdivisions of this scale ; these second subdivisions are marked at the side running upwards from E to C, at every second point, viz., 2, 4, 6, 8; where the second subdivisions of the former scale are marked at the side running downwards from D to F, in the same manner. The reason why all the subdivisions, both first and second, from 1 to 10, are not marked on the former scale, is simply because there is not room to mark all the figures distinctly; and the reason why the first subdivisions are not marked at all on the second-scale is, that there is no room to place them with any degree of distinctness on this scale; but the second subdivisions of this scale are marked similarly to those of the former scale, but in a reverse order, as they must be reckoned from the bottom upwards, while the first subdivisions, though not marked, must be numbered from right to left, and the larger divisions, as before observed, from left to right. The explanation of fig. 2, which contains the Trigonometrical and other Lines of the Plane Scale, being its obverse side, must be deferred for want of room till our next Lesson in Instrumental Arithmetic.
In most sentences having an adverbial phrase, there may also be an adverb ; e.g., The sick man drank in his chamber copiously.
Instead of an adverb and an adverbial phrase, you may have two adverbs, or even more; e. g., The sick man drank water eagerly and copiously.
Position of the Adverb.
The ordinary place for the adverb is immediately before or after the verb. Euphony, as well as idiom, has an influence in determining the position of the adverb. Sometimes an adverb is placed before the verb in order to allow the verb and its object to stand together ; e. g., The sick man copiously drank water. The position of the adverb has much to do with the sense. There is a great difference between these two statements:— Only the man went out. The man only went out. The first states that the man went out and no one else ; the second states that the man did nothing but go out. Agreement of Adverbs. Adverbs, though so called because they are put to verbs, qualify adjectives as well as verbs; e.g., “Any passion that habitually discomposes, our temper, or unfits us for properly discharging the duties of life, has most certainly gained a very dangerous ascendancy.”—Blair Adjectives may also be said to qualify participles, but as the participle is only a part of the verb, a separate statement of the fact is hardly necessary. There are elliptical forms which seem to make some adverbs independent of any verb. But the independence is only apparent. In reality every adverb on examination will be found to qualify an affirmation. The words yes and no are exceptions. When I ask a child “Do you love me?” and the child answers “Yes,” the adverb gyes is only an abbreviated form of the sentence I do love you, No and mat are often misused. No is the answer to a question when no other answer is given; not is prefixed to the verb employed in giving the answer; e.g., Are you ill 2 No. Are you ill 2 I am not ill. Hence in all sentences not should be used; consequently “whether or no '' is wrong ; it should be whether or not. When not is prefixed to the verb, and so affects or negatives the whole affirmation, if a negative is required with a succeeding member, or should be used; but if the not (or neither) negatives only one word or one phrase, then with the succeeding or corresponding word or phrase employ mor; e. g., For two months I could not think or speak. He allowed me not to speak nor to write. He gave une neither money nor clothes.
. No one, when employed thus in separation, may be considered an indefinite pronoun (not one) of the singular number, and of course requiring the verb to be in the singular. When combined, as in *0%, the pronoun implies plurality, and has its verb in the plural; e.g., “How many are come * “None are come.” “What, not one * “No, not one is come.” The word qinen may seem to be independent. But it is a Hebrew term, signifying so let it be, and forms a part of the preceding sentence or paragraph, and indeed is in itself a sentence expressive of a wish or a prayer. There are cases in which the adverb seems to qualify a preposition; e. g., . “This mode of pronunciation runs considerably beyond ordinary discourse.”—Blair. But the verb consists of the two words runs beyond, beyond being an uncombined or free affix, here appended to the verb run, so that the adverb really qualifies the affirmation, which is that this mode of profounciation runs beyond, &c. When we say “not all that glitters is gold,” the negative is applied to all, and applied with such effect as to give the idea that something that glitters is gold. -Yo has sometimes the force of an adjective ; e.g., “There is no flying hence nor tarrying here.”—Shakspeare.
In their directions for the use of ever and never in such phrases as “never so rich,” grammarians have varied and blundered. The only way to determine whether you should use ever or never is to consider whether the proposition is affirmative or negative; if the former employ ever, if the latter employ never. Dr. Blair has been blamed for saying “seldom or never can we expect,” and yet is he completely correct. The proposition is that we can expect a certain thing in few instances, nay, perhaps in no instance, that is not at all, or never.
Exception has been taken to sentences constructedlike the following, and ever has been substituted for never:—
“Which will not hearken to the voice of charmers, charming never so wisely.”
Never is right; the proposition in the second member is “ though he (the charmer) charm so wisely as none ever before charmed;” the proposition is therefore negative, and requires never.
Some adverbs perform the office of adjectives. When adverbs
| perform the office of adjectives, they may be accounted adjectives;
together with beverage is governed by drinks. In general it may be stated that participles admit of concord and dependence. - to - & , . & Participles perform other offices besides that which is strictly their own.” The present participle is used as a noun sometimes without, sometimes with a pronoun, also sometimes with and sometimes without as object; e. g., “Describing a past event as present has a fine effect in language.”—Kames. • “My being here, it is, that holds thee hence.”—Shakspeare. The present participle may have the force of an infinitive; e. g., “Avoid being ostentatious and affected.”—Blair. The present participle has the force of an infinitive also when combined with the past participle; e.g., “Habits are soon assum’d ; but when we strive To strip them off, 'tis being flay’d alive.”—Cowper. The present participle unites with a verb to complete its signification; e.g., “To be left pausing on a word of no meaning is disagreeable.”— Murray. The present participle is used in the way of explanation :“But ever to do ill our sole delight, As being the contrary to his high will.”—Milton. The present participle refers to the subject of the sentence:— “Professing themselves to be wise, they became fools.”— (Rom. i. 22.) The present participle may agree with the object; e. g., “They stoned Stephen, calling upon God and saying.”—(Acts vii. 59.) It must be regarded as an inaccuracy when a present participle beginning a sentehce is not followed by a subject ; e.g., “By admitting such violations of established grammatical distinctions, confusion would be avoided.”—Murray.
Better “you (or they) would avoid confusion,” for then the
participle admitting has a subject, namely you, and the sentence is
regularly formed. Usage, however, has sanctioned the use of the present participle in an independent manner, or absolutely, that is, as disjoined in eonstruction, and expressive of a cause or reason :“I then quit the society; to withdraw, and leave them to themselves appearing to me a duty.” A present participle may at the same time have the force and construction of a participle and a moun:— “Mr. Dryden makes a very handsome observation on Ovid's writing a letter from Dido to Æneas.”—Spectator. The construction in this last example deserves study ; the preposition on governs writing as a noun; writiny as a noun governs Ovid's, and writing as a participle governs letter. When a present participle performs the twofold function of a noun and a participle, being alike governed and governing, it is said to have a gerundial force, that is the force and construction of the Latingerund, or of the participle ending in dus. With the present participle used gerundially a past participle may be united; e.g., “Some of these irregularities arise from our having received the words through a French medium.”—Allen. The present participle used as a noun may have a preposition or an adverb in combination with it : e. g., Their hope shall be as the giving-up of the ghost.”—(Job xi. 20.) The two constructions of the participle with a participial force, and as a noun, must not be placed together in the same sentence, as in this, “Poverty turns our thoughts too much upon the supplying of our wants; and riches, upon enjoying our superfluities.”—Addison.
Correct. “No mistake can arise from using either form ‘’
* Cw:mp --e what I have said on the participle as forming the subj, ct of a preposition.
Participles in general have the government of the verbs from which they come consequently the question whether or not a preposition should be appended to a participle depends on the usage of the Verb; often of is inserted where it is not needed, especially by the untaught in conversation ; e.g., &
Incorrect. “They left beating of Paul.”—(Acts xxi. 32.)
. Some verbs take a present participle after them instead of an infinitive ; e. g., Verbs of desisting. “They have done speaking.”—Harris.
Verbs of omitting. “He omits giving an account of them.”—
Toolce. Verbs of preventina. “Our sex are prevented from engaging in. these turbulent scenes.”—Kest. Verbs of avoiding. “He might have avoided treating of the origin of ideas.”—Tooke. After verbs expressive of the operations of the senses the participle or the infinitive may be used, but with a slight difference in. the meaning ; the participle describing the act as at the moment actually proceeding; e. g., f I saw the bird fly. I saw the biru flying. I have spoken of a participle as being used absolutely or independently. A word is said to be used absolutely or independently, when it stands disconnected in construction from what precedes, and sometims from what follows as well. Instead of one word the absolute construction may contain two words or more. Take as examples of this construction,
Be failing, who shall meet success 2
“Or I only and Barnabas, have not we power P’’—(1 Cor. ix. 6.) Nay but, O man, who art thou that repliest against God *— (Rom. ix. 20.) “O rare we!”—Cowper. “Miiserable they !”—Thomson.
The construction in full involves two subjects; e. g.,
The sun rising, the darkness fleeth away. William being dead, Victoria succeeded.
A question has been raised as to what is the absolute case in English. With the view we have taken of cases, the question has. little meaning or importance. For the sake of a name you may call the construction in question the absolute construction, and when pronouns are employed in that construction you wiki generally find them in the nominative. Yet Milton says “me miserable l’’
The construction is elliptical, and whether the noun (or pronoun) employed should be subject or object depends on the way in which the ellipsis is supplied.
SKETCHES FOR YOUNG THINK ERS. (Continued from page 269, vol. III.)
Two or three observations will suffice our second instance. We refer to John Milton. Much as this illustrious individual accomplished as an author and a politician, his name will always be most prominently associated with “Paradise Lost.” He was not a wealthy student. His path was an ascent, uneven, steep, and rugged. The poet's soul was not daunted with difficulty, and although he feelingly laments that wisdon, was “at one entrance quite shut out,” yet his soul was bathed in light, and that light streamed from him, as the rays from the meridian sun. IIe finished his poein. It was ready for the press, and although he had drunk deeply at
“Siloa’s brook that flow’d Fast by the oracle of God,”
and “soared above the Aonian mount,” yet “the bard of immortal subjects, and immortal fame” offered the copyright of “Paradise Lost’’ for five pounds ! The book over which a world has poured its plaudius and which has secured its author
SKETCHES FOR YOUNG THiiN
declare, that all young men or amateur poets may become
Miltons, or that all young mathematicians may become Newtons. Variety would thus become lost in one lofty, though monotonous uniformity. One sun in the sky is sufficient. We love to see the moon and stars, no less because there is a sun. Let all those stars blaze with equal intensity as the sun, and men would be dazzled to blindness, or scorched to death. Let the orb of day maintain its sphere, the moon shed her soft effulgence, and the stars sparkle in the lofty dome, and there will be beauty, sublimity, and usefulness; but if the arrangement be disturbed, there will be disorder and confusion. We like the stars in the firmament, and the flowers on the earth, and the music in the air; we admire the order, and adore its author; so must it ever be in the mental creation. There will be sun, moon, and stars there. Let them all shine. Light is useful wherever it may arise. Every man should be a centre of light, illuminating every circle, and dispelling the shades of ignorance, error, and vice. It will be observed that it has formed no part of the writer's design to furnish the biography of the individuals to whom reference has been made. Mere illustration was required, and this is all which will be found. It were easy to fill a volume with extracts from the lives of the eminent already published, but the design in the present case, was to work in the examples simply as illustrations of the sentiments which are here advanced. This will account for the brevity of the notices, and the abruptness and rapidity of some of the transitions. We have by no means exhausted the all-but boundless stores of instances illustrative of the theme. Time would fail us to tell of Cellini, Matsys, Ibbetson, Kent, Towne, Rirby, Ichiavoni, and Caslon, among the artists ; of Descartes, Jonson, Buchanan and Cervantes, anong soldiers; of Dampier, Davis, Drury, Falconer, Giordani, Fransham, Oswald, Columbus, Cook, Vancouver, and Collingwood, among sailors ; of Homer, Milton, Salinas, Stanly, Scapinelli and Huber, among blind men; and of Lithgow, Niebuhr, Ledyard and Belzoni, among travellers. Biography will unfold this, and to the written memoirs of these distinguished men the reader must be referred. This Essay is intended rather to whet than to satiate the appetite. It is a finger-post pointing along the road leading to intellectual excellence; or, changing the figure, it is a guide pointing to the footprints of previous travellers, and saying as it points, “this is the way, walk ye in it.” The temple is at the further end of this road, no tax will be required, but labour and patience. These will clear and smooth the way. Longfellow in his admirable “Psalm of Life,” has well sung, “Learn to labour and to wait.” This counsel is the secret of success. Some men have learned to “labour” but have not learned to “wait.” Their impatience has been so overmastering, as to render them disquieted and miserable. They have cast in the seed and watered it, but the harvest tarries and they murmur. Desert does not always meet with immediate success; the “gem of purest ray serene” often lies long in the “deep unfathomed caves of ocean,” and the “flower” often “blushes unseen,” for a lengthened period, or perhaps it may “waste its sweetness on the desert air.” Desert moreover is not always to be measured by success. Many succeed who are undeserving, but such success is not always to be envied. The clown may assume the manners of a philosopher, but he is a clown after all. The jackdaw may be arrayed in the feathers of the peacock, but well will it be for him if a righteous indignation does not strip of the assumed covering, and expose the delinquent in his native insignifiCan Ce. There are some general principles deducible from this train of illustration. A brief review of these may be of service, as tending to impress the facts more strongly, and bring the subject to a more practical and successful conclusion.
I. INTELLECTUAL ExCELLENCE brings with it a peculiar pleasure. It is seif rewarding, and soakes a taan more and more self-dependent. The uniettered and uncultivated mind must go out of itself, and feed on excitement. Solitude to such an one is misery. Study is an unmeaning term. In early days the mind was allowed to develop without discipline; the shrub having been neglected, the tree refuses to be trained. The man of cultured intellect is not dependent on contingencies for his happiness. He has a fountain within him, supplying what is necessary in the hour of need. He who knows the pleasure of retiring within himself, and depending on his own resources, would not readily forego the enjoyment. Here a distinction must be made between absence of mind, and the pleasure of which we are now speaking. We have not much faith in “absence of mind.” In a large proportion of instances, we have reason to believe it a studied eccentricity. We know that some profound thinkers have been so deeply engrossed in thought, as to be oblivious of what was proceeding in their presence, but we protest against those instances being quoted as apologies for all the rude, boorish, and offensive stupidity in the world. We can sympathise with Newton when buried in mathematics, with Dwight when absorbed in theology, or Johnson when pondering on his ethics, without being compelled to subscribe to all the ridiculous tales which are told regarding the mental absence of many distinguished men. If men are to be absent-minded, let it be real; bona fide, not assumed and fictitious.
To the intellectual man, all nature is a teacher. He finds
enjoyment in everything. He discovers
“Tongues in trees, books in the running brooks, Sermons in stones, and good in everything.”
The whole world to him is an immense library. It is a living source of enjoyment. If his spirit be what it ought, the worlä will be full of types and symbols, concerning the spiritual and unseen. Every star that twinkles will teach him lessons every flower will be suggestive of thought. The planet will remind him of “the bright and morning star;” the flower will bring to his remembrance “the rose of Sharon.” This may be called fanaticism, or sentimentalism, or rhapsody. To call names, however, is not to disprove; if it were so, we should have every principle in the world overturned at once.
We envy not the man who can walk through the world, and see no cause for thankfulness; who regards all things as the result of accident, and as at the mercy of a blind and capricious chance. This must necessarily cast a gloom over the world. The thought insults our common sense, and fills our spirits with revulsion. If there be no God, the world in itself is the most mysterious, confounding, and insoluble of problems. The intellectual man enjoys the world; it is filled with objects of attraction and instructive interest to him. We have no sympathy with the rant that is always bickering against the world. Neither have we esteem for the man who can look upon it without thankfulness, and as devoid of design. Apart, however, from the physical world, the intellectual man has sources of enjoyment. He converses with the illustrious dead. He luxuriates amid the sumptuous provisions of literature. Though the authors have returned to their kindred dust, their works remain behind. Their spirits are in their writings; they thus speak from the grave, and shed light from the sepulchre. Time and space are annihilated by the power of mind. We go at once thousands of years back, and listen to Moses, as in strains of sublime simplicity he relates the history of the world's creation. We sit by Homer as he writes his imperishable lines, and we look with prophets into the events of unborn time. While the body remains in one place, the mind traverses the world, and drinks knowledge from fountains which were opened centuries before its own existence. We have here a velocity which defies the lightning. For the sake of happiness, then, we urge the acquisition of knowledge. We cannot see that “ignorance is bliss.” If this were the rule, then the brute creation would enjoy more bliss than man. The mind would be the greatest obstacle to the attainment of happiness. We would have to attend to the necessities of our physical nature, cultivate sensual desires, despise knowledge, burn every book, close every reading-room, proscribe the press, and
desert the pen, as the best possible means of ushering in the Inillenium of bestiality, stupidity, and vice . A little learning is not “a dangerous thing ”; it is a ray, and brings light into the mind, and if the student does not remain content with a single beam, he will diligently seek for more light, and his mind will shine more and more unto the “perfect day.” One acquisition prepares the way for another ; knowledge is contagious and self-multiplying, and if well selected will invariably prove a blessing, wherever it is cultivated and prized. Knowledge is not merely a pleasure, it is a power; so Lord Bacon has weightily observed. Perhaps it would not be exaggerative to assert, that it is the greatest power which man can exercise. By this he is enabled to invent and wield such instruments as a barbarous mind could not possibly have devised. Nature is made tributary to man’s purposes. Science assists him in understanding the elements, and harnessing them for the accomplishment of his designs, Science teaches man how to
husband physical strength, and to make the most of its power.
The barbarian, by dint of brute force, may remove a given
weight, but the civilised and enlightened European, with his lever, pully, or screw, attains the object with the most perfect ease. How so? Because mind has devised the means. Those instruments are so many embodied thoughts. They were in the snöld first, and the skilful hand wrought out the idea into mechanical form and its intended adaptations. What is machinery in all its multiformities, but a development of thought, a convincing , proof that “knowledge is power.” Every steam engine that rushes along the rail, or darts the boat through the wave, seems to exclaim in its rapidity, “knowledge is power.” To the pleasures of intellectual pursuit there is no end. Especially does this appear to the believer in the soul’s immortality. He believes that when the soul is freed from its physical companion, it will continue to think, and multiply in knowledge. The grossness of nature will be thrown off, and the soul left at liberty to explore the amplitudes of the immeasurable universe !