Multiply the area of the base by 1-3 of the perpendicular altitude;--the product will be the answer. Thus: Suppose a triangular pyramid to be 45ft. high, and each side of the base 10ft.; what is its cubic contents? 45÷3=15×43.3=649.5, cubic contents. OBS. 1. Suppose the figure of the pyramid to have been quadrangular, or a square base, each side 10ft. and the perpendic ular altitude 45ft.; what is its cubic contents? Ans. 1500ft. 10X10-100ft. area of the base. [See square surfaces, Rule 1, page 543.] 45÷3=15X100=1500 cubic ft. OBS. 2. Suppose the given figure had been circular, and the diameter of its base 10 feet, and its perpendicular height 45 feet, the solid contents might have been found by multiplying the area of its base into 1-3 of its height. Thus: 10×10 100, square of the diameter, X.7854-78.54, area of the base, [see Obs. 1, Case 2. Circles, page 555.] Then, 45÷3=15X78.54-1178.10, Cubic contents. NOTE. The above circular figure is called a CONE, and is nearly represented by a loaf of fine sugar. OBS. 3. The superficial content of a cone or a pyramid, may be determined by the following RULE. Multiply half the girth of the base by the slant height, and, to the product, add the area of the base; the sum will be the superficial content. Thus: Suppose the base of the pyramid to be square, and each side 10ft. and its slant height 48ft.; what is the measure of its exterior surface? Ans. 2020ft. 10+10=20+10=30+10=40ft. girth of the base, and 40X48-1920ft; and 10×10=100, area of the base. Then, 1920+100=2020ft. OBS. 4. A frustum of a pyramid or a cone, is that part of either, which is left when the top is cut off by a plane, parallel to the base. The solid contents of such figures may be found by the following RULE. 1. Find the area of both extremes, and extract the Square root of their product. 2. To this root add the areas of the two extremes, and mul tiply the sum by 1-3 of the perpendicular height; the product will be the contents. Thus: Suppose that each side of the larger base of the frustum of a square pyramid be 10ft. and the sides of the smaller base 6ft, each, and the altitude 25ft.; what is its cubic contents? Ans. 1633.+ 10X10=100, area of the greater base. OBS. 5. The superficial contents of a frustum of any may be found by the following kind RULE. Add the girth of both bases;---one half of which multiplied by the slant height, will give the curve surface; to which add the area of both bases, and the sum will be the superficial contents. OBS. 6. The slant height of any frustum may be found by the following RULE. As the difference between the diameter of the two bases, is to the perpendicular altitude; so is the diameter of the greater base, to the slant height. REMARKS, &c.-LESSON 36. Fourthly. I will here observe, that when the property of use, with regard to words and phrases, appears to be divided, and either term in question is susceptible of two or more meanings, while the other has but one application, the latter has the preference: as, proposal, for a matter submitted, is better than proposition; because the latter may imply a mathematical question, or a certain position. To purpose, a thing when it implies an intention, is better than to propose it;--which may also imply to submit or lay before. And I mistake, is better than I am in an error, on more accounts than one. Fifthly. In all doubtful cases, the choice must be determined by analogy. The phrase, Though he were ever so good, is more consonant to the idiom of the language, than, Though he were never so good. On each side, referring to both sides, is better than on either side. Whether he will or not, is better than will or no;-for the ellipsis of the verb requires the first form. Sixthly. When the terms in question appear to possess perfectly equal claims, in respect to all the foregoing provisions, then regard to simplicity and the demands of the ear, must dictate the decision. Accept my book, is more simple and pure, than to say, accept of my book. And, address him a line, is better than, address to him a line. Delicacy pleases the ear more than delicateness;—and authenticity, more than, authenticateness. Who would not exchange vindicative for vindictive? Seventhly Words and phrases which are harsh and void of harmony,- -as well as those that are low, cantish, and inelegant, should always be rejected, though they may have the authority of use. Unsuccessfulness, unharmoniousness, peremptobleness, holily, godlily, &c. are harsh and unpleasant terms, and readily admit of substitutes much more inviting. I had as lief, or lives, and, I had rather, are faulty connexions; the helping verb had, is employed for would, the legitimate conjugation. Besides, lief and lives are too common to express a preference. NOTE. The foregoing remarks, &c. are such hints as I have thought proper to submit to the consideration of the learner, with a view of rendering him some assistance in the correction of his own productions. If, however, he would become an able, ready writer,-a judge of general composition, and a just and confident critic, he must apply himself to the study of the great laws of criticism, in more extensive and systematic publications. CHAPTER 35. SPELLING.-LESSON 1. cru-ci-fix-ion krô-se-fiks'yun em-i-gra-tion ĕm-e-gra ́shin cur-ve-lin-ear kur-ve-lin'yar em-u-la-tion ĕm-u-la'shun dec-i-ma-tion dès-se-mă ́shun en-er-get-ic ĕn-ĕr-gět'ik dec-la-ma-tion děk-lã-mã ́shŭn en-er-va-tion en-ĕr-va'shun def-i-ni-tion děf-e-nish'un ep-i-dem-ic ĕp-e-děm ́ik deg-ra-da-tion deg-grã-da'shun ep-i-lep-tic ĕp-e-lěp'tik det-es-ta-tion dět-es-ta'shun e-qui-noc-tial e-kwē-nõk'shǎl det-o-na-tion dět-ō-nā'shŭn er-u-di-tion ĕr-u-dish'un det-ri-men-tal dět-re-men'tăl ev-a-nes-cent év-a-něs ́sent di-a-cou-stics di-a-kòû'stiks eu-ro-pe-an yu-r0-pê ăn di-ar-rhe-a di-ǎr-rē'ă dil-a-ta-tion ex-ha-la-tion ěks-ha-la'shun dil-la-ta'shun ex-hi-bi-tion ěks-he-bish'un dim-i-nu-tion dim-mē-nu'shun ex-hor-ta-tion ěks-hòr-tā'shun dip-lo-mat-ic dip-lō-măt'ik ex-pi-ra-tion ěks-pe-ra'shun dis-po-si-tion dis-po-zish'un ex-po-si-tion eks-pō-zish'un dis-qui-si-tion dis-kwē-zish'un ex-su-da-tion ěks-su-da'shun U2 div-i-na-tion eb-ul-i-tion div-e-na'shun ex-tir-pa-tion ěks-ter-pa'shun ĕb-ul-lish'un ex-ul-ta-tion ĕks-ul-ta'shun ed-u-ca-tion ĕd-yu-kā'shūn fer-men-ta-tion fĕr-men-ta'shun ef-fer-ves-cence ĕf-fĕr-věs sense fluct-u-a-tion flukt-yū-ā ́shũn ef-fi-ca-cious ĕf-fe-ka'shus fo-li-a-tion fō-lé-a'shun ef-flo-res-cence ĕf-flō-rěs'sense fun-da-men-tal fun-da-ment'ǎl el-le-gi-ac ĕl-lē-ji'ǎk gen-er-a-tion jen-ĕr-a'shun glad-i-a-tor glăd-e-a'tur grat-u-la-tion grăt-yu-la'shun el-e-men-tal el-e-va-tion ĕl-e-měn'tăl ĕl-ē-vă'shun el-o-cu-tion ĕl-ō-kü'shun grav-i-ta-tion grav-e-ta'shun el-on-ga-tion ěl-ong-ga'shun hes-i-ta-tion em-an-a-tion hĕr-e-tē'shun ĕm-a-na'shun hi-e-rarch-al hi-e-ràrk ́ăl em-bar-ca-tion ĕm-bàr-ka'shunhor-i-zon-tal hor-e-zon'tăl em-blem-at-ic ĕm-blem-ǎt'ik hy-dro-stat-ics hi-drō-stat'iks em-en-da-tion ĕm-měn-dā ́shŭn hy-me-ne-al READING.-LESSON 2. hi-me-ne al Conversations between a Father and his two sons on the subject of Government, &c. NOTE. These conversations are said to have been had between a Mr. Brown, a thrifty farmer of the State of New York, and his two sons, Horace, a lad of fifteen, and Philo, who was about two years younger. The business of the farmi had been closed, and the boys had commenced their winter studies in one of the District Schools. The subject was incidentally introduced by Horace while at the supper table with the family. Father, said Horace, I this day read a few pages in "Goldsmith's Rome," which was highly interesting; but there were some parts of it which I did not understand:-for instance, the word government; what does it mean? The term, my son, has several applications; but when referred to communities of men, it very properly implies the form or manner in which the power, necessary for the administration of public affairs, is disposed of. I suppose, then, said Horace, there are several ways of disposing of the power; but how are they distinguished? They are distinguished, returned the father, by the different kinds of government which the different modes of disposing of the power necessarily produce. How many kinds of government are there? asked Philo. There are only three legitimate kinds, replied Mr. Brown; Monarchical, Aristocratical, and Democratical; every other form is a mere modification of one or more of these. We should be pleased to know how the monarchical form of government is distinguished from the other forms? said. Horace. It is that form of government in which the supreme power is vested, unconditionally, in the hands of one person, styled a monarch, king, or emperor, whose will is the law of the land. If he governs in a severe and arbitrary manner, he is called a despot;-and if with cruelty and oppression, he takes the name of tyrant. Should the powers of the king be limited by laws, then the government is a limited monarchy, and the laws which limit him are called a constitution. If others, such as a council, or an assembly, are associated with him in the exercise of power, it is termed a mixed government;— such are the institutions of Great Britain and France. I hope, sir, said Philo, you will now explain to us the nature of an aristocratical government. I will, my son. An aristocracy, which is sometimes called an oligarchy, (ŏl'le-gràtsh-e) is that form in which the supreme power is lodged in the hands of a few of the nobility, who exercise it conjointly. The third form, you observed, said Horace, is a democracy; how is that distinguished? In a democracy, replied the father, the supreme power is confided to the whole body of the people. Should the people delegate that power to officers appointed by themselves for limited periods, then the form of government becomes a democratic republic. I beg to ask, said Horace, where the supreme power comes from, and what constitutes it? It comes from the people, said the father; they possess it from the hands of their Creator; and the portion justly exercised by government, is formed from the small parts which every man tacitly yields for the benefit of the whole, in order to constitute a sum total for government. How much, asked Horace, does every man give up in order to make the sum possessed by government? Just so much, my son, as will secure to him and his associates, the enjoyment of life, liberty, property, and the pursuit of happiness, in the most effectual manner. All that is claimed or exercised by government beyond this, is manifest usurpation. What form of government do we live under? asked Philo. Ours, said Mr. Brown, is a democratic republic, of the confederate order: for, all political power with us, is in the |