260 



THE POPULAR EDUCATOR. 



latter case J, as I sleep ; and in the former, it has before it they, 

 as they sleep. The same principle of repetition is observed in the 

 past tense, where slept is repeated ; and the same principle oJ 

 distinction is pursued by means of the personal pronoun. Instead 

 of inflection, then, the English verb is formed by repetition and 

 pronominal distinction. Yet is the English not without inflec- 

 tions, as appears from the second and third person singular, in 

 which the root sleep is changed into slcepest and sleeps. These 

 inflections are, however, unnecessary, for the second person 

 is sufficiently marked by t hou, and the third person by he. Of 

 these two inflections, indeed, the former is rarely used, and the 

 latter might be spared. There would thus seem to be a decrease 

 of inflectional usage in the English tongue. Such a decrease has 

 been going on from the time when the English left its Anglo- 

 Saxon parent. Nor is the change to be regretted, for thereby the 

 language gains in simplicity and adaptation. That the English 

 once possessed inflection in a more decided manner is clear from 



THE PRESENT TENSE OF THE VERB "TO BE." 



Persons. Singular. Plural. 



1. I am. We are. 



2. Thou art. You are. 



3. He is. They are. 



Here, including the infinitive to be, we have five separate forms 

 for three which occur in the verb to sleep. 



Usage, then, has led us to the acknowledgment of distinctive 

 forms for the three persons of the present and the past. But 

 having a complete present and a complete past tense, we are 

 without a future. Is the English language without a future 

 tense P By tense in grammar is meant a specific form corre- 

 sponding to a specific meaning in relation to time. Thus, in 

 Latin, amo is I love; but if I want to say I will love, I change 

 amo into amabo. Does any such change take place in English ? 

 Unquestionably not ; the term love of the present, remains love 

 in the future. The English language, then, has no future tense. 

 Nevertheless, the English people can express a future act, and 

 this they do by the employment of a second verb, namely, the 

 verb will and the verb shall, as I shall love, he will love. 



By means of other verbs, commonly called auxiliaries, we are 

 able to express other varieties of meaning. These varieties, 

 however, are so numerous, and in part so indeterminate and un- 

 fixed, as to defy the systematic arrangements of tense and mood. 

 Here the very genius of the language seems to require that 

 freedom from forms which is a marked feature in the character 

 of those who employ it. The simple truth is, that the forms of 

 the English verb are reducible to three, namely, sleep, sleeping, 

 slept. Of these three the first is either a noun verbally used, 

 that is, converted into a verb by the pronouns I, ive, etc. ; or in 

 what is called the infinitive mood, or, in its abstract form, it is 

 very like a noun. We have then the noun sleep, used ab- 

 stractedly as an infinitive, and used also affirmatively as a verb, 

 with the aid of the personal pronouns. This form sleep passes 

 into sleeping, which is called a present participle, and which 

 too is often used as a noun. The only part which has and 

 retains an exclusively verbal force is the past form slept. 

 Whatever be the nature of these three parts, certain is it that 

 of only three parts does the English verb ultimately consist. 

 Sleep, sleeping,^ slept there is the English verb. Etyraologi- 

 cally, you find in it only two tenses, one mood, and one voice no 

 future, no subjunctive, no passive. Logically, other forms are 

 possible. By combination you may make a passive voice, but by 

 combination you may make also sentences, paragraphs, chapters, 

 a volume. If, for instance, you invent a subjunctive mood, 

 why not invent a, potential? and if you invent a potential mood, 

 why not invent an optative as in Greek ? The ideas involved in 

 classical moods and tenses can be expressed in English ; but in 

 grammar we seek for set forms, not possibilities of expression. 

 And if you make use of may to form a potential mood, why not 

 make use of let to form a permissive mood, and must to form a 

 compulsory mood ? And even if you so far gave reins to in- 

 vention, you would find that instead of exhausting the subject 

 by analysis, you had only brought on yourself difficulties which 

 analysis could not solve nor classification arrange; for might, the 

 past form of may, differs from may in signification, and should 

 does not in meaning analogically follow shall. Indeed, any 

 attempt to compass the almost unlimited powers of the English 

 verb within the narrow and stereotyped limits of a system of 

 moods and tenses, is as futile as it is unwise. 



LESSONS IN LAND-SURVEYING. I. 



THE lessons upon Mensuration which have preceded this have 

 not been framed with any idea of treating the subject exhaus- 

 tively. Our object has been to embrace only those problems 

 which will prove of use in their application to land-surveying, and 

 to omit such as are in this view purely interesting. 



It will be as well to introduce our subject by a brief notice of 

 the instruments commonly employed in surveying. These have 

 been constructed with the view of giving effect practically to one 

 or other of the problems we have already introduced. The 

 Guntor's chain has been alluded to. It forms the indispensable 

 companion of the land-surveyor. By its use lineal measurements 

 are with facility reduced to superficial areas. Its length is 66 

 feet. This is equivalent to 4 poles, 160 of which in square 

 measure equal one acre. Consequently, as there are 100 links in 

 a chain, 100 X 100 = 10,000 square links =4 X 4 = 16 square 

 poles, and ten times each of these products shows us that 

 100,000 square links = 160 square poles = 1 acre. 



The construction of the chain has been explained, and as 

 from frequent use the links either open or become elongated, the 

 chain is not always correct in its measurement. It should, there- 

 fore, be periodically tested. The error will, of course, always be 

 found to be an excess of length ; hence one or more links or rings 

 must be taken out according to the extent of error. 



In using the chain care must be taken that it is fully ex- 

 tended. An upward jerk of the hand so as to produce a wave in 

 the chain, whilst at the same time a moderate strain is kept 

 upon it, will generally suffice to rid it of locks in the links and 

 entanglements on the ground, and it will then lie evenly between 

 its extremes. Its direction is always controlled by the man at 

 the back or starting end, and it must be carefully directed in 

 the exact line of the point it is intended ultimately to arrive at. 



The instrument of next importance to the chain is the cross- 

 staff, or some substitute for it, its use being to erect one line 

 perpendicular to another. 



It will be seen by reference to Problem X. that the area of a 

 triangle can be ascertained if the base and altitude be known. 

 Now the chain will give us the lengths of both the base and the 

 altitude, but it is by the cross-staff that the point where the per- 

 pendicular diverges from the base is found. 



The ordinary cross-staff consists of a piece of hard wood fixed 

 on the top of a staff, and having two very narrow slits or saw- 

 cuts in it at an exact right angle with each other. Upon the 

 accuracy of the cuts, and upon their fineness, depends its 

 reliability. If the cuts are wide the field of view is wide, and it 

 then becomes difficult to determine by the judgment what is the 

 centre of that field ; the slit should therefore be so narrow that 

 the eye can only just penetrate it. The mode of using the cross- 

 staff is readily explained. 



Suppose it is desired to erect a perpendicular upon tha line 



Fig. 1. 



B 



A B (Fig. 1) at such a point as 

 that it shall pass through the 

 point C, which may be regarded as 

 the vertex of the triangle ABC. 

 The staff is carried along the line 

 A B, and when the observer judges he is near the point D, from 

 which D c will be perpendicular to A B, he plants the staff in the 

 ground vertically, and adjusts one of the slits, so that he 

 can see both the points A and B through it. Then, without 

 moving it, he looks through the other, or cross slit, towards c. 

 If his eye observes the point c fairly in the middle of the field of 

 view, he has placed the staff on the point whence to measure the 

 perpendicular c D. If not, he must move it either backward or 

 forward until he hits upon the point D. This, after a very little 

 experience, he will quickly do. Having thus ascertained the length 

 of A B and c r> in links, the area of the triangle is at once found. 

 EXAMPLE 1.- -Suppose A B = 725 links, and c D 432 



432 

 links. Then 725 X -g- = 156,600 square links; and as 100,000 



square links = 1 acre, we have 



156,600 ^ 100,000 = 1-566 acre 



4_ 



2-264 roods 



_40_ ; 



10-560 poles 

 The area is therefore 1 acre 2 roods 10'56 poles. 



