334 



THE POPULAR EDUCATOR. 



which is the ordinary position in which the instrument is em- 

 ployed. The telescope, its level, the arc to which it is fixed, 

 the pivot on which it and tho arc moves, and the supports on 

 which the pivot rests, may be regarded as forming one part of 

 the entire instrument. 



The whole of this part is now fixed upon a horizontal circular 

 plate which turns horizontally upon another plate beneath it. 

 The edges of these two plates meet on a slope, and are also 

 accurately divided ; the lower one into degrees and half degrees; 

 the upper or vernier plate, as it is termed, into two opposite 

 verniers. Two spirit-levels arc fixed upon the upper plate, 

 at right angles to each other. 



This combined arrangement forms the theodolite proper, and 

 is connected with a series of levelling screws below, the whole 

 being attached to a brass cap fitted by well-made hinges to 

 the top of a tripod. 



In the field of the telescope are placed exceedingly fine 

 lines, either of gossamer web or platinum wire, at right angles 

 to each other, the point of intersection being in the optical 

 axis ; by means of these the axis of the glass can be brought 

 to bear very accurately upon a small distant object. 



The vernier plates above alluded to are short scales, differing 

 slightly in the length of the divisions from tho length of tho 

 divisions on the lower plate, the difference being in the pro- 

 portion of 11 to 10 ; and their use is to obtain a greater degree 

 of accuracy in estimating the length of the arc through which 

 the upper plate has moved as compared with the lower. The 

 coincidence of a division on the vernier with one on tho lower 

 scale indicates what the reading to the third place of decimals 

 is to be. The lines are extremely fine, and the coincidence can 

 only be accurately defined by the use of a magnifying glass, 

 two of which are attached to a theodolite, one to take off hori- 

 zontal readings, and one vertical readings. 



There are two clamping screws in connection with the hori- 

 zontal plates one to bind the two plates together, tho other 

 to fix the lower plate to the cap. 



From the description we have given, the reader will have 

 but little difficulty in following our description of the manner 

 in which the instrument is used. 



The first thing to be done is to adjust the legs of the tripod 

 so as approximately to level the circular plates, without much 

 inequality in the position of the levelling screws. This being 

 done, the levelling screws can be used to ensure a perfect level. 

 Having brought the bubble of both levels to the centre of the 

 glass tube, loose the lower clamping screw, and move the 

 plates round through 180 ; if tho bubbles still remain central, 

 the instrument is levelled. Next level the telescope. The 

 instrument is now ready for use. 



Carefully bring the arrow of the vernier plate into concidence 

 with 360, or zero, on the lower plate, and clamp the two plates 

 together. Now turn the whole instrument horizontally until 

 the cross wires in the field of view exactly intersect some small 

 but well-defined distant object an upright rod, for instance. 

 This done, tighten the lower clamp. Then unclamp the upper 

 plate, and turn the telescope round until the cross wires inter- 

 sect some other well-defined object, and re-clamp the upper plate. 

 Now bring the microscope to bear upon the vernier plate, and 

 read off the number of degrees, minutes, etc., at which the 

 lines coincide. This number will show the angle through which 

 the telescope has turned since it rested upon the first object. 

 In other words, you have ascertained what is the angle formed 

 by two straight lines converging from the two distant objects 

 and meeting in the centre of the theodolite. 



The reader will remember the uses to which angles were 

 applied in the measurement of lines and surfaces in our Lessons 

 on Mensuration, and it would be superfluous to enlarge upon 

 the immense use of an instrument such as we have described, 

 by which these angles can be correctly measured. Of course 

 considerable practice will be required to render the student' pro- 

 ficient in the use of the theodolite, and to ensure perfect accu- 

 racy in the readings, it will be found of advantage to double, 

 triple, and even quadruple the angle observed, and to take the 

 mean. 



An angle is taken vertically by using only the telescope and 

 the arc attached to it. The centre division of the arc, or zero, 

 is adjusted to the arrow of the vernier attached, and clamped, 

 and the telescope levelled. Bring the cross wires to bear upon 

 the given object, then unclamp, and raise or depress the telescope 



until the second object is intersected by the cross wires. Clamp 

 the arc and observe the reading. This will give the vertical 

 angle required. 



Our description of surveying instruments might include 

 several others, as, for instance, the optical square, !>y which 

 perpendiculars of greater length than those usually set off by 

 tho cross-staff can be more accurately arranged ; the prismatic 

 compass, an instrument for measuring horizontal angles with 

 great facility, but without that extreme accuracy obtained by 

 the theodolite ; the pantagraph, a most useful instrument 

 for reproducing plans upon either the same scale, a larger, or 

 a smaller ; the protractor, an instrument for laying down 

 upon paper the angles measured on the field. 



Wo think, however, that in the brief outline we have given 

 of the subject sufficient has been explained to give the student 

 a fair insight into it; indeed, if he has rightly followed our 

 remarks, he will have gained sufficient knowledge of it to render 

 a more minute investigation easy. 



Our concluding lesson will ccntara a more full and compre- 

 hensive field-book for practice than we have hitherto given. 



KEY TO EXERCISES IN LESSONS IN LAND-SURVEYING. I. 

 1. 62 acres, roods, 99 poles. | 2. 3 acres, 2 roods, 7'6 poles. 



LESSON'S IN GERMAN. LX. 



68. VERBS. 



(1.) A verb is that part of speech which defines tho condition 

 of a subject ; that is, shows whether it acts, is acted iipon, or 

 merely exists. 



(2.) In respect to form, verbs are either regular or irregular, 

 simple or compound. 



(3.) In respect to meaning, verbs are active transitive, active 

 intransitive, passive, neuter, reflective, or impersonal. These 

 terms have in German tho same general signification which they 

 have in English. 



(4.) The German, like the English verb, has its moods, tenses, 

 numbers, persons, and participles. 



(5.) There are five moods ; viz., the indicative, the subjunc- 

 tive, the conditional,* the imperative, and the infinitive. 



(6.) There are six tenses ; viz., tho present, the imperfect, 

 the perfect, tho pluperfect, the first future, and the second 

 future. 



(7.) Both moods and tenses designate in German just the 

 same things which the corresponding ones do in English. For 

 their general signification, see the paradigms ; and for explana- 

 tion of their uses, see the Syntax. 



69. PARTICIPLES. 



(1.) There are three participles ; viz., the present, which ter- 

 minates in ent>, and answers in signification to the English par- 

 ticiple in ing ; as, lofienfc, praising. 



(2.) The perfect, which, besides prefixing in most cases the 

 augment gc, ends, in verbs of the Old Form, in en or n ; and in 

 those of the New Form, in et or t; and has a meaning correspond- 

 ing to our participle in ed ; as, getragcn (ge + trag-f- en), carried; 

 gelo&t (ge + leb + t), praised. 



(3.) The future, which is ' produced by prefixing the particle 

 311 (to) to the form of the present participle (lobcnb) ; thus, 311 

 tobenb, which means to be praised, that is, praiseworthy. 



(4.) The particle ge, mentioned above as being generally pre- 

 fixed to the perfect participle, was originally designed, it would 

 seem, to indicate completed action. The instances in which it 

 is altogether omitted are these : 



First : in the case of all verbs compounded with inseparable 

 prefixes (see 94) ; as, bdetyrt (not gebeldjrt), informed. 



Second : in the case of verbs from foreign languages, which 

 make the infinitive in iren or teren; as, fiubtvt (from ftisbircn), 

 studied; instead of gcfhtfcirt. 



* The conditional is made up of the imperfect subjunctive of the 

 auxiliary verb n>erben (which see), and the present and perfect infini- 

 tive of another verb. It is used to denote what is also often denoted 

 by the subjunctive (imperfect and pluperfect), namely, a supposed con- 

 dition of things, i.e., possibility without actuality. By some it is treated 

 as a distinct mood ; by others, it is made to consist of two tenses : its 

 use is the same in both views. 



