THE 



317 



THE 



tude of the place, and the vertical circle may be increased 

 accordingly. 



It is perhaps requisite to give some description of 

 the mode of adjusting the vertical circle. Where the 

 supports are high enough to allow the telescope to 

 pass when turned round in a vertical plane, all the ad- 

 justments are the same as in the altitude and azimuth 

 circle. [CIRCLE.] When the telescope is too long for this, 

 the circle must be lifted out of its Y's in order to bring 

 the line of sight again upon the object to be bisected, 

 and then set down again. The operation is in fact the 

 same, whatever be the nature of the vertical arch, and the 

 adjustment is to be effected either by altering the level or 

 the horizontal wire until the reading is the same in both 

 positions of the telescope. If the observer has a Y level 

 or collimator, he can set the cross of his level-wires hori- 

 zontal, and this being bisected by the telescope of the 

 theodolite, the vernier must be made to read zero, and the 

 bubble of the level be brought to the middle by its proper 

 screws. Or if the observer possess two stands (and there 

 is a great convenience in having more stands than one in 

 surveying), he may place the stands at a considerable dis- 

 tance" from each other, and, fixing the instrument on one 

 stand and a mark of exactly the same height as the tele- 

 scope-axis on the other, observe the mark, noting its eleva- 

 1ion or depression. Now exchanging the instrument and 

 mark, he must reobserve the depression or elevation exactly 



lore. On drawing the figure, it will be seen that if li^ht 

 move in a straight line, 90 elevation at lower station=90 

 depression at higher station + the angle between perpen- 

 diculars to the earth's surface at each station, which last 

 quantity is known from the distance between the stations, 

 and may l>e easily calculated, i.e. depression elevation =r a 

 known "angle. But if the zero is wrong, depressions will 

 be increased while elevations are diminished, and versd 

 ricf, so that depression observed elevation observed 

 the known angle, instead of being = 0, will be 2 

 error of the vernier, which may be corrected accordingly 

 either by the adjustment of the level or of the horizontal 

 wire. Or, lastly, if the telescope has so much motion as 

 that a star can be observed directly and by reflexion from 

 mercury or any other fluid, the index-error of the vertical 

 circle may be most accurately determined thus. Take any 

 star in the meridian, and having observed it directly, ob- 

 serve it immediately after by reflexion. If great nicety 

 is required, the observations should be repeated alternately 

 several times, and the partial results reduced to the 

 meridian. The mean reading between the meridian 

 altitude and meridian depression is the reading which cor- 



nds to the horizon, and the difference of this from 0, 

 in- HO", according as the circle reads altitudes or zenith dis- 

 tances, is the error of the instrument, which may either be 

 corrected or allowed for. This method, though very ac- 

 curate, requires some knowledge of the time, and is rather 

 restricted by the choice of stars. It is nearly as safe to 

 observe a star not far from the east or west point, first di- 

 rectly, then by reflexion, and lastly directly, making the 

 contacts at following whole minutes, or at even or odd mi- 

 nutes if the interval of a minute is not sufficient. As the 



rise nearly uniformly in this part of the heavens, the 

 mean of the first and third observations should give an 

 altitude equal to the depression observed midway; the 

 discrepancy between these results will he the double index- 

 error as before, which may lie corrected or allowed for. 

 By some of these methods, the index-error of the verticle 

 circle or sector is to be found. 



In some of the older theodolites the telescope rides in 

 Y's at the top of the vertical arch, and is reversible as a 



. The horizontal position of the telescope Y's can 

 therefore be found as in any other level, and the verniers of 

 the vertical circle set to zero when the telescope is hori- 

 zontal. The vertical angles measured by these instruments 



i<>t however to he greatly depended on. They are usu- 

 ally greatly out of balance in all positions of the telescope, 



pt the horizontal position, and therefore they make 

 better levels than altitude instruments. This error may 

 be partially got rid of by having a second level fixed to 

 the ; which is parallel to the plane of the verti- 



cal circle, and adjusted to the telescope level when that 

 is hori/ontul. If this supplementary level is pretty well 

 graduated, it will show the tilt which is given the plane of 

 the instrument by want of balance, and so give the correc- 

 tion required. 



It may be as well to mention here that the principal 

 adjustment being that of setting the plane of the theodo- 

 lite horizontal, or, more correctly speaking, the principal 

 axis vertical, any horizontal level anywhere placed is 

 sufficient for the purpose, though the cross-levels are a 

 little handier. A box-level is convenient, if a stand and 

 repeating-table are used, to bring the planes nearly hori- 

 zontal, and to make both ends of the bubbles visible at first. 



Many surveyors give themselves and the instrument- 

 maker a great deal of unnecessary trouble by being very 

 difficult on the chapter of excentricity, which they con- 

 found with error of division. The English dividing- 

 engines, up to the present time, do not divide the circles 

 upon their centres ; and therefore it frequently happens 

 that the point round which the circle turns is not the point 

 round which it is divided. When this error is not abso- 

 lutely monstrous, the only effect is that one vernier gains 

 what another loses, and that the mean of two opposite, or 

 of three, four, or more equidistant readings, is precisely the 

 same as if there were no excentricity. The advantage of 

 a little excentricity is, that it gives you the benefit of an 

 unbiassed reading at every vernier as well as the first : 

 again, if all the verniers are recorded, it is a check on the 

 dishonest observer, who might read one vernier and set 

 down the rest. The instrument-maker must please his 

 ignorant customer, and so either hammer his circle after it 

 is divided, which may deform his work, or have an adjust- 

 ment, which injures its solidity. 



In Ramsden's great theodolite, and several others which 

 have been made, the circle is read off' by micrometer 

 microscopes. Sometimes the microscopes revolve with 

 the telescope (as the verniers do in our figure) ; sometimes 

 the microscopes are fixed, and the circle revolves with the 

 telescopes, as in Ramsden's theodolite. 



Ertel of Munich has made several astronomical theodo- 

 lites in which the rays entering into the telescope are re- 

 flected along the horizontal axis by a prism. The observer 

 therefore looks in at the end of the horizontal axis, what- 

 ever the position of the star may be. The eye and body 

 of the observer are more satisfactorily placed, and the sup- 

 ports are kept close and snug to the horizontal circle. 

 The instrument is well adapted to one of its principal 

 objects, observing stars at their passage over tne prime 

 vertical [TRANSIT] ; but there is some trouble in finding 

 an object when you have no better direction to look for it 

 than your eye affords. Excellent latitudes have been 

 determined by instruments of this class used in the prime 

 vertical, and even the small vertical circle seems from 

 some accounts to possess more power than from its 

 dimensions we should have thought probable. As a 

 general rule, the greater the number of readings, the less 

 the effect of bad division, but beyond a limited number, 

 the trouble and difficulty of reading-off is found in practice 

 to counterbalance the advantage. Two opposite readings 

 annul the effect of excentricity ; three or four equidistant 

 readings destroy such an error as would arise from the cir- 

 cles becoming elliptic after it was divided, or any error 

 which follows the same law. In small stoutly-made theo- 

 dolites we think two the most convenient number, and they 

 can be much more conveniently read off than a larger 

 number. When the circle is so much as 8 inches in dia- 

 meter and the telescope good, we should prefer three or 

 foui 1 readings. The vertical circle or sector may have two 

 opposite readings. For many matters connected with sur- 

 veying on the most extensive and accurate scale, see the 

 memoirs published and to come of the English, Scotch, 

 and Irish Trigonometrical Survey ; and the ' Base Me- 

 trique,' or account of the French measurement of an 

 arc of the meridian, although that survey was conducted 

 by a different instrument. Similar operations have been 

 carried on in many countries during the last half-century, 

 and the memoirs which relate to these surveys contain 

 the best information which can be had on the subject. 



THEODO'RA. [JUSTINIAN.] 



THEODORE OF CORSICA. [CORSICA.] 



THEODORE, or THEODORUS, of Mopsuestia, a 

 learned bishop of the Oriental church. He was descended 

 from a rich and distinguished family at Antioch, and was 

 1 he brother of Pol ychronius, who became bishop of Apamca. 

 He studied rhetoric, together with his friend John Chrysos- 

 tom, under Libanius, who resided at Antioch from the year 

 A.D. 3.">4. His teacher of philosophy was Andragathns. 

 After having finished his studies, he intended to marry a 



