: 1§| ;^hr: ■ 7>/7 ;•- : --■*» m - - --•'. .1' ,' * i, !rf * agis- Mi?: v ••• V.v- -% '. ... *%■-, f m f' ■ .. v ■ " , '.v ; 1 ■'. • •. • ' ■: A 2 .1 ; . '•?' . \ . •\1. - ■ ■ • . ■ V ' . :\ *jS V •• 1 jV-;?' . ' ;f ~ .v ' /- 7 .•,: * •' • Ufa; C-'-^i^yy r'~• 7 ■“7*'C7?>' .fit • V-•; . I \x- S->- • • • •..■ - • •-. - • • >'.^n ..._V •. - • ; '.7*-‘: -' .r.f--’, ' ' '• r*sWik' * v=.. v \-r- Sp'&'cAi '.'7 . ■-■ ■ 15,?: v -77 -.*■ 7>; ” v # .' • v’V&V*,‘ • •• A TREATISE . •! ■^77' .. V j • I* •.' • -: . ?• r 7 - 7 > ON THE ■ ' r. V . ''S'-vL" *.-»■■!! ! , ' PRINCIPAL MATHEMATICAL INSTRUMENTS i • i• • .. ' USED IN SURVEYING, LEVELLING, AND ASTRONOMY, fyc. Sf€. Price Five Wk 77'J ; t!. ... ^ V/': : -. A .««:r if • •••■<• pig|«|i^Kv-:; ^ « ;7;,*1 : ' i- ■7 •' • •; • '••' •' ' A TREATISE ON THE PRINCIPAL M AT II EM ATI C A L INSTRUME NTS, EMPLOYED IN SURVEYING, LEVELLING AND ASTRONOMY, Sfc. Sfc. Digitized by the Internet Archive in 2018 with funding from Wellcome Library f https://archive.org/details/b29298854 A TREATISE ON THE PRINCIPAL MATHEMATICAL INSTRUMENTS EMPLOYED IN SURVEYING, LEVELLING, AND ASTRONOMY: EXPLAINING THEIR CONSTRUCTION, ADJUSTMENTS, AND USE. WITH AN aittr Cafclrsc -- BY FREDERICK W. SIMMS, ASSISTANT AT THE ROYAL OBSERVATORY, GREENWICH, AND FORMERLY EMPLOYED ON THE ORDNANCE SURVEY. LONDON: PRINTED BY T. BENSLEY, CRANE COURT, AND SOLD, FOR THE AUTHOR, BY MESSRS. TROUGHTON AND SIMMS, 136, FLEET STREET. 1834. iEntcretr at stationers’ P?atL PR E F A C E. rn I he want of a work containing a concise and popular description of the principal Instruments used in Practical Astronomy and Surveying has long been felt, as the requi¬ site information with respect to such instruments can only be obtained by consulting various expensive publications, which are not within the reach of many to whom such information is highly interesting and important. It was the original object of the writer of this little tract, to place at the disposal of the young surveyor a description of the instruments which are required in his profession, and such an account of the method of examining and rectify¬ ing their adjustments, as would enable him to obtain from them the most accurate results ; but he found that, without greatly increasing the size of the book, he might materially add to its utility, by including in his plan the most approved Astronomical Instruments, that amateur astrono¬ mers as well as scientific travellers might have at hand a manual of instructions, which would enable them to use their instruments with the utmost advantage. Usefulness being the author’s chief object, he has not scrupled to extract from the works of others whatever he found adapted to his own purpose; and to some kind lite¬ rary and scientific friends he is under obligations, for which, if he had obtained their permission, he would be glad to thank them by name in this place. Of Surveying Instruments, those only have been de¬ scribed which are applied in modern practice, no reference VI being made to those which, having been superseded by better ones, may be said to be out of use. To the article on Levelling has been added a description of Mr. Troughtqn’s Improved Mountain Barometer, with an easy and accurate method of computing differences of level from barometrical observations. Table II. employed for this purpose, has been carefully recomputed from Mr. Baily’s Formulae. The other tables will, for their several purposes, be found convenient and useful. Tables I. and vin. are new. Much attention has been paid to the accuracy of the formulae given for performing the various computations, and each has been thrown info the form of a practical rule, that persons unacquainted with algebraic notation may be enabled notwithstanding to make the requisite calculations. With respect to such astronomical problems as appertain chiefly to Navigation, and require extensive and special tables for their convenient solution, it has been thought better to omit all reference to them in this work, as in Mr. Riddle’s Treatise on Navigation, Captain Thompson’s Lunar and Horary Tables, and other similar works, all ne¬ cessary information on the subject may be readily obtained. The Appendix relates chiefly to the protraction of the work after a survey has been completed, and seems a suit¬ able supplement to the account of Surveying Instruments given in the preceding part of this treatise. C 0 N T E N T S. SURVEYING INSTRUMENTS. The Land Chain.Page 1 The Surveying Cross and Optical Square. 2 The Prismatic Compass... 3 The Vernier. 4 The Theodolite... 7 Adjustments of the Theodolite. 10 Method of observing with the Theodolite. 14 The Plane Table. lb Method of using the Plane Table. 19 LEVELLING INSTRUMENTS. The Y Spirit Level. 21 Adjustments of the Y Level. 22 Troughton’s Improved Level. 23 Adjustments of Troughton’s Improved Level. 25 The Method of determining Distances by a Micrometer Scale 26 Levelling Staves.!. 26 Troughton’s Levelling Staves. 27 On Levelling. 28 „ With the Spirit Level. 29 ,, With the Theodolite. 30 Description of the Mountain Barometer... 31 Levelling with the Mountain Barometer... 32 ASTRONOMICAL INSTRUMENTS. The Sextant . 55 The Principle of its Construction. 34 Description of the most approved Sextant. 55 Adjustments of the Sextant. 36 Method of Observing with the Sextant. 39 Troughton’s Reflecting Circle. 41 Directions for observing with the Reflecting Circle.. 44 The Box Sextant.:. 44 Adjustments of the Box Sextant. 46 The Artificial Horizon. 46 Roof Horizon... 47 Plane Glass Horizon. 47 The Dip Sector. 48 Method of observing with the Dip Sector ... 50 VI11 The Portable Transit Instrument.Page 51 The Adjustments of the Transit Instrument. 55 Methods of determining the Meridional Deviation of Transit. 55 by a Circumpolar Star. 55 by two Circumpolar Stars. 56 by High and Low Star... 58 Method of observing and registering Observations. 59 Finding the Error of a Time-Keeper. 62 Correcting observed Transits for the Error of Collimation. 64 ,, ,, for Error of Level. 65 ,, ,, for Meridional Deviation. 66 Method of Determining the Longitude by Observed Transits of the Moon and Moon Culminating Stars. 67 Professor Bessel’s Method of finding the Latitude with a Transit Instrument... 70 The Altitude and Azimuth Instrument. 71 The Adjustments of the Altitude and Azimuth Instrument. 74 Description and Adjustments of the Reading Microscope. 76 Use of the Altitude and Azimuth Instrument. 78 To compute the Reduction to the Meridian. 79 To determine the Latitude of a Place. 80 Method of Observing equal Altitudes and Azimuths. 81 Determination of Time by equal Altitudes. 82 ,, the True Meridian by equal Azimuths. 85 ,, ,, by a Circumpolar Star. 85 ,, ,, by the Azimuth of a Celestial Object. 86 Method of finding Differences of Latitude and Longitude by Trigonometrical Measurement. 87 Method of finding the Longitude by the Eclipses of Jupiter’s Satellites. 88 APPENDIX. On the Protraction of Angles. 89 Method of performing and plotting a Road Survey... 91 Description of the best Circular Protractor. 95 Plotting Scale. 97 Station Pointer, &c. 98 TABLES. 1. To Reduce the Apparent to the True Level. II. For determining Altitudes with the Barometer. III. For Converting Intervals of Sidereal into corresponding Intervals of Mean Solar Time. IV. For Converting Intervals of Mean Solar into corresnonding Intervals of Sidereal Time. V. & VI. For Computing the Longitude from the Observed Transits of the Moon and Moon Culminating Stars. VII. For Computing the Reduction to the Meridian. VIII. The Length of a Second of Longitude and Latitude in Feet, for different Latitudes. A DESCRIPTION OF THE PRINCIPAL INSTRUMENTS EMPLOYED IN SURVEYING, LEVELLING, # ASTRONOMY, WITH THEIR ADJUSTMENTS AND USE. SURVEYING INSTRUMENTS. THE LAND CHAIN. Gunter’s Chain is the one now commonly used in taking the dimensions of land; it is sixty-six feet, or four poles, in length, and is divided into 100 links, each of which is joined to the next by three rings ; the length of each link, including the connecting rings, is 7,92 inches, and at the end of every tenth link is attached a piece of brass (each of a different shape,) for more readily count¬ ing the odd links. “ The English acre contains 4840 square yards, and Gunter’s chain is 22 yards in length, and the square chain, or 22 multiplied by 22, gives 484, exactly the tenth part of an acre; and ten square chains are equal to one acre; consequently, as the chain is divided into 100 links, every superficial chain contains 100 multiplied by 100, that is 10,000 square links ; and 10 superficial chains, or one acre, contains 100,000 square links. " If therefore the content of a field, cast up in square links, be divided by 100,000, or, (which is the same thing) if from the con¬ tent we cut off the last five figures, the remaining figures towards the left hand give the content in acres, and consequently the num¬ ber of acres at first sight; the remaining decimal fraction, multi¬ plied by 4, gives the roods, and the decimal part of this last product, multiplied by 40, gives the poles or perches.” Short distances, or off-sets from the chain line, are usually mea¬ sured with a rod, called an off-set staff, the most convenient length for which is 6 feet 7,2 inches, being equal to 10 links of the chain, and it should be divided accordingly. With the chain must be provided ten arrows, which may be made of strong iron wire, about 12 or 15 inches long, pointed at one end for piercing the ground, and turned up at the other, in the form of a ring, to serve as a handle: their use is to fix in the ground at each extremity of the chain whilst measuring, and to point out the number of chains measured.