with Dairyman Peters, near the bridge of Aughahall, about three miles east of Bansha. I remained two years with Mr. Cox, and then bade farewell to hospitable and learned Munster, where, with a few exceptions, all the great mathematical and classical schools were kept, until the samine plague of 1848 broke them up. I next found myself in Athleague County, Roscommon, with Mr. Mathew Cunnill, who was an excellent constructor of equations, and showed the application to the various arts. I received my diploma as certified Land Surveyor on the sixth of September, 1836, after a rough examination by Mr. Fowler, in the theoretical, and William Longheld, Esq., in the practice of surveying. I soon got excellent practice, but wishing for a wider field of operation, for surther information, I joined the Ordnance Survey of Ireland. Worked on almost every department of it, such as plotting, calculating, registering, surveying, levelling, examining and translating Irish names into English. Having got a remunerative employment from S. W. Parks, 1sq., land surveyor and civil engineer, in Ipswich, County of Suffolk, England. I left my native Isle in April, 1838. Surveyed with Mr. Parks in the counties of Suffolk, Norfolk, and Essex, for two years, then took the field on my own account. I left happy, hospitable, and friendly England in April, 1842, and sailed for Canada. Landed in Quebec, where I soon learned that I could not survey until I would serve an apprenticeship, be examined, and receive a diploma. I sailed up the St. Lawrence and Ottawa Rivers to Bytown,-then a growing town in the woods, —but now called Ottawa, the seat of the Gov. ernment of British America, I engaged as teacher in a school in Aylmer, nine miles from Bytown (now Ollawa). At the end of my term of three months, I joined John McNaughton, Esq., land surveyor, and justice of the peace, until I got my diploma as Provincial Land Surveyor for Upper Canada, dated December 16, 1843, and my diploma or commission for Lower l'anada, dated September 12, 1844. I spent my time about equally divided between making surveys for the Home (British) Goverment four years, and the Provincial Government, and private citizens, until I lest Bytown in September, 1849, having thrown up an excellent situation on the Ordnance Department. I never can forget the happy days I have been employed on ordnance surveys in Ireland, under Lieutenants Brougton and Lancy. In Canada, under the supervision of Lieutenants White and King, and Colonel Thompson, of the Royal Engineers. In my surveys for the Provincial Government of Canada, I. always fomd llon. Andrew Russell and Joseph Bouchette, SurveyorGenerals, and Thomas Devine, Esq., Head of Surveys, my warmest friends. They are now-October 7, 1878- living at the head of their respective old Departments, having lived a long life of usefulness, which I hope will be prolonged. To Sir William Logan, Provincial Geologist, I am indebted for much information. I lived nearly cight years in Ottawa, Canada, where my friends were very mumerous. The dearest of all to me was Alphonso Wells, Provincial Land Surveyor, who was the best surveyor I ever met. Ile had been so badly frost-bitten on a Government survey that it was the remote cause of his death. On one of my surveys, far North, I and one of my men were badly frostbitten. Ile diul shortly after getting home. I lost all the toes of my left foot and seven fingers, leaving two thumbs and the small finger on the a ngn hand. After the amputation, I soon healed, which I attribute to my strictly temperate habits, for I never drank spirituous liquor nor used that narcotic weed-tobacco. In Sept., 1849, I left the Ordnance Survey, near Kingston. Having surveyed about 120 miles of the Rideau Canal, in detail, with all the Gov. ernment lands belonging to it. On this service I was four years employed. I came to the City of Milwaukee, September, 1849; could find no survey. ing to do. I opened a school, October 1. Soon gathered a good class, which rewarded me very well for my time and labor. Here I made the acquaintance of many of the learned and noble-hearted citizens of the Cream City— Milwaukee, amongst whom I have found the popular Doctors Johnson and Hubeschman; I. A. LAPIAM; Pofessor Buck; Peters, the celebrated clock-maker; Byron Kilbourne, Esq.; Aldermen Edward McGarry, Moses Neyland, James Rogers, Rosebach, Furlong, Dr. Lake; John Furlong, etc., etc. I found extraordinary friendship from all Americans and Germans, as well as Irishmen. I was appointed or elected by the City Council, in the following April, as City Engineer, sor 1850 and part of 1851. I was reappointed in April, 1851, and needed but one vote of being again elected in 1852. I made every exertion not to have my name brought up for a third term, because, in Milwaukee the correct rule, " Rotation in office is true democracy,” was adhered to. In accordance with a previous engagement, made with Wm. Clogher, Esq., many years City Surveyor of Chicago, I left Milwaukee with regret, and joined Mr. Clogher, as partner, in April, 1852, immediately after the Milwaukee election. Worked together for one year, and then pitched my tent here since, where I have been elected City Surveyor, City Supervisor, and had a hand in almost is not all the disputed surveys that took place here since that time. I have attended one course of lectures on chemistry, in Ipswich, Eng. land, in 1840, and two courses at Rush Medical College, under the late Prof. J. V. 2. Blaney, and two under Dr. Mahla, on chemistry and pharmacy. By these means, I believe that I have given as much on the subject of analysis as will enable the surveyor or engineer, after a few days application, to determine the quality and approximate quantity of metal in any ore. To the late Sir Richard Griffith, I am indebted for his “Manual of Instructions," which he had the kindness to send me, May 23, 1861. He died Sept. 22, 1878, at the advanced age of 94 years; being the last Irishman who held office under the Irish Government, before the Union with England. He was in active service as surveyor, civil engineer, and land valuator almost to the day of his death. The principles of geometry and trigonometry are well selected for useful applications. The sections on railroads, canals, railway curves, and tables for earthwork are numerous. The Canada and United States methods of surveying are given in detail, and illustrated with diagrams. Sir Richard Griffith's system of valuation on the British Ordnance Survey, and the various decisions of the Supreme Courts of the United States are very numerous, and have been sometimes used in the Chicago Courts as authority in surveys. Hydraulics, and the sections on building walls, dams, roofs, etc., are extensive, original, and comprehensive. The sections and drawings of many bridges and tunnels are well selected, and their properties examined and defined. The tables of sines and tangents are in a new form, with guide lines at every five min a minutes. The traverse table is original, and contains 88 pages, giving latitude and departures for every minute of four places, and decimals, and for every number of chains and links. The North and South polar tables are the results of great labor and time. The table of contents is full and explicit. I believe the surveyors, engineers, valuators, architects, lawyers, miners, itavigators, and astronomers will find the work instructive. I commenced my traverse table, the first of my Manual, on the 15th of October, 1833, and completed my work on the 8th of October, 1878. The oldest traverse table I have seen was published by D'Burgh, Surveyor General, in Ireland, in 1723, but only to quarter degrees and one chain distance. The next is that by Benjamin Noble, of Ballinakil, Ireland, entitled “Geodesia Hibernica,” printed in 1768, were to 4 degrees and 50 chains. The next, by Harding, were to 4 degrees and 100 chains. In my early days, these were scarce and expensive; that by Harding, sold at two pounds two shillings Sterling, (about $10.50). Gibson's tables, so well known, are but to 4 degrees and one chain distance. Those by the late lamented Gillespie, were but to 4 degrees, three places of decimals, and for 1 to 9 chains. Ilence appears the value of my new traverse table, which is to every minute, and can be used for any required distances. Noble gave the following on his title-page: “Ye shall do no unrighteousness in meteyard, in weight, or in measure. Leviticus, chap. xix, 35; “Cursed be he that removeth his neighbor's landmark.” Deuteronomy, chap. xxvii, 17. I lost thirty-two pages of the present edition of 1000 copies in the great Chicago fire, Oct. 9th and roth, 1871, with my type and engravings; this caused some expense and delay. The Manual has 524 pages, strongly bound, leather back and corners. MICH'D MCDERMOTT. GENERAL INDEX. Section. Square. Area, diagonal, radius of inscribed circle, radius of the circumscribing circle, and other properties,... 14 Rectangle or parallelogram, its area, diameter, radius of circumscribing circle. The greatest rectangle that can be inscribed in a semicircle. The greatest area when a = 2 b. Hydraulic mean depth. Stiffest and strongest beams, out of OF THE TRIANGLE. Areas and properties by various methods, 23 To cut off a given area from a given point, 38 To cut off from P, the least triangle possible, 41 To bisect the triangle by the shortest line possible, 43 The greatest rectangle that can be inscribed in a wiangle, 44 The centre of the inscribed and circumscribed circles, . Various properties of, . . . . 52 Strongest form of a retaining wall, 58 OF THE CIRCLE. Areas of circles, circular rings, segments, sectors, zones, and lunes,.. 60 Hydraulic mean depth,. 77 Inscribed and circumscribed figures, 78 To draw a tangent to any point in the circumference, 87 To find the height and chorl of any segment, 137 To find the diameter of a circle whose area, -, is given, 141 Important properties of the circle in railway curves and arches, . 78 OF THE ELLIPSE. How to construct an ellipse and find its area, 8, 115 Various practical properties of, 89 Segment of. Circumference of, 116 PARABOLA. 20 Construction of, 123. Properties, 124. Tangent to, 128. Area, 1:29. Length of curve, 130. Parabolic sewer, 133. Example, 33. Remarks on its use in preserence to other forms, 134. Essa shaped, 140. Hydraulic mean depth, 136. Perimeter, 139 Artificers' works, measuremerit of, ... 310x9 PLAIN TRIGONOMETRY--HEIGHTS AND DISTANCES. Right angled triangles, properties of,, 148 The necessary formulas in surveying in finding any side and angle,. 17lb Properties of lines and angles compared with one another,.... 194 Given two sides and contained angle to find the remaining parts, 203 Given three sides to find the angles, Heights and distances, chaining, locating lots, villages, or towns, 211 How to take angles and repeat them for greater accuracy, . 212 How to prove that all the interior angles of the survey are correct,.. 213 To reduce interior angles to quarter compass bearings, . 204 To reduce circumferentor or compass bearings to those of the quarter compass, 214 How to take a traverse survey by the English Ordnance Survey method, 2:6 De Burgh's method known in America as the Pennsylvanian), 217 Table to change circumferentor to quarter compass bearings, 218 To find the Northings and Southings, Eastings and Westings, by commencing at any point, 219 a Section. Inaccessible distances where the line partly or entirely is inaccessible, 221 This embraces fourteen cases, or all that can possibly be met in practice. I'rom a given point P to find the distances PA, 1 B, PC,... in the triangle A BC, whose sides AB, BC, anci C D are given, this embraces three possible positions of the observer at P', 238 SPIIERICAL TRIGONOMETRY. Properties of spherical triangles. Page 7211*9, 34.5 Solution of right angled spherical triangles, 302 Napier's rules for circular parts, with a table and examples, 303 Quadrantal spherical triangles, 364 Oblique angled spherical triangles, 36.3 Fundamental formula applicable to all spherical triangles, 366 Formulas for finding sides and angles in every case, 367 SPHERICAL ASTRONOMY. Definitions and general properties of refraction, parallax dip, greatest azimuth, refraction in altitude, etc., etc., 375 Find when a heavenly body will pass the meridian, 376 l'ind when it will be at its greatest azimuth, . 384 Find the altitude at this time, 384 Find the variation of the compass by an azimuth of a star 383 Find latitude by an observation of the sun, 377 Fin: latitude when the celestial object is off the meridian, 378 Find latitude by a double altitude of the sun, 379 Find latitude by a meridian alt, of polaris or any circumpolar star, 380 Find latitude when the star is above the pole, 38) Find latitude by the pole star at any hour, . 382 Trrors respecting polaris and alioth in Ursamajoris when on the same vertical plane. Mote.). 389 Letters to the British and American Sautical Ephemeris offices, 389 Application and examples for Observatory House, corner of Twenty. sixth and Halsted streets, Chicago. Lat. 41°, 50', 30". Long. 87, 34', 7", W.,.... : 8 Remarkable proof of a Supreme Being Page 7211*24, 386 True time; how determined; example, . 387 True time by equal altitudes; example. Page 7.24*2), 390 True lime bv a horizontal sundial, showing how to construct one, .390* Longitude, difference of,... 392 Longitude by the electric telegraph, 39: Longitude; how determined for Quebec and Chicago, by Col. Craliam, U. S. Engineer. 393 Longitude by the heliostat. Page :21*30, . 393a Longitude by the Drummond light and moon culminating stars, 394 Longitude by lunar distances; Young's method and example, . :95 Reduction to the centre, that is reducing the angle taken near the point of a spire or corner of a public building, to that is taken from the centre of these points; by two methods, 24 Inaccessible heights. When the line A B is horizontal, 246 When the ground is sloping or inclined, three methods, 249 TRAVERSE SURVEYING. Methods of. Sec. 213 to 217 and 23.3 To find meridian distances, 237 Method I. Begin with the sum of all the East departures, 258 Method II. First meridian pass through the most Westerly station,. 239 Method III. First meridian pass through the most Northerly station, 260 Offsets and inlets, calculation of, 261 Ordnance method of keeping field-books, 02 Supplying lost lines and bearings (Four cases.). 263 To find the most Westerly station, 20+ To calculate an extensive surve where the first meridian is made a base line, at each end of which a station is made, and calculated by the third method, 264 CANADA SURVEYING. Who are entitled to survey, 301 a |