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I have been born on the 10th day of Sep., 1810, in the village of Kilmore, near Castlekelly, in the County of Galway, Ireland. My mother, Ellen Nolan, daughter of Doctor Nolan, was of that place, and my father Michael McDermott was from Flaskagh, near Dunmore, in the same County, where I spent my early years at a village school kept by Mr. James Rogers, for whom I have an undying love through life. Of him I learned arithmetic and some book-keeping. He read arithmetic of Cronan and Roach, in the County of Limerick. They excelled in that branch. John Gregory, Esq., formerly Professor of Engineering and Surveying in Dublin; but now of Milwaukee, read of Cronan, which enabled him to publish his "Philosophy of Arithmetic,” a work never equalled by another. By it one can solve quadratic and cubic equations, the diophantine problems, and summation of series.

After having been long enough under my friend Mr. Rogers, I went to the Clarenbridge school, kept by the brothers of St. Patrick, under the patronage of the good lady Reddington. I lived with a family named Neyland, at the Weir, about two miles from the school, where I had a happy home on the sea-side. There I read algebra, grammar, and bookkeeping. After being nearly a year in that abode of piety and learning, I went to Mathew Collin's Mathematical school, in Limerick. He was considered then, and at the time of his death, the best mathematician in Europe. His correspondence in the English and Irish diaries on mathematics proves that he stood first. I left him after eight months studying geometry, etc., and went to Castleircan, near Cahirconlish, seven miles from Limerick, where I entered the mathematical school, kept by Mr. Thomas McNamara, familiarly known as Tom Mac, and Father of X, on account of his superior knowledge of algebra, he was generally known by the name of "Father of X." Of him I read algebra and surveying; lived with a gentleman farmer-named William Keys, Esq., at Drimkeen, about one and one-half iniles south-east of the school. Mr. Mac had a large school, exclusively mathematical, and was considered the best teacher of surveying. After being with him nearly a year, I left and went to Bansha, four miles east of the town of Tipperary. Here Mr. Simon Cox, an unassuming little man, had the largest mathematical class in Ireland, and probably in the world, having 157 students, gathered from every County in Ireland, and some from England. Like Mr. McNamara, he had special branches in which he excelled; these were the use of the globes, spherical astronomy, analytical geometry, and fluxions. The differential and integral calculus were then slowly getting into the schools. I lived

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 famine plague of 1848 broke them up. 1 next found myself in Athleague County, Roscommon, with Mr. Mathew Cunniff, 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 Longfield, Esq., in the practice of surveying. I soon got excellent practice, but wishing for a wider field of operation, for further 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, Esq., 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 Government of British America. I engaged as teacher in a school in Aylmer, nine miles from Bytown (now Ottawa). 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 Canada, 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 left 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 found Hon. 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 eight years in Ottawa, Canada, where my friends were very numerous. The dearest of all to me was Alphonso Wells, Provincial Land Surveyor, who was the best surveyor I ever met. He 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. He died 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

right 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 Government lands belonging to it. On this service I was four years employed. I came to the City of Milwaukee, September, 1849; could find no surveying 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. LAPHAM; 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, for 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 if not all the disputed surveys that took place here since that time.

I have attended one course of lectures on chemistry, in Ipswich, England, in 1840, and two courses at Rush Medical College, under the late Prof. J. V. Z. 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

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, navigators, 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. Hence 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 10th, 1871, with my type and engravings; this caused some expense and delay.

The Manual has 524 pages, strongly bound, leather back and corners.



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Square. Area, diagonal, radius of inscribed circle, radius of the cir-
cumscribing circle, and other properties,
Rectangle or parallelogram, its area, diameter, radius of circumscribing
circle. The greatest rectangle that can be inscribed in a semi-
circle. The greatest area when a 2 b. Hydraulic mean depth.
Stiffest and strongest beams, out of



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Areas and properties by various methods,
To cut off a given area from a given point,
To cut off from P, the least triangle possible,
To bisect the triangle by the shortest line possible,
The greatest rectangle that can be inscribed in a triangle,
The centre of the inscribed and circumscribed circles,
Various properties of,...

Strongest form of a retaining wall,

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Areas of circles, circular rings, segments, sectors, zones, and lunes,.. 60 Hydraulic mean depth,

Inscribed and circumscribed figures,

To draw a tangent to any point in the circumference,
To find the height and chord of any segment,

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To find the diameter of a circle whose area, A, is given,
Important properties of the circle in railway curves and arches,

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Construction of, 123. Properties, 124. Tangent to, 128. Area, 129.
Length of curve, 130. Parabolic sewer, 133. Example, 133.
Remarks on its use in preference to other forms, 134. Egg-
shaped, 140. Hydraulic mean depth, 136. Perimeter,
Artificers' works, measurement of,...

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Right angled triangles, properties of, .

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The necessary formulas in surveying in finding any side and angle,. 171b
Properties of lines and angles compared with one another,.
Given two sides and contained angle to find the remaining parts,
Given three sides to find the angles,

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Heights and distances, chaining, locating lots, villages, or towns,
How to take angles and repeat them for greater accuracy,
How to prove that all the interior angles of the survey are correct,.
To reduce interior angles to quarter compass bearings,
To reduce circumferentor or compass bearings to those of the quarter

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De Burgh's method known in America as the Pennsylvanian,
Table to change circumferentor to quarter compass bearings,
To find the Northings and Southings, Eastings and Westings, by
commencing at any point,.

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How to take a traverse survey by the English Ordnance Survey method,

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