COLBY'S BASE-MEASURING APPARATUS. 429

level d, the cross hairs of the microscopes attached to these bars occupying the position of the dots on the longer ones.

"The starting point of the base was a stone pillar with a platinum dot let into its centre. A transit instrument was set up over this, and the coffers carefully adjusted to the line by means of sights at their extremities. When the first coffer was levelled by the levels shown at K, K, Figs. 241, 242, and the microscope stand adjusted so that the cross hairs of one microscope were over the starting point, the adjacent point of the first bar was brought under the cross hairs of the other microscope by means of three slow motion screws attached to the coffer in which each bar was fixed, so that the coffer could be moved on one side, backwards or forwards, as required.

"The microscopes were usually 6 in. apart, but when the uneven surface of the ground made it difficult to bring the bars to the same level at this distance, the interval was altered. Microscopes of different lengths were also used when the ground made it necessary to lay the coffers at different levels, so that the platina dots might be brought into the focus of each microscope.

"The coffers were laid on trestles s, s, Fig. 242, equidistant from their centres, so that they might always have the same bearing. A stand with screws was similarly adjusted at the other end of the first bar, the second coffer laid and levelled, and its adjacent dot brought under its microscope; the third, fourth, and fifth bars were similarly adjusted, and thus 52 ft. were measured. The first coffer was then carried forward and similarly placed in front of the fifth bar, and the operation repeated, and so on.

"An average distance of about 250 ft. was measured per day; five coffers or a length of 52 ft. being levelled and laid together. About 400 ft. of the base was across the river Roe, in which piles 5 ft. 3 in. centre to centre were driven to support the coffers. At the end of each day's work a triangular stone was sunk at the end of the last bar laid, with a cast-iron block fitting into it, having a brass plate, adjustable by screws, with a dot let into it. This dot was brought exactly under the cross hairs of the extreme microscope and served as a starting point on the next day. A sentinel was always left in charge of the stone, which was secured by a wooden cover screwed over it.

"The total length of base thus measured was about 8 miles. Two miles were afterwards added by the method of prolonging a

base described on page 455, making the total length of base rather more than 10 miles."

In 1849 the base on Salisbury Plain was again measured with Colonel Colby's apparatus. The length of the Lough Foyle Base was then calculated from this measurement and the intervening triangles. The difference between the computed and measured lengths of the Lough Foyle Base was found to be only 5 in., thus affording a final proof of the accuracy of the English triangulation.

The base lines of the Trigonometrical Survey of India were measured with Colonel Colby's base-measuring apparatus. To test the apparatus, the last base at Cape Comorin, 8,912 ft. long, was measured four times with a view to ascertaining the actual error in measurement. The difference between the several measurements and the mean of the four, +.0017, - .0049,- .0015, +.0045 ft. According to Colonel Walker, Surveyor-General of India, the average probable error of a single measurement of a base with Colonel Colby's apparatus is ± 1.5 millionths. The average rate of measurement with Colby's apparatus in India was about 1 mile in five days; the length of bars used in this case was 10 ft.

United States Coast and Geodetic Survey Basemeasuring Apparatus.-A similar base-measuring apparatus is used in the United States Coast and Geodetic Survey. It also consists of a bar of brass and a bar of iron. They are, however, connected at one end, so that the entire contraction or expansion takes place at the other end. The whole apparatus is covered by a double tin tubular case, only the ends of the sliding rods being open. The observations are made through glasses in the sides. The length of the bars is 6 metres, and two tubes are employed in measuring a base, each tube being supported by two trestles. On one base 7 miles long, the greatest possible error was calculated to be less than in. On another base 63 miles long, the probable error was under in., and the greatest possible error less than3⁄4 in.

With the above apparatus 1.06 mile was measured in 8 hours, and under favourable circumstances 1 mile a day can be measured. To test the apparatus to the utmost the base at Atlanta, Georgia, was measured twice in winter and once in summer, 1872-73, at

temperatures 51°, 45°, 90° F.; the difference of first and second measurements was +.30 in., and of second and third measurements +.34 in., the actual length and computed probable error in metres being 9338.4763 ± 0.0166.

The Great Theodolite of the United States Coast and Geodetic Survey. The great theodolite of the United States Coast and Geodetic Survey was 2 ft. 6 in. in diameter, divided to 5 minutes, and read to single seconds by three micrometer microscopes, placed 120° apart. The focal length of the telescope was 4 ft.

The Great Theodolite of the Ordnance Survey.— The great theodolite was used for measuring the angles of the primary triangles. It was made by Ramsden, and the circle or divided limb was of brass, 3 ft. in diameter. It had only two verniers. The focal length of telescope was 36 in., aperture 2 in., magnifying power 54. Its weight was about 200 lbs. or nearly 2 cwt. The stand, steps, stools, tent, &c., weighed about another 200 lbs. It was found that the effect of heat and cold on the limb would produce considerable errors if the instrument was subjected to currents of air. This was avoided by keeping up the walls of the tent in windy weather, and leaving only an opening sufficient to take the observation. In calm weather the tent was put down.

There were altogether four large instruments used on the Ordnance Survey of the United Kingdom, two 3 ft. diameter, one 2 ft. diameter, and one 1 ft. 6 in. These were all made by Ramsden in 1798, except the 2 ft. diameter, which was made by Troughton & Simms. They are still to be seen in good condition in South Kensington Museum.

Portable Scaffold.-A portable scaffold was made for the purpose of raising the instrument above the ground. It consisted of an inner scaffold for supporting the instrument and an outward one for the observers, not touching or in any way connected with each other. These scaffolds were in two parts, altogether 30 ft. high; so that one half could be used when it was only necessary to raise the instrument 15 ft. A wooden threesided vertical shaft which turned on an axis protected the silk thread which suspended the plumb bob from wind.

Portable Signal.-A portable signal was made consisting of a tripod ladder about 35 ft. high, which carried at its top either a globe lamp, a white light, or a flagstaff as necessary. A heavy plumb bob was used to centre this over the station to be observed.

Portable Crane.-A portable crane was used for raising the great theodolite to the top of churches, towers, or other buildings, or to the top of the scaffolding.

Permanent Station Marks. The main stations were marked by permanent marks so that they might be found and the observations repeated at any time, or new work connected with the original primary triangulation.

12 in. Theodolite of the Ordnance Survey. The angles of the secondary triangles were observed with a 12 in. theodolite.

7 in. and 5 in. Theodolites of the Ordnance Survey. -The angles of the tertiary triangles were measured with 7 in. and 5 in. theodolites, principally with a 7 in. instrument.

TRIANGLES OF THE ORDNANCE SURVEY OF GREAT BRITAIN AND IRELAND.

Primary Triangles -The length of the sides of the primary triangles averaged from 40 to 60 miles, and the total number of stations was about 250. The longest side of one of the largest triangles and connecting the West Coast of Scotland with Ireland was about 95.20 miles. Some of the triangles in Ireland exceeded 100 miles in the side.

Secondary Triangles.-These averaged 10 or 12 miles

a side.

Tertiary Triangles.-These averaged from 1 to 3 miles a side.

Having given the chief principles of a trigonometrical survey and a brief outline of the Ordnance Survey of the United Kingdom, which is one of the best examples of a trigonometrical

* The largest triangle has one angle at Snowdon in Wales, another on Slieve Donard in Ireland, and a third at Scaw Fell in Cumberland. Each side is over 100 miles, and the spherical excess is 64′′.

survey, these will serve as a guide to the main features. proceed to describe the various operations in detail.

We now

General Form of Triangulation. The surface of Great Britain is uniformly covered with triangulation. The most usual method, however, is that of chains of triangles in the direction of the meridian, and perpendicular to it. The principal triangulations of France, Spain, Austria, and India are so arranged. Oblique chains of triangles are formed in Italy, Sweden, and Norway, also in Germany and Russia and in the United States. These chains are composed merely of consecutive triangles, sometimes and more frequently in India, of combinations of triangles forming consecutive polygonal figures. In this method of triangulation the sides of the triangles are generally from 20 to 30 miles in length, seldom exceeding 40 miles.

I

Reconnaissance and Selection of Stations. One of the first points to be noticed in the selection of stations is that no triangle should have an angle less than 30° or more than 120°. A small angle may be measured as accurately as a large one, but a given error, say 1 second, in a small angle, gives a much greater error in the resulting calculated distance than an error of 1 second in a large angle. The distances are proportional to the sines of the angles, and the differences of the sines of small angles near 。° are very much greater than the differences of the sines of large angles near 90°, which are nearly zero; the error in distance due to a given error in a small angle is therefore much greater than the error in distance due to the same error in a large angle. The best-conditioned triangle is the equilateral triangle, and the bestconditioned quadrilateral is the square.

As the accuracy, time of execution, and cost of the survey depend in the first instance on a judicious selection of the stations, this is one of the most important duties of the chief engineer of the survey, and should be personally attended to.

The points to be particularly noted are:-That triangles are well conditioned; the amount of cutting and clearing necessary to see between stations selected; probable amount of damage; height, expense, and convenience of access of stations; liability to movement of stations during progress of survey; preservation of stations after survey is completed.