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tered their own errors. The idea of forming self-compensating measuring-bars originated in England. There is no doubt its author-whether he was Colby or Drummond-knew of Harrison's gridiron pendulum; and that whatever of originality there was in the idea lay in the plan for effecting the compensation for temperature at the extremities of the bars. Harrison's pendulum was in common use; and that self-compensating compound bars might somehow be formed, was as obvious as that pendulum was familiar. It seems to be generally admitted that the inventor of the measuring bars was altogether unacquainted with the pendulums of Elliot, Frotheringham, and Deparcieux.

The manner of effecting the compensation at the extremities of the Colby-Drummond bars was exceedingly ingenious. But, before describing it, let us see how it was possible that the compensation could be effected.

If two bars of different metals be solidly connected at the centre, they will expand or contract together when exposed to the same thermometric changes. Suppose them to be made of the same length at some definite temperature. The question is, Is it possible to fix points, one at each end of the bars, to mark that length, however the bars themselves may expand or contract under changes of temperature?

Let A a, Bb be the bars, and let them, at that temperature at which they are equal in length, be solidly connected in the middle at pq; and let Aa be that whose rate of expansion and contraction is the greater. Then, if we join the extremities of the bars a, b, and A, B, there are points n, n', in the lines ab and AB produced, through which lines joining the extremities of the bars at any other temperature must always pass,

provided the increments, or decrements, of the bars, due to changes of temperature, are produced in the same time.

Let a a' be the increment or decrement of ρα for any increase or decrease in temperature, and bb′ the corresponding increment or decre

ment of qb. Join a', b', and produce the line a'b' till it cuts the line a b produced in n. In the triangles a' a n, b'bn we have

or,

aa' an :: bb : bn

aa : bb :: an : bn

i.e. the increment or decrement of bar pa: the increment or decrement of bar qb:: the distance of n from bar pa: its distance from bar qb. Now, if a a', bb' increase and diminish together at the same rate in time, so as to leave the ratio a a': bb' always

a'

a

the same, it appears that the ratio an: bn will also be constant. In other words, the point n will be a fixed point, through which a line joining the extremities at any temperature must always pass. And, the like conditions being satisfied, there will be a corresponding fixed point n' at the other extremity of the bars.

The Colby-Drummond bars were made on this principle, and were accompanied by a contrivance at each extremity for always marking the points in the bars n, n', which are called the compensated points. These are always at the same distance from one another, viz., the length of the bars when equal. This length was 10 feet 1.5 inch. The bars were composed, the

one of brass, and the other of iron; they were half an inch broad, one and a half inch deep, and placed 1.125 inch apart. They were firmly fixed together at their centres by transverse steel cylinders, and free to expand from or contract towards their centres, independently of each other. They were, of course, provided with proper supports to prevent bending; but these, and the protections provided for the rods when in use, need not here be described. The bars, and the compensation microscopes which were used along with them, are fully described by Captain Yolland in his "Account of the Measurement of the Base of Lough Foyle." There were in all six sets of compensation bars formed, and seven compensation microscopes.

A notion of the contrivance for marking the compensated points may be obtained from an inspection of the annexed figure. a'n is

αι

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a flat steel tongue, at right angles to the bars at their extremities, when they are of equal length. The tongue moves freely on conical pivots rivetted into the bars, the axes of the pivots being perpendicular to the surface of the tongue, and allowing it to be inclined at slightly different angles to the bars, according as they expand or contract. On the tongue, and flush with its surface, near the extremity n, a silver pin, with a dot marked upon it, indicates the compensated point. From its capacity for free motion, this tongue represents, as it were, the line joining the points a', b', and

n

the dot at the point n represents the point through which that line always passes.

To complete this general account of the measuring apparatus, it is necessary to refer to the compensation microscopes, which are used along with the bars. A great degree of accuracy in the measurement might have been attained without complicating the apparatus by the employment of the microscopes. But without them the bars must have been brought together in the measurement, so that the compensated point at the end of the one might be superimposed on the corresponding point at the end of the other. And, in effecting the super

imposition, there would be danger of the end of one bar being accidentally moved against that of another, and thence of disturbance in making the alignment and contact. To avoid this, an interval of six inches was left between the compensated points on the adjoining bars; and to bridge the interval, it was necessary to employ instruments having the principle of compensation applied in their construction, as in that of the measuring bars themselves: hence the compensation microscopes. Each of them consists of three microscopes embraced by two bars, one of brass and the other of iron; one microscope in the centre, called the telescopic microscope, and one at each extremity of the including bars, at a distance of three inches from the central microscope. The two bars, carrying with them the outer microscopes, are free to expand from, or contract towards, the central microscope, independently of each other; and thereby to cause the outer microscopes to form with it small angles of inclination, similar to those of the steel tongues of the compensation bars; the compensated point of each outer microscope is so adjusted as to be in the outer focus of its object-glass. It will be seen that the com

pensated points of the outer microscopes are thus always six inches apart. The instrument, admitting of all the necessary movements, and of being put in position with the necessary degree of accuracy, is fixed to the end of the wooden box containing a set of the measuring bars. The dot or compensated point of the latter is brought into good focus of one of the outer microscopes, and the box containing the next set of measuring bars is then put into position, and its dot or compensated point brought into the focus of the other outer microscope. The distance between the two sets of bars is thus accurately bridged; so that the measurement may go on free from all the dangers of inaccuracy incident to the making of contacts between adjoining bars, or effecting superimpositions of their compensated points.

The work of effecting the compensation, and fixing the compensated points, as well in the microscopes as in the bars, was performed by Mr Drummond. The first difficulty which he encountered in this work arose from the rates of changing temperature in the brass and iron being unequal. The mode in which this difficulty was overcome, is described in a paper published by Captain Yolland, in his Account of the Measurement of the Lough Foyle Base, compiled from MSS. written by Mr Drummond. The method is as ingenious as the experiments for working it out were refined and delicate.*

"The mode adopted for equalising the rates of changing temperature in the two metals consisted in maintaining the surface of one of the bars, namely, that of the brass, constant, and varying the surface of the iron till the requisite effect was produced. For this purpose the brass bars were bronzed and

* Yolland's "Account," &c., p. 11.

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