of dilation or contraction of the substance of which the measure was composed. Of course, every care had to be used to prevent changes in the length other than those due to temperature, e.g., changes due to bending or twisting. Such care being taken, a great degree of accuracy was obtainable in measuring with simple rods or chains, through making the necessary corrections for variations of temperature as the process proceeded. The corrections that thus constantly fell to be made were, however, not a little precarious, and were, moreover, unqestionably most annoying.

The bars with which the base at Lough Foyle was measured were so constructed as to be self-compensating for changes of temperature. Certain points near their extremities maintain the same distance from one another at all temperatures.

The fact that different metals expand under heat at different rates had previously been made use of in various ways to maintain the constancy of the distance between two points. Graham, the inventor of the mercurial pendulum, was the first to turn the fact to practical account; while by his experiments, published in the "Philosophical Transactions" for 1715, he laid the foundation for the subsequent inquiries and improvements which led up to the measuring bars. His pendulum consisted of a steel rod, carrying a jar of mercury at its extremity. The upward expansion of the mercury counteracted the downward expansion of the rod, and kept the centre of oscillation always at the same distance from the centre of suspension. Mr John Harrison's gridiron pendulum was the next application of the fact, and seems to have been executed without the least knowledge of what Mr Graham had done before

him. He secured the constancy of the distance between the centres of suspension and oscillation by such an arrangement of sets of steel and brass rods in the same plane, that the upward expansion of the one set was. counteracted by the downward expansion of the other. After him, Mr Frotheringham, M. Deparcieux, and Mr Elliot, much about the same time (1738), independently constructed compensation pendulums, consisting of two bars, one of brass and the other of steel, fastened together by screws, with an arrangement of levers to raise or let down the pendulum bobs. In these the compensation was effected at the extremity of the bars, and not, as in the gridiron pendulum, at the centre. After this date, there were numerous beautiful contrivances introduced, for the purpose of eliminating the errors to which pendulums of this construction were found to be liable. We see, then, that a century of invention had been devoted to the subject of compensation for changes due to temperature, in combinations of steel bars and brass bars for pendulum purposes, before the subject was thought of in connection with geodesy.t

The French geodesists were the first to employ compound measuring bars to measure base lines. But in the French bars, the unequal expansion of metals was not used to secure the constant length of the measure. These compound bars, by an ingenious device, were made to measure and indicate their variations in length due to temperature, so that the use of the thermometer in connection with them was superseded. They regis

* See a Paper contributed by Mr Short to the "Philosophical Transactions" for 1752.

+ See Yolland's "Account of the Measurement of the Lough Foyle Base," p. 7. Lond. 1847. Longman and Co. 1 vol. 4to.

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 pa 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

a'

a

A

6"

n

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 aa': bb' always 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

a'

b

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