PENDULUM OF COMPENSATION". 219 



longer than their correspondent steel bars k 1 and m n, the ^^^^^ "P""^ 



t ^ r ^ n ... . , . , • Change of tem- 



whole ot the flexure will take place without any strain or perature, 



tension of any practical importance, in the thin parts at o, o, 

 and the faces k m will be brought nearer together, and so like- 

 wise will a and d ; by which means the pendulum rod will be 

 shortened, and this shortening may, by the due adjustment of the 

 clamps, be made precisely to compensate for the lengthening of 

 the rod, caused by its direct expansion by the same increase of 

 temperature. 



I believe the happy expedient of confining the flexure to a Hardy's 

 thin part of the bar was first used by Mr. Hardy, in his expan- t>alance. 

 sion balance. 



In order to show the quantity of effect, let fg, h I (Fig. 2*) Principles of 

 represent one pair of the bars, of which og, cl are the thin parts, fo^^he^ auan- 

 and c the depth of the notch ; and suppose o e to be the effect tity of efFect. 

 of the expansion by one degree of heat in the thin brass part 

 beyond that of the steel bar 3 which will be 000000331 in 

 unity. 



Or, g being equal to c 0, the quantity e will be= 

 O"000O033lX depth of notch. 



But the whole excess of expansion will be greater in propor- 

 tion as the whole bar is longer than c 0, or the depth of notch, 

 that is, 000000331 X length of bar = whole excess of 

 expansion. 



And as this excess will cause an angular deviation in the line 

 c oio c e and beyond, and will also cause a similar deviation in 

 gf, the linear deviation of the extremity /will be greater than 

 that of 0, in proportion as the whole bar is longer than co, or 

 the depth of notch ; that is, depth of notch : length of bar :: 

 excess of expansion = 00000331 X length of bar: linear 



^ ^ length of bar'^X 0-00000331. 



deviation of y= 



depth of notch. 

 In order to adjust the compensation, the effective length of 

 the bar is variable by means of the clamps, and the deviation of 

 the parts of the pendulum rod, above and below the set of bars ' 



from a precise right line, would not exceed ten minutes, if the 

 parts were inflexible, and the bars very short ; but the spring of 

 suspension is practically sufficient to preserve the right line. 



