EXPANSION OF SOLIDS WITH RISE OF TEMPERATURE. 19 



boiling. One observer at the left-hand microscope took care to keep the 

 upright U (and therefore the left end of the bar) in its original position, 

 by means of the adjusting screws SS ; while another observer at the 

 right-hand microscope, measured the displacement of the image of the 

 right hand cross wires at u' across his field of view, by means of the 

 micrometer m. The displacement of the object-glass U' in terms of 

 the micrometer divisions was determined thus. In a preliminary ex- 

 periment, two vertical fibres fixed at u, one on each side of the diagonal 

 fibres and exactly -^ inch apart, were viewed by the microscope, and 

 the distance of their images apart measured by the micrometer. To this 

 was added the value in micrometer divisions of y^-inch motion of the 

 micrometer thread, and the total gave the value of ^-inch motion of 

 the object-glass. For, if LM, 

 Fig. 1 1 , be the two vertical wires 

 at u' and Im their images, when A <>' 



o is moved to o' t a distance 

 equal to ML, the image of L 

 moves to Z', where LZ' is parallel 

 to Mm, and therefore ml' - oo' = 

 LM. Hence, ll' = lm + ml' = lm 

 + LM; or, the distance apart FlG> 



of the images of LM + the dis- 

 tance apart of the objects, is the displacement of the image of them by a 

 motion of o through a distance LM. 



Ramsden's results may be put thus : 



Standard brass scale, 1,000,000 parts at expanded to 1,001,855 at 100. 

 Brass rod 1,001,893 



Brass trough 

 Steel rod 

 Iron rod 

 Glass rod 



1,001,895 

 1,001,145 

 1,001,109 

 1,000,808 



Ramsden also found that on dividing the interval from to 100* 

 into three equal steps, the expansion for each step upwards in tempera- 

 ture was the same, within the limits of errors of observation. This 

 result has been shown to be not quite true when the measurements are 

 made with extreme accuracy ; but assuming it as sufficiently exact for 

 ordinary purposes, it follows that a rod expands by the same fraction of 

 its length at for each rise of 1. This fraction is termed the co- 

 efficient of expansion, and is usually denoted by k. Hence, if 1 l t are 

 the lengths of a bar at and t", 



The method of Ramsden has been since modified by attaching a 

 micrometer to the object-glass o', instead of to the eyepiece. The 

 expansion is then measured directly by the distance through which the 

 object-glass must be moved back after expansion to give coincidence 

 again. 



Modern Form Of the Method. A very similar arrangement to 

 that of Ramsden is adopted at the Bureau International des Poids et 

 Mesures at Paris, for the determination of the expansion of metre scales. 

 The general plan consists in keeping one scale at a constant temperature, 



