22 



HEAT. 



and the same accuracy will be obtained. This may be seen at once from 

 Fig. 14. 



If mm be the position of the mirror which reflects the central division 

 c of the scale S into the telescope, when the mirror turns to mm' 

 through an angle mOm the division reflected into the telescope will be a 

 where aOc = 2mOm'. Hence, what we may call the reflected line of sight, 

 Oa, passes over twice as many divisions of the scale as the normal to the 

 mirror On, and therefore over as many divisions as the line of sight of a 

 telescope at 0, directed along On to a, on a similar scale S' at the full 

 distance. It may be worth noting that on contrasting Lavoisier and 

 Laplace's telescope method with the mirror-telescope method with scale 

 and telescope close together, and using the same telescope and scale in 



each case, there is no gain in 

 5' sensitiveness by the use of the 

 mirror. For though the scale is 

 half the distance from the mirror 

 in the second method, it is still 

 the original distance from the 

 telescope, and the size of the 



j m ^^ f *\n^~~~ ' image is the same in both 



\ ^--'^--- r methods, and, as we have seen, 



the same number of divisions 

 correspond to the same rotation. 

 If, however, the telescope can be 

 brought quite close to the mirror, 

 the scale being left at the half 

 distance, then the number of 

 divisions passed over is the same, 

 but the size of the image is 

 doubled, and the accuracy of 

 estimation is increased. We 



should, therefore, by this last arrangement, both economise space and 

 increase the sensitiveness. 



The following are a few of Lavoisier and Laplace's results : 







FlO. 14. Mirror Method of Reading 

 Deflections. 



The length at is in each case 1. 

 Length at 100". 



Untempered steel 

 Tempered steel 

 Silver . . . 

 Copper . . 

 Brass . . . 

 Iron (soft) . . 

 Iron wire drawn . 

 Glass with lead 

 Glass without lead 



1-00107912 

 1-00123956 

 1-00190974 

 1-00171733 

 1-00187821 

 1-00122045 

 1-00123504 

 1-00087199 

 1-00087572 



Coefficient of expansion between 

 and 100 obtained by divid- 

 ing in each case the total in- 

 crease in length by 100. 



The increments in length here given contain five or six significant 

 figures, but the accuracy of the methods does not justify us in placing 

 confidence in more than the first two or three figures. The determination 



