10 DR. F. NORTON ON THE EFFECTS OF CHANGES OF TEMPERATURE 



of'N, aiid we have 



T = -V 4- 



1 n /XT 



9 (N + ar) ' 



In order to measure AB and BC the telescope used had a fine horizontal scale in 

 the eyepiece, and. as a general illumination of the field of view of the telescope made 

 it difficult to see the flashes, the scale was illuminated by the light from ;i sm;ill 

 rectangular slit in a dark screen placed in front of a lamp. The light was reflected 

 into the telescope by means of a small right-angle yrism, a piece of ground glass was 

 placed in front of the slit to make the illumination more uniform, and also a piece of 

 green glass, for it was found that the flashes could be best seen when the scale was 

 illuminated with this colour. 



In order to see what degree of accuracy this method is capable of, it must be noticed 

 that an error can only arise in the fraction x, and only an inexcusably careless 

 observer could be '1 out in the value found If we take N as 20 (a mean value) 

 we see that 



1 as/N , i 



~J approximately ; 



9 (N + x) 9N 



the error occurs in a'/9N 2 and is therefore not greater than 



1/(90 X 20 2 )= -000027 second. 



If N is less than 20 it follows that the flashes are "losing" more rapidly, and hence 

 the distances to be measured in the telescope are larger, and the value of x can be 

 more accurately found. If on the other hand N is larger than 20, the distances 

 between two consecutive 37th flashes is smaller, and consequently x is more difficult 

 to measure ; but in none of the cases dealt with could the error have been as large 

 as '1, and it must l>e observed that the larger N becomes of less importance is the 

 fraction x. 



In what has been said above it is assumed that the vibrator is gradually losing on 

 the 37 second period. This is of course not always the case. It may be gaining and 

 making 9 vibrations in a little under 37 secconds and 9 (N + x) vibrations in 

 37 (N -|- x) 1 seconds ; whence 



T 21 _ _ L_ 



it (N + x) ' 



In this case each 37th flash appears to g;iin on the previous 37th, and so to move 

 out from the centre of the field in the opposite direction to that already considered. 

 After N periods it is now the With flash which nearly coincides with the fixed one. 

 The coincidence period is of course not ahvavs :\7 . To find it the time of vibration 

 must first be approximately known. This is found by GAUSS'S method, using a chrono- 

 meter. Suppose it to l>e -I'll 54 seconds. Such a number of seconds is required as is 



