266 A. BOYD. 
It will be found that the value of © is so small that the 
second portion of the expression may be considered unity, 
thus 
Pierre hess 2 ‘Sea Sa Be 
o = 4040 in circ. meas. = 50 about. 
sinw = ‘00029; cos» = 1°00000. 
cos 2 »=1°00000; tan » = °00029. 
cos2o0 __ 1 ' fides fase 
is 1 and aE sin » = 0°000004. 
The correction is thus quite negligible. 
thus 
In this method of measuring, it is evident that the dis- 
tance rod will extend under the action of its own centri- 
fugal force. The extension of the portion between the 
prism and the free end of the rod will have no effect on the 
mirror, whereas the extension of the portion between the . 
fixed end and the prism will cause rotation of the mirror. 
The deflection as read in the telescope must therefore be 
corrected for this extension, the correction being of plus 
or minus sign according as the mirror is facing towards the 
fixed or moveable end of the rod. 
The extensions of each rod for a given range of speed 
were worked out and plotted in the diagram (fig. 7), the 
extensions being reduced to scale divisions. The method 
of calculation is as follows:— 
Let M = weight of unit volume of metal of rod. 
wo = angular velocity. 
R = distance from centre to end of rod. 
EH = modulus of elasticity of metal. 
Then it may be shewn by a process of integration that the 
expansion of the rod due to its own centrifugal force is 
M wo R? 
96 E 
Let M, be weight of attachments at end of rod distant 
R, from centre, and 4=area of cross section of rod. Then — 
