ON A QUARTZ THREAD GRAVITY B ALAN (I 235 



through the thread hy about three degrees when upsetting takes place. This is in 

 exact accordance with our observations in so far as they are able to test it, and 

 imlicates that the simplified theory is fairly applicable to the actual instrument. 



The accuracy with which a setting of the microscope may be made upon the mark 

 at the end of the lever depends upon the value of d\ji/d0, and is, therefore, greater the 

 nearer the position of the lever at the moment of observation is to the upsetting 

 position. When the observing position of the microscope has been chosen, tj> and i/ 

 become constant. In the present instrument it is found possible to observe so clow 

 to the upsetting position of the lever that the microscope can be set much closer than 

 the circle can be read. It is because of this fact that we have adopted the plan of 

 increasing the effective circle sensitiveness by giving the thread three whole turns. 

 The circle has a radius of 7 inches, and with our present experience, we are inclined 

 to think that it would be better for the future to use a larger circle and reduce the 

 twist of the thread. 



The sensitiveness of the instrument to gravitational changes is given by the value 

 ofdG/dg, and from (l) this is 



dO ml sin -^ 



dg~ r 



This is greater the nearer the position of the lever chosen for observation is to the 

 horizontal plane, in so far in accordance with the last result. 



Effect of Variation of Temperature. 



We find that the relation between and the temperature as given by our platinum 

 thermometer scale, for the small changes in the latter factor which we encounter in 

 practice, is a linear one, within the limits of accuracy of our observations. We may 

 therefore include all the effects of a change of temperature in a single coefficient. 

 Equation (I) may be written 



As <j> and | are independent of the temperature, and as 6 decreases as the tempe- 

 rature rises, to make this a working formula we must re-write it thus 



(2), 



where a is the temperature coefficient and t is the platinum temperature. In con- 

 sequence of the fact that the constants in this equation can only be approximately 

 determined, we are limited to the consideration of relative values of y, so we may 

 write the equation 



where K and C are constants. 



2 H 2 



