EARTH'S POWER EXPRESSED BY DIFFERENT UNITS. 73 



the distance of their centers is 1, the angular momen- 

 tum produced in S' by S broadside-on (using the first 

 term only of the formula of force), is 1. 



In general, the two operations (deflexion and 

 vibration) can be performed in so short a time that the 

 effects of change of temperature and change in the 

 Earth's force may be neglected. If it is thought 

 necessary to recognise them, reference must be made, for 

 temperature-correction, to the experiments of Article 31, 

 and for the terrestrial change, to observations of minute 

 changes (to be mentioned hereafter, Article ^) Cor- 

 rections for torsion-force of the suspension-thread ought 

 to be applied on the principles of Article 25. There is 

 also another small correction, for magnetism induced in 

 the needle A by the Earth's action : for this we must 

 refer to a succeeding section, Article j^ *7 LL 



33. Investigation of the proportion in which the 

 numerical value for E will be altered, when, instead of 

 using the foot and the grain as units, we use other units, 

 as the millimetre and milligramme. 



Let the foot p millimetres, and the grain =q 

 milligrammes. Suppose the observations of Articles 

 28 and 31 adopted without any modification of chv 

 cumstances, and let us examine how the resulting 

 formulae will be modified by use of the new units. 

 The experiment of Article 27 practically gives 2A.c~ 3 



E 2 



= E. sin <f>; or . = - - c~ 3 . With the new units, sin 6 

 A sm$ 



will not be altered, but c (numerically) will be p times 



