Intelligence and Miscellaneous Articles, 403 



flat, and similar to the object for two different distances of the object, 

 the image of any other plane object perpendicular to the axis will be 

 distinct, flat, and similar to the object. 



When the object is at an infinite distance, the plane of its image 

 is the principal focal plane, and the point where it cuts the axis is 

 the principal focus . The line joining any point in the object to the 

 corresponding point of the image cuts the axis at a fixed point called 

 the focal centre. The distance of the principal focus from the focal 

 centre is called i\\Q principal focal length, or simply the /oca/ length. 



There are two principal foci, &c. formed by incident parallel rays 

 passing in opposite directions through the instrument. If we sup- 

 pose light always to pass in the same direction through the instru- 

 ment, then the focus of incident rays when the emergent rays are 

 parallel is the first principal focus^ and the focus of emergent rays 

 when the incident rays are parallel is the second principal focus. 

 Corresponding to these we have first and second focal centres and 

 focal lengths. 



Now let Qi be the focus of incident rays, P^ the foot of the per- 

 pendicular from Qj on the axis, Q^ the focus of emergent rays, Pg'the 

 foot of the corresponding perpendicular, FiFc^ the first and second 

 principal foci, AjAg the first and second focal centres, then 



PiFi^PiQi^F,?, 



AiFi P2Q2 f^a; 



lines being positive when measured in the direction of the light. 

 Therefore the position and magnitude of the image of any object is 

 found by a simple proportion. 



In one important class of instruments there are no principal foci 

 or focal centres. A telescope in which parallel rays emerge parallel 

 is an instance. In such instruments, if m be the angular magnifying 



power, the linear dimensions of the image are — of the object, and 



m 



the distance of the image of the object from the image of the object- 

 glass is — of the distance of the object from the object-glass. Rules 



were then laid down for the composition of instruments, and sug- 

 gestions for the adaptation of this method to second approximations, 

 and the method itself was considered with reference to the labours 

 of Cotes, Smith, Euler, Lagrange, and Gauss on the same subject. 



LI. Intelligence and Miscellaneous Articles, 



NOTE ON THE EMPLOYMENT OF INDUCTION APPARATUS. MER- 

 CURIAL INTERRUPTOR. BY L^ON FOUCAULT. 



TN most kinds of induction apparatus, the inductive current id 

 •*■ rendered intermittent by the action of an interruptor which peri- 

 odically produces contact between the extremities of the circuit. 



