of Telegraphic Electromagnets. 179 



the prope* signals, are reduced in a greater proportion than 

 the proper signals themselves. 



3. Now let R and L belong to the electromagnet alone, and 

 Rx and L x be the resistance and electromagnetic capacity of 

 the remainder of the circuit. Then (2) becomes 



r= E (s\ 



^(R + E^ + rnXL + Li) 2 ' * v } 



In solenoidal electromagnets, if n is the number of wind- 

 ings of the wire in unit of length, and the number of layers in 

 unit of thickness, R varies as r&. L also varies as n 4 , while 

 the magnetizing force due to the unit current varies as n 2 . 

 Applying this to equation (3), if F is the magnetizing force, 

 F is a maximum, n being variable, when 



R 2 + L 2 m 2 = R? + LX> W 



Ri and L x being considered constant, as belonging to the line. 

 We may write (4) thus, 



_V ..... (5) 







Now ^- is constant for the same line-wire, whatever its 

 length, since both L x and R x are proportional to the length of 

 the line. Also ^ is constant for the same coil, if only the dia- 

 meter of the wire is variable, since both L and R vary as /i 4 . 



But the time interval =~ for the electromagnet is in general 



L 

 much greater than the time interval ^ for the line- wire ; 



.til 



whence it follows, by inspection of (5), that R must be much 



less than R x to produce the maximum magnetizing force ; and 



the higher the speed, which is proportional to m, the less 



should R be. 



The calculation of =~- is easy, since the line-wire is long, 



1 . L 



straight, and parallel to the earth ; but the calculation of — 



is not so easy, owing to the variety of shapes assumed by elec- 

 tromagnets used for telegraphic purposes, with their cores, 

 polepieces, and armatures, which all influence the electromag- 

 netic capacity, though they do not influence the resistance. 

 It is therefore impossible to enunciate a general law, that the 



N2 



