On an Instrument for Drawing Parabolic Curves. 57 



For this purpose replace A by AV 6 and the work of hysteresis 



A 1 

 becomes -^-^i 1 ' 6 , which is thus the formula of Steinmetz. 



In the case where a secondary exists, the number of turns 

 of wire being n l and the current y 1 , we have simply to replace 

 ny in the above formula by ny + n^y 1 and change the phase of 

 the hysteresis term so as to be 90° from the combined mag- 

 netizing force, ny + rfiy 1 . The equations of the currents will 

 then be, by Maxwell's formula, 



Which suffice to determine both y and y\ The result is too 

 complicated to be attractive. The equations show, however, 

 that the odd harmonics must appear in either the electromotive 

 forces or the primary or secondary currents, if not in all of 

 them at once. The exact distribution is only a case of com- 

 plicated calculation. 



It is to be specially noted that all formula by which self- 

 induction is balanced by a condenser will not be correct when 

 applied to an iron transformer but only to an air transformer. 

 They will, however, apply approximately to iron transformers 

 in which the magnetization is small, and thus probably will 

 apply better to transformers with an open magnetic circuit 

 than with a closed one. 



Also an iron transformer should not be compared with an 

 air transformer, or two iron transformers with different mag- 

 netizations with each other. 



In conclusion I may add that the mathematical difficulties 

 might be overcome by another mode of attack, but other work 

 draws me in another direction and I leave the matter to be 

 worked up further by others. 



VII. On an Instrument for Drawing Parabolic Curves. 

 By Richard Inwards, F.R.A.S.* 



THIS instrument, which I have now the pleasure of show- 

 ing to the members of the Physical Society, is designed 

 for the purpose of drawing by one simple operation any para- 

 bola of short focus, such as might be wanted for setting out 

 the curve of a lamp-reflector, or in making a diagram of the 

 path of a comet or of a projectile. 



* Communicated by the Physical Society : read May 13, 1892. 



