436 Mr. S. U. Pickering on the Recognition of 



in which the higher harmonics would be greatly magnified 

 in importance. 



To show the magnitude of the terms in (2) I will take 

 a well-known 1500-watt transformer, unloaded, as a choking 

 coil. Here ^ = 7837. The total average power wasted inheating 

 the iron being 40 watts, I assume that this is altogether due 

 to eddy currents. Power wasted in eddy currents being 

 n 2 Y 2 /2rW, we have n*/r = 2-117, when V = 2828. An eddy- 

 current coil which would replace all the eddy-current circuits 

 is a coil of 2 turns whose resistance is about 1*9 ohms, short- 

 circuited on itself. 



£ = 038, if £=600. 

 It is obvious that e is proportional to k and to the square of 

 the radius of the iron wire. 



Assuming constant permeability and no eddy currents, 

 C = -074sin(fo-90°). 



With some saturation but no hysteresis, 

 C = -079 sin (kt-6d°-2)~ '0148 cos 3fo- -0037 cos 5kt, 

 if b=0% m = -05. 



These values of b and m are usually employed by me for 

 such magnetizations as are common in transformers. When 

 I assume the existence of hysteresis, I take/ about 20 degrees. 



L. The Recognition of Changes of Curvature by Means of 

 a Flexible Lath. By Spenceb Umfreville Pickering, 

 F.R.S* 



IF when a number of experiments are plotted out they form 

 a figure exhibiting any sudden changes of curvature, it 

 will very rarely happen that the position of these changes can 

 be located, or even that their existence can be recognized, by 

 mere inspection. To search for them by deducing various 

 equations mathematically, involves an expenditure of time 

 which is quite prohibitory, at any rate in the case of a figure 

 with many breaks in it ; and it is therefore highly desirable 

 that some more expeditious method, such as the graphic 

 method which I have adopted in my work on Sulphuric Acid 

 (Chem. Soc. Trans. 1890, pp. 64, 331), should be shown to be 

 reliable. I trust that the following examination of various 

 cases will show : — (1) that this method leads to the same con- 

 clusions as does the mathematical method, which, as Mr. 

 Lupton says, has been found to express physical facts "in the 

 great majority of cases in Physics and Chemistry " — that of 

 fitting on parabolas of the form 



y — a-\-bx -K . ,zx n ; 

 * Communicated by the Author, 



