372 Prof. F. L. 0. Wadsworth on 



Dividing the first by the second we have 



D, 2 _ 1+ cos ft 

 D/"~ 1 -cos ft' 

 from which 



, D,»-D,' 



The reflexion is examined in a telescope with micrometer 

 eyepiece, having two separate scales so that the lines on these 

 scales may be made perpendicular to the long and short dia- 

 meters of the ellipse. It makes no difference what the scale- 

 divisions are, if they are alike on both scales. 



When the ellipse becomes a straight line, D 2 2 = and 

 cos </> = l, from which </> = 0, or the currents are in phase. If 

 the ellipse becomes a circle, D^=zD 2 2 and the numerator be- 

 comes 0, consequently cos </> = 0, and <p = 90°, or the currents 

 are in quadrature. 



The amount of self-induction in the apparatus itself is in- 

 appreciable, and the loops keep well in time with the current. 

 Even a considerable variation in period does not hinder the 

 vibrations, which in this case are forced. This is possible since 

 the mirrors, while moving very slightly, still vibrate sufficiently 

 for telescopic observation. 



Thus we have overcome the two great difficulties of many 

 forms of this apparatus, namely, self-induction and the in- 

 ability of the vibrating wires to follow a change of period. 

 And with these objectionable features eliminated and a method 

 of finding the exact value of cos (f> } we have a practical means 

 of determining the difference of phase. 



Worcester Polytechnic Institute, 

 Worcester, Mass. 



XXXVIII. A Note on Mr. Burch's Method of Drawing 

 Hyperbolas. By F. L. 0. Wadsworth, E.M., M.E., 

 Assistant Professor of Physics, University of Chicago* . 



IN the January number of the Philosophical Magazine 

 Mr. Burch describes a very simple and convenient 

 method of drawing an hyperbola by the use of two similar 

 triangles. This method is very similar to one which I have 

 been using for some time and which I have described in my 

 lectures for the past two years, although I have never pub- 

 lished it. Mr. Burch's invention of the method antedates 



* Communicated bv the Author. 



