Focal Lengths of Mirrors and Lenses. 59 



Let us suppose that in the case we are dealing with — 



comes out at 32 (an actual example, see ' The Engineer/ 

 April 6th, 1894). 



Set the index slide to 2 '45 and place cursor accurately 

 opposite middle 1 on scale A (use one of end lines on 



slide to centre with), and set index line to *32 ( — 1 on scale 

 A (over to the left, fig. 5). u<l/ 



Now using one of the end lines on slide read on scale A 

 opposite to intersection of index line on scale D, but read 

 backwards from the centre 1. This will be found to give "37, 

 or the theoretical efficiency of an Otto engine having ratio of 

 expansion *32 is .37. 



6. To determine x in such an expression as 

 7* =3. 



Here x will be a fractional index, and we shall first find - . 



Set cursor to 1 in centre of scale A. x 



Set index line to 7 on scale A, and keeping it there move 

 slide of cursor till index line intersects scale D opposite 

 figure 3 on scale A (use end line of slide). 



Now read result on index-scale 



= 1-76 



Or x = j^ = -568. 



IV. Graphical Method for finding the Focal Lengths of 

 Mirrors and Lenses. By Edwin H. Barton, D.Sc, 

 F.R.S.E., Senior Lecturer and Demonstrator in Physics at 

 University College , Nottingham*. 



IN his ' Geometrical Optics ' Aldis gives a graphical method 

 for exhibiting simultaneously the focal length of a conk- 

 cave mirror and the distances from it of any two conjugate 

 foci (page 30 in third edition) . The present note consists of 

 the extension of this principle to the cases of a convex mirror 

 and thin lenses and its application to the practical problem of 

 finding focal lengths. This experiment is usually a little 

 perplexing to junior students in a physical laboratory. It is 

 therefore hoped that by giving publicity to this method 

 (which, simple and obvious though it is, does not seem to 



* Communicated by the Author. 



