346 



♦ KNOWLEDGE ♦ 



[April 24, 1885. 



drawn toward the observer the star-disc begins to expand, 

 and if the mirror be a truly spherical one the expanded 

 disc will be equally illuminated, except the outer edge, which 

 usually shows two or more light and dark rings due to dif- 

 fraction, as already explained. Now, if we push the eye- 

 piece toward the mirror the same distance on the opposite 

 aide of the true focal plane, precisely the same appearance 

 will be noted in the expanded star disc. If we now place 

 our plane surface anywhere in the path of the rays from the 

 great mirror, we should have identically the same phenomena 

 repeated. Oi course it is presumed and is necessary that the 

 plane mirror shall be much less in area than the spherical 

 mirror, else the beam of light from the artificial star 

 will be shut oflf, yet I may here say that any one 

 part of a truly spherical mirror will act just as 



either side of the focal plane. I might go on to elaborate 

 this method to show how it may be made still more exact, 

 but as it will come under the discussion of spherical sur- 

 faces I will leave it for the present. Unfortunately for 

 this process, it demands a large truly spherical surface, 

 which is just as difficult of attainment as any form of 

 regular surface. We come now to an instrument that does 

 not depend upon optical means for detecting errors of 

 surface, namely the spherometer, which, as the name would 

 indicate, means sphere measure ; but it is about as well 

 adapted for plane as it is for spherical work, and Professor 

 Harkness has been using one for some time past in deter- 

 termining the errors of the plane mirrors used in the transit 

 of Venus photographic instruments. At the meeting of the 

 American Association of Science in Philadelphia there was 

 quite a discussion as to the relative merits of the sphero- 

 meter test, and another form which I shall presently 

 mention. Professor Harkness claiming that he could, by the 

 use of the spherometer, detect errors bordering closely on 

 one-five-hundred-thousandth of an inch. Some physicists 

 express doubt on this, but Professor Harkness has no 

 doubt worked with very sensitive instruments and over 

 very small areas at one time. I have not had occasion to 

 use this instrument in my own work, as a more 

 simple, delicate, and efficient method was at my com. 

 mand, but for the measurement of convex surfaces j 



Fig. 3. 



well as the whole surface, there being of course a loss 

 of light according to the area of the mirror shut oflf. This 

 principle is illustrated in Fig. 3, where a is the spherical 

 mirror, b the source of light, c the eye-piece as used when 

 the plane is not interposed, d the plane introduced into the 

 path at an angle of 45° to the central beam, and e the posi- 

 tion of eye-piece when used with the plane. When the 

 plane is not in the way, the converging beam goes back to 

 the eye-piece, c. When the plane, d, is introduced the 

 beam la turned at a right angle, and, if it is a perfect 

 surface, not only does the focal plane remain exactly of the 

 same length, but the expanded star-discs are similar on 



Fig. 4. 



know of nothing that can take its place. I will briefly 

 describe the method of using it. The usual form of the 

 instrument is shown in Fig. 4 ; ra is a steel screw working 

 in the nut of the stout tripod frame b ,■ c c c are three legs 

 with carefully prepared points ; t^ is a divided standard 

 to read the whole number of revolutions of the screw 

 a, the edge of which also serves the purpose of a 

 pointer to read off the division on the top of 

 the milled head e. Still further refinement may 

 be had by placing a vernier here. To measure a 

 plane or curved surface with this instrument, a perfect 

 plane or perfect spherical surface of known radius must be 



