enough to lift off either or all of the legs, and the plate is gently tapped with the finger, a rattle is heard, which is the tell-tale of imperfect contact of all the points.  The screw is now reversed gently and slowly until the moment the rattle ceases, and then the reading is taken.  Here the sense of hearing is brought into play.  This is also the case when the electric contact is used.  This is so arranged that the instant of touching of the point of screw, a, completes the electric circuit, in which an electromagnet of short thick wire is placed.  At the moment of contact, or perhaps a little before contact, the bell rings, and the turning of the screw must be instantly stopped.  Here are several elements that must be remembered.  First, it takes time to set the bell ringing, time for the sound to pass to the ear, time for the sensation to be carried to the brain, time for the brain to send word to the hand to cease turning the screw, and, if you please, it takes time for the hand to stop.  You may say, of what use are such refinements?  I may reply, what use is there in trying to do anything the very best it can be done?  If our investigation of nature’s profound mysteries can be partially solved with good instrumental means, what is the result if we have better ones placed in our hands, and what, we ask, if the best are given to the physicist?  We have only to compare the telescope of Galileo, the prism of Newton, the pile of Volta, and what was done with them, to the marvelous work of the telescope, spectroscope, and dynamo of to-day.  But I must proceed.  It will be recognized that in working with the spherometer, only the points in actual contact can be measured at one time, for you may see by Fig. 6 that the four points, a a a a, may all be normal to a true plane, and yet errors of depression, as at e, or elevation, as at b, exist between them, so that the instrument must be used over every available part of the surface if it is to be tested rigorously.  As to how exact this method is I cannot say from actual experience, as in my work I have had recourse to other methods that I shall describe.  I have already quoted you the words of Prof.  Harkness.  Dr. Hastings, whose practical as well as theoretical knowledge is of the most critical character, tells me that he considers it quite easy to measure to 1/80000 of an inch with the ordinary form of instrument.  Here is a very fine spherometer that Dr. Hastings works with from time to time, and which he calls his standard spherometer.  It is delicately made, its screw being 50 to the inch, or more exactly 0.01998 inch, or within 2/100000 of being 1/50 of an inch pitch.  The principal screw has a point which is itself an independent screw, that was put in to investigate the errors of the main screw, but it was found that the error of this screw was not as much as the 0.00001 of an inch.  The head is divided into two hundred parts, and by estimation