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 can be read to 1/100000 of an inch. Its constants are known, and it may be understood that it would not do to handle it very roughly. I could dwell here longer on this fascinating subject, but must haste. I may add that if this spherometer is placed on a plate of glass and exact contact obtained, and then removed, and the hand held over the plate without touching it, the difference in the temperature