March 1, 1887.] 



♦ KNOW^LEDGE ♦ 



]11 



amount depending upon, and calculable from, the amount of 

 that fall. But in the work of measuring a terrestrial base- 

 line considerable difficulty will arise from variation of tem- 

 perature in different parts of the line to be measured, and 

 hence it becomes important to u.se measuring i-ods of an in- 

 variable length. Fig. G illustrates the extremely ingenious 

 manner in which the absolutely unvarying length of these 

 rods is insured. 



n h r r'l' a' 



iii 



Fig. 6. 



Reference to any work on physics will show that the linear 

 expansion of brass is to that of iron in the i)roportion of 1894 

 to 11(56 for any given increase of temperatures. Very well, 

 then. We will suppose that h h' and i i' represent a brass 

 and an iron bar- respectively, connected by a steel tie, s : h p 

 and b'p' being two flat steel tongues at their ends, moving on 

 conical brass pivots, so as to permit them to move through 

 small angles with the Hues (l>p, b'p' in our figure above) 

 square to the bars. These tongues are so adjusted that the 

 lengths b p, b'p' are to the lengths / p, i'p as 1894 : 11G6, 

 i.e. roughly as 5:3. Then a little attention will show 

 that if the bars are made of precisely the same length at a 

 temperature of, say, 62°, the tongues will be at that tem- 

 perature accurately perpendicular to the bars, and p p' will 

 be at their precise length (say 10 feet) apart. If, though, 

 we suppose that a change of temperature either expands 

 bb' to a a', or contracts it at c c', then as bp : i j) : : ba : Ik, 

 and by similar triangles the points 2^ ^'id p' ^^'iH remain at 

 an invariable distance. Returning from this digression, 

 we may just add that bars of this construction are laid end 

 to end in wooden troughs in an alisolutely straight Hne, 

 and, if they could be brought into absolute contact, the 

 process of measuring by their aid would be a comparatively 

 simple one. To permit them to jostle, however, would be 

 to introduce an element of possible serious inaccuracy. 

 Hence they are brought as close together as they con- 

 veniently can be without coming into actual contact, and 

 the intervening minute space is carefully measured by a 

 micrometer microscope in a manner analogous to that pre- 

 viously described. 



So far we have proceeded on the assumption that the 

 bisection of the fiducial points whose distance is to be 

 measured is made by the eye ; but it is gravely doubtful if 

 that organ is trustworthy for such a purpose beyond the 

 -pjj-jjLjj-fith of an inch. How, then, are more minute quanti- 

 ties still measured 1 A very brief account of Sir Joseph 

 AVhitworth's perfectly marvellous machine, which measures 

 unei-riugly to the one-millionth of an inch (1), may enable 

 us to understand how this is effected. In this case the 

 measurement is tactile and not visual, and is effected in a 

 manner which may be summarised thus. Premising that 

 this astonishing piece of mechanism is only capable of 

 measuring e?i(7-lengths, we may say that it consists of a 

 massive cast-iron bed, with head-stocks at each end, some- 

 thing like those of a lathe. Extending centrally along the 

 top of the bed is a V-groove running the whole length 

 between the head-stocks. In this groove slide two square 

 bars so accurately fitted to the groove that they slide 

 with no perceptible friction and with absolute steadiness. 

 The ends are worked rigidly square to their .sides and (what 

 we may call) their inner ends, or those furthest from the 

 head-stocks, are turned up in the lathe, so as to present two 

 rigidly flat circular discs. Through each head-stock runs a 

 micrometer screw, made with extreme ca.re, by turning 



which the bars are advanced along the Y-groove. Each of 

 these screws has 20 threads to the inch. The micrometer 

 head of the left-hand screw is divided into 250 parts : so that 

 if we turn this forward through one division it advances the 



bar against which its free end abuts -.iV X 



?.TiT '••*• TTTiTo" 



th 



of an inch. The right-hand screw is driven by what is 

 called a worm-wheel, or endless screw, of 200 teeth, and 

 the screw gearing into this carries a micrometer head with 

 250 divisions. Hence it will be seen that the advance 

 through one division of this last-named head must move the 

 bar touched by the primary screw -^^ X ^r^jr X Trytrtli of ^^ 

 inch — in short, through exactly the one-millionth of 

 an inch. Of course each of the micrometer heads has 

 a fixed index, by which it can be read. Suppose, 

 now, that we have a standard inch bar with which we 

 pi'opose to compare a duplicate. Our standard is constructed 

 just like the original bars, and, as in their case, fits accu- 

 rately into the V-groove in the bed of the engine. The 

 free end of the left-hand screw is in actual contact with the 

 left-hand end of the standard ; but between its right-hand 

 end and the free end of the right-hand screw is interposed 

 a steel plate with rigidly parallel sides, called by Sii' Joseph 

 Whit worth a '• feeler " or "gravity piece." This has two 

 handles (something like those of a tap-wrench) which rest 

 on two shelves fixed one ou each side of the bed. When 

 the pressure exerted by the screw is imperceptible, if we 

 lift one of these handles the feeler drops again by its own 

 weight. When, however, the pressure is so regulated that 

 the feeler can be moved and yet does not fall when the 

 handle is relea.sed, the instrument is in adjustment. We will 

 imagine this to be the case with our standard inch bar. Then 

 the reading of the right-hand micrometer head is accurately 

 noted. We now turn it backwards, release the gravity 

 piece and the standard, and take the latter out, replacing 

 it by the duplicate to be tested. If the micrometer head 

 goes back to the same position as it at first occupied, then 

 are the bars of identically the same length ; if not, the 

 number of divisions gives the millionthsof an inch by which 

 they differ. The motion of the screw through one division 

 of the micrometer head will release the feeler when the 

 instrument is accurately adjusted. 



Merely as a matter of course the instrument which we 

 have been endeavouring to describe is almost infinitely too 

 delicate for use in the workshop. At the same time, how- 

 ever, patterns and templates are now worked to a degi'ee of 

 rigid accuracy which would almost strike the engineers of 

 the early part of the century dumb with amazement, and 

 for the purposes of those refined measurements now im- 

 perative. Sir Joseph Whitworth has devised a somewhat 

 more simple form of engine. This consists, in eflect, of a 

 small bed, like that of a lathe, upon which are mounted 

 two head-stocks, very much like the poppet which carries 

 the back centre in an ordinary turning lathe. Here the 

 right-hand head-stock is a fixture, and the left-hand one 

 slides along the bed by means of a screw within it, the face 

 of the bed being graduated in inches. This graduation 

 enables the head- stocks to be at once placed approximately 

 at the required distance apart. The movable head-stock has 

 a screw within it of one-twentieth of an inch pitch, 

 furnished with a micrometer head with 250 divisions upon 

 it. As in the case of the more elaborate instrument, how- 

 ever, this left-hand head, once adjusted, is a fixture, and the 

 measuring is effected by the right-hand one, through which 

 travels a screw also with 20 threads to the inch, whose 

 head is graduated into 500 parts. Hence it will measure a 

 difference of length equivalent to ^V ^ shi' oi" -ruiuo*li of ^^ 

 inch. With the description of a more simple instrument 

 still, the pocket thousandth gauge sold at Churchill's and 

 other tool warehouses, we may conclude our account of 



