Dec. 4, 1873 



NATURE 



89 



measures. Several descriptions of comparing appa- 

 ratus with micrometer microscopes have been con- 

 structed at various times, but all are made upon the 

 same principle. The microscope is fixed in a vertical 

 position, and is provided with a spirit level and with 

 screws for accurate levelling and focal adjustment. The 

 defining marks of the two standard measures to be com- 

 pared are brought successively under it, their height 

 being adjusted to the focal distance of the microscope. 

 Any difference of length between the defining marks of 

 the two measures is read off from the graduated head of 

 the micrometer. This part of the apparatus consists of an 

 endless screw with the very finest threads, having a large 

 head divided into 100 parts. The screw is placed in a 

 horizontal position, and when turned carries with it a nut 

 moving in horizontal guides, together with an open frame, 

 which has cobweb lines stretched across it. Two of these 

 lines {b b Fig. 20) cross each other at equal angles to the 

 axis of the screw, and so that a line bisecting them is 

 normal to its axis. Two other lines {c c) are placed nearly 

 close, and parallel to each other and normal to the 

 axis of the screw ; and there are two longitudinal lines 

 {(Id) parallel to the axis of the screw, by means of which 

 this axis is made parallel to the axis of the measure 

 under observation. When turning the screw, the number 

 of revolutions is read off by the aid of a pointer from a 

 rack ((?) placed at the edge of the open frame and parallel 

 to the screw, whilst the number of divisions in one revolu- 

 tion is read off on the graduated head of the screw, from a 

 fixed line marked on the upper surface of the microscope. 

 Looking through the eye-piece of the microscope at 

 the magnified first ten hundredths of the inch 36 — 37 

 marked on the subdivided standard yard of the Standards' 

 Department (here inverted), the field of the microscope is 

 seen as represented in Fig. 20. 



In this figure the cross lines are used for observation, 

 and are seen adjusted to the o'o3 in. line. The pointer 

 at the rack shows the screw to be turned between one and 

 two revolutions from the middle of the field. 



All micrometer microscopes used for the comparison of 

 standard measures of length are constructed upon the 

 principle thus described. But there are various kinds of 

 arrangements for supporting the standard measures in a 

 proper position, and for more conveniently bringing their 

 defining marks under the microscopes. Under one of the 

 arrangements, a single micrometer microscope is used, 

 and fixed over the supporting apparatus, which, for the 

 purpose of comparison, has both a transversal and a 

 longitudinal displacement. 



The two standard measures (denoted as A and B) being 

 placed with their axes exactly parallel, and their defining 

 marks as nearly as possible in the same line normal to 

 the axes, the left-hand defining mark of A is brought 

 under tjic microscope, and the position of the micrometer 

 read otT on the index scale and noted. By the transver- 

 sal displacement, the left-hand defining mark of B is next 

 brought under the microscope, and the reading of the 

 index scale noted. The two measuring bars are then 

 moved their whole length by longitudinal displacement, 

 and the right-hand defining marks of A and B suc- 

 cessively read off and noted, thus affording the means 

 of ascertaining the difference of length of the two stan- 

 dard measures. The temperature of the bars at the 

 beginning and end of the observations must be deter- 

 mined by thermometers, and the mean temperature noted, 

 and allowance must be made by computation for any dif- 

 ference of length arising from unequal expansion or con- 

 traction of the two bars, when this temperature differs 

 from the standard temperature. For this purpose it is 

 absolutely necessary that the coefficient of expansion of 

 each standard bar must be previously determined. 



This method of comparing with a single microscope is 

 used in France, but not in England, where the risk of 

 error arising from the longitudinal movement of the bars 



is avoided by using two microscopes, and only a trans- 

 versal displacement of the bars during the observations, 

 although there are also means of longitudinal displace- 

 ment for the purposes of adjustment. The objection 

 raised against the use of two microscopes, that the dis- 

 tance between them may vary during the period of ob- 

 servation by the expansion or contraction from alteration 

 of temperature of the material which unites them, is ob- 

 viated by fixing them firmly and independently upon a 

 solid stone support. 



Placing measuring bars directly upon a plane support is 

 objectionable. It has been proved that there is a risk of 

 discordances in comparisons being caused by almost un- 

 discoverable inequalities in planed surfaces, as well as by a 

 difference of temperature in the plane surface and the 

 under surface of the measuring bar, when thus placed. 

 To guard against this risk, the bars are supported 

 upon rollers, and the measuring bars ought to be stiff 

 enough to bear to be supported upon a few points at which 

 rollers can be conveniently applied. For a short bar two 

 rollers are sufficient ; for a longer bar more supports are 

 required. The standard yard bars are supported upon 

 eight rollers, and it is always requisite that each support 

 should exert the same vertical pressure upwards, in order 

 that the interval between two points upon the surface of 

 the bar may not be altered by the flexure. This object 

 is attained by a proper arrangement of levers ; and it is 

 easily seen that an arrangement of levers by which equal 

 pressure upwards may be exerted at four or eight points is 

 very simple. Each bar rests upon two brass lever-frames. 



It has been shown by the Astronomer Royal, in his 

 paper printed in the Royal Astronomical Society's 

 Memoirs, vol. xv., that the value of the intervals (supposed 

 equal) which ought to exist between different supports of 

 a bar, each support exerting the same vertical pressure 

 upwards, is as follows : ;; being the number of supports, 

 the resulting intervals of supports is : — 

 length of bar 



In order to ascertain with scientific precision how far 

 the results of comparisons of standards obtained by the 

 use of weighing and measuring instruments are to be 

 depended upon for their accuracy, a calculation is to be 

 made of the probable error of every such result, whether 

 it be the result of a single comparison, or the mean result 

 of any number of .comparisons. And when other elements 

 are to be taken into account, it is necessary that the 

 probable error of each computation should be determined 

 and allowed for before the final results of comparison can 

 be determined and allowed for. 



The mode generally adopted for calculating the probable 

 error is based upon the method of least squares, and is 

 fully stated by the Astronomer Royal, in his " Theory of 

 Errors of Observation," pp. 44-7. 



H. \Y. Chisholm 



EAR TH-SCULPTURE * 

 II. 



YOU are aware that the revival of the half-forgotten 

 doctrines of the early Scottish .School of Geology has 

 not been without vehement protest on the part of the 

 older geologists, who have been inclined to treit them 

 rather as novelties and departures from the older and 

 purer faith. No one resisted them more determinedly 

 tlian my much-missed friend and benefactor, the late Sir 

 Roderick Murchison. He looked with regret, and even, 

 perhaps, sometimes with a little alarm, upon their ad- 

 vance, and to the last he battled against them. He was, 

 indeed, in this country the leader of his party, which has 

 been called the " Convulsionist School," and his death 



* Opening Address to the Edinburgh Geological Society, by Prof. Geikie 

 F.R.S. (continued from p. 52). 



