833 



WEIGHTS AND MEASURES, STANDARD. 



WEIGHTS AND MEASURES, STANDARD. 



831 



near to one of these extremes, we have little doubt the truth really 

 lies. Accordingly, the Roman uncia is much nearer to our ounce aver- 

 dupois than to our ounce troy ; and many metrologists have supposed 

 that the former was originally the uncia. 



We have never had any means of knowing whether the fundamental 

 points of connection between the Greek and Roman measures are exact 

 or only approximate. These are, that the foot is longer than the 

 Roman by one twenty-fourth, and the Philetserian foot by one-fifth ; 

 that the /lei-pjjTijs is an amphora and a half, and that the amphora of 

 water or wine weighs an attic talent. Taking these relations for 

 granted, we have for the Greek foot 12'10 English inches or 1'OOS feet, 

 for the Philefaerian foot 13 P 94 inches, for the metretes 8'4879 gallons, 

 and for the attic talent 56'586 pounds averdupois. There is one 

 stadium left at Athens [STADIUM] which is 630 English feet, giving 

 for the Greek foot I'Oo feet English ; but there is not much dependence 

 to be placed on the measure. Such buildings as have been examined 

 at Athens, in the manner already described, give as a mean 136 69 

 Paris lines, or 12'] 4 English inches. We may therefore say that the 

 Greek foot was longer than the English one by the tenth part of an 

 inch. The statements then as to the relations between the Greek and 

 Roman measures appear to have been tolerably exact, and our know- 

 ledge of the relations between our measures and theirs, though not 

 sufficient for scientific comparison, is abundantly exact for the purposes 

 of the classical student, far more so than could have been expected to 

 have been attainable by those who remember that for a long period all 

 means of comparison were lost.* 



WEIGHTS AND MEASURES, STANDARD. In this article we 

 separate from the general subject of WEIGHTS AND MEASURES those 

 preliminary considerations which refer to the manner in which weights 

 and measures are verified and preserved, so far as they can be entered 

 upon hi a work partly of reference, partly of general information. We 

 do not pretend to complete a scientific account, but shall be satisfied 

 with preparing the unpractised reader to look with some degree of 

 interest on the sources of more elaborate information to which we 

 shall refer. 



Measures are wanted for two distinct objects, the commercial and 

 the scientific. The wants of natural philosophy have grown up within 

 the last two centuries ; while so early as Magna Charta it was one of 

 the concessions to the grievances of the subject that there should be 

 one weight and one measure throughout the land. But though a few 

 acts of parliament were sufficient, in process of time, substantially to 

 establish the political rights which that charter was intended to grant, 

 hundreds of them, down to the present time, have been ineffectual in 

 producing the use of one weight and one measure. Some of these we 

 shall afterwards refer to [WEIGHTS, Ac.] ; in the meanwhile we have 

 here only to state that, as may be supposed, this unity was for com- 

 mercial, not scientific purposes ; and that the resemblance of natural 

 objects was supposed to be a sufficient reliance for obtaining it. Some 

 of the old statutes expressly make the inch to be the length of three 

 barleycorns, placed end to end, round and dry, from the middle of the 

 ear. Standards were made, no doubt, from this definition ; or at least 

 it was supposed that if the existing standard should be lost, the barley- 

 corns would enable its restoration to be effected. Our readers may 

 smile at what they think so rude a contrivance ; but the same prin- 

 ciple, carried a Uttle further, might be made very efficient in preserving 

 a measure. Suppose for example, that the government were now to 

 think it desirable to recover the three-barleycorn inch, or at least to 

 invent one which should be capable of being recovered. They x would 

 put together not three barleycorns, but three thousand, or' thirty 

 thousand; or many different collections of three thousand or more. 

 The average inch deduced from these would be capable of being re- 

 covered at any time from the same grain grown in the same soil. A 

 commercial standard might be easily recovered from many different 

 modea of proceeding : for example, the average height of the barometer 

 at a given place throughout any period of five years is so nearly the 

 same from one five years to another, that a commercial standard might 

 be sufficiently well obtained from it. It would be of little consequence 

 if the yard were wrongly recovered by one-hundredth or even one- 

 tenth of an inch, in any matter of buying and selling. 



It is the identijic standard at which the government has been aiming 

 during the last century. The object here is, first, to measure the old 

 standards to the utmost accuracy of which our senses, assisted by 

 microscopes, are capable; secondly, to discover the means of recon- 

 structing a lost standard. In the more delicate operations of natural 

 philosophy and astronomy, our knowledge cannot go down to posterity, 

 unless they know within the thousandth of an inch what it is that we 

 call a yard. The public at large has never understood the reason why 

 so much trouble has been taken ; and perhaps the members of different 

 administrations, while trusting such investigations to men of science, 

 and relying on them for the whole conduct of the matter, may have 

 wondered at the great difficulty which there seemed to be in the way 

 of furnishing the shopkeepers of all generations with the yard measures 



* For further information on ancient weights, coln, and measures, the 

 reader i> referred to the following work, ' Metrologische Untersuchungen uber 

 Uewiehte, Miinzfuwe, und Masse des AlterthuiM in ihrem Znsammenhange, 

 ron August Boeckh,' Berlin, 1838; and to a review of this work in the 

 'Clinical Museum,' No. 1, by Mr. Orote. 



ARTS AJTD SCI. DIV. VOL. VIII. 



and pound weights of the same values. It is our principal object in 

 this article to endeavour to point out the nature of these difficulties, 

 and the extent to which they have been overcome : it being remem- 

 bered however that the object ia scientific, not commercial, and that 

 the standard of length is chosen as the most important illustration. 



To elucidate the principle merely of the manner in which scales are 

 compared, we must first show how it is that very small lengths can be 

 measured. A screw can be very accurately constructed, say with 

 threads one-twentieth of an inch apart : if this screw be the axis of a 

 circular plate, which turns with it, and the edge of the plate be divided 

 into 100 parts, each of these parts will be very perceptible, if the plate 

 be three-quarters of an inch or more in diameter, and it will not be 

 difficult to estimate the half or quarter of one of the divisions. Let 

 there be an index attached to the frame, which does not move with 

 the screw, by which it may be seen, when the plate (and with it the 

 screw) is turned, how many divisions it is turned through. Now 

 since a whole turn of the screw moves the end of it forward through 

 one-twentieth of an inch, a motion of the plate which passes one of 

 the divisions over the index, or the hundredth part of a turn, sends 

 the end of the screw forward through only oue two-thousandth of an 

 inch, and a quarter of a division answers to one eight-thousandth of 

 an inch. Suppose a couple of such screws, each of which is attached 

 to a pointer, as in the following diagram, in which the pointers only 

 are inserted, and one of the scales which are to be compared ; the 

 screws which move the pointers, and all the frame-work, being omitted. 

 Observe also that this is not the apparatus employed, but only a con- 

 venient illustration of it. 



It is supposed that A and B can be moved, by the screw motion, in 

 such a manner that a motion so small as the eight-thousandth of an 

 inch may be given to either. The scale at present used is E F, on which 

 are two points, c and D, which are, or are supposed to be, exactly a 



V 



I 



CO 



DH 



yard asunder. Let the screws be moved until the ends of the pointers, 

 which all but touch the scale, are exactly over and D ; then if the 

 scale be removed, the length o D is retained in the distance between 

 the points of the pointers. Now let another scale be introduced, and 

 let its points be brought as near as may be, conveniently, to the 

 pointers : it is supposed that the distances 'c D and o H are very nearly 

 equal, for workmen used to the construction of mathematical instru- 

 ments never fail in making two yard measures agree within a fiftieth 

 of an inch. Perhaps the reader will say the point a might be brought 

 exactly under the pointer A, and then the pointer B alone would show 

 whether the present scale is shorter or longer than its predecessor : but 

 as the pointer is much less cumbrous than the scale, it is easier and 

 safer to put the scale in a convenient position than to attempt to 

 place it in one exactly given. This being done, move the pointer 

 A from c to o, and observe how many turns, or how much of a 

 turn, of the screw, is required to do it : say it makes 874 divisions of 

 the plate pass the index. Also move the pointer B from D to H, which 

 makes, say, 97} divisions of the plate pass the index. Now we ob- 

 viously have 



OH = CD + DH CG; 



and since D H is longer than c o, it appears that a H exceeds c D by the 

 excess of D H over c o, answering to 97| 87J, or 10J divisions of the 

 plate, being 10J times the two-thousandth of an inch, or -005125 of an 

 inch. This experiment may be repeated any number of times, and as 

 may be expected, the results will not agree, since it is not to be sup- 

 posed that any .two persons, or the same person at two different times, 

 will agree in their estimation of exact coincidence between the pointers 

 and the ends of the scales. As in other cases, the averaging of the 

 discordant results will bring out the truth very nearly. 



The difference between the apparatus which was actually used in the 

 next experiments and that above described was as follows. The 

 pointers were MICROMETER* microscopes, hi which the intersection of 

 two fine spider-threads, placed at the focus, was the point which was 

 made, by a slow screw motion, to coincide with the centre of the 

 (magnified) dot (or line) which formed the extremity of the scale. 

 The micrometer head (the circular plate of the preceding illustration) 

 was divided into 100 parts, each of which was found to be equivalent 

 to one 20,000th of an inch ; or a whole turn of the screw altered the 

 position of the intersection of the spider's webs by one 200th of an 

 inch. The magnifying power used was about 27 times in linear 

 dimension. It was attempted, in each experiment, to estimate tenths 

 of the divisions of the micrometer-head, or to attaint the 200,000th 



* The principle is the same as that of the beam compasses, and the apparatus 

 might be called microscopic beam-compasses, or beam-microscopes. 



f Every attempt at measurement strives to be ready for more than there 

 is any reasonable hope of attaining. It is certainly not likely, at present, that 

 even the mean of a large number of measures would settle the question within 

 so small a quantity ; but if ever the day shall arrive when the 200,000th of an 

 inch is attainable, the previous attempts to obtain it will point out the cause of 

 their own failure, and probably be a source of information. 



3 II 



