817 



WEIGHTS AND MEASURES. 



WEIGHTS AND MEASURES. 



813 



the Roman system was taken for granted. Roger Bacon, when speak- 

 ing of a foot or a mile, compares statements of Ptolemy, Pliny, and 

 writers of his own time, without a word of suspicion that there could 

 be any difference between the several measures ; though his own state- 

 ments from modern travellers [MiLE] prove that they had a mile 

 very different in length from that of the Romans. In the Geography* 

 of Laurentinus Corvinus (Basel, 1496), all that he says on measures is 

 in six words, explaining the single addition which had been made to 

 the Roman system : " Italorum quatuor unicum miliare nostrum men- 

 su'rant." Lebrixa or Antonius Nebrissensis (' Cosmographise Intro- 

 ductio.' Paris, 1533), lays it down that his own foot and his own pace 

 are those of the Romans, he being a man of moderate stature ; and 

 having once arrived at a conclusion respecting the Roman pace, he 

 takes it for granted he has the proper foot of his own time : he adds 

 that he has made some verifications on itinerary distances. This idea 

 of the actual use of the human members was a very common one : 

 George Agricola, whose work, ' De Ponderibus et Mensuris,' was much 

 in use, and several times reprinted (Paris, 1533 ; Venice, 1535 ; Basel, 

 1550, and perhaps oftener), would almost seem to hint, in addition to 

 what we have already cited, that the actual measures of his day, as 

 used among merchants, were taken from the body ; the measures of 

 length, he says, are " membra human! corporis, pertiree, arundines, 

 funiculi." This can hardly mean that measures, such as the foot, the 

 cubit, &c., were only originally derived from the human body ; for 

 such an explanation would require us to say that the arundo and the 

 fnnicidui were names of measures, which was certainly t not the case. 

 The word pertica is ambiguous; it is both a pole and the measure 

 derived from that pole : had it not been from the double meaning 

 of that word, we should have been quite positive of wliat we now think 

 by far moffe probable, namely, that Agricola means to say that people 

 in his time measured by the parts of the body, poles, reeds or canes, 

 and strings. This work of Agricola, though intended to be on the 

 weights and measures of his own time, is in reality wholly occupied by 

 discussions on the Greek and Roman measures. He is the first, he 

 says, who in modern times recovered the distinction between the Greek 

 and Roman measures, which had been entirely lost, or at least never 

 mentioned, by his immediate predecessors. It was not uncommon to 

 illustrate the table of measures by drawings of the human body, with 

 descriptions of the foot, palm, &c., as in the ' Cosmographia ' of Peter 

 Apian, reprinted several times in the first half of the 16th century. 

 No other reference to a standard of length is given ; and the table and 

 drawings are made in such a manner, that nothing but our habit of 

 using other modes of measurement would make any one doubt for a 

 moment that actual reference to the human body is intended. The 

 complete table of the 16th century is as follows : the breadth (not the 

 length, as is particularly stated) of four barleycorns makes a digit, or 

 finger-breadth ; four digits make a palm (measured across the middle 

 joints of the fingers) ; four palms are one foot ; a foot and a half is a 

 cubit ; ten palms, or two feet and a half, are a step (gressus) ; two 

 steps, or five feet, are a pace (passus) ; ten feet are a perch ; a hundred 

 and twenty-five paces are an Italic stadium ; eight stadia, or a thou- 

 sand paces, are an Italic mile ; four Italic miles are a German mile ; 

 .Mid five Italic miles are a Swiss mile. It will appear most probable 

 from the preceding statement, that the foot was considerably less even 

 than the ancient Roman foot of 1 1 '6 English inches. The average human 

 foot certainly has not that length ; the average foot of an adult English- 

 man is 10'26 inches. The table just mentioned, derived, as we shall 

 see, from the Romans in most of its parts, is founded upon a notion 

 which is very near the truth in a well-proportioned man, namely, that 

 the breadth of the palm is the 24th part of the height; the length of 

 the foot, the sixth ; and the length of the cubit, or from the elbow to 

 the ends of the extended fingers, the fourth. 



It was the practice of the 16th century, in which books were written 

 for all Europe, and not for that part of it alone in which the writer 

 lived, to set down on the page printed lines representing the length of 

 a foot, or palm, according to what the page would admit. The term 

 frequently used was " figuratio : " thus a long line extending down the 

 page, marked " figuratio pedis," means that the length of this line at 

 the time it was printed is that of which the author speaks. No 

 instance was ever* produced in which such a line was merely a repre- 

 sentation, put down for the purpose of showing subdivisions, or in 

 which it was treated by any succeeding writer as other than an 

 absolute facsimile. 



The figured foot, or paper-foot as we may call it, requires to be 

 lengthened, as an allowance for the shrinking of the paper. The 

 surest case in which we can accurately ascertain in what proportion 

 this shrinking has taken place, is in the plate of Dr. Bernard's work on 

 English weights and measures, in which a line which is described as 

 7 English inches has shrunk to 6 inches and jgths, or in the proportion 



Remarkable as being probably Ihc last work in which America is not 

 mentioned. 



t We do not forget the canna, bat this was only an isolated Italian measure, 

 not likely to be named aa a technical term by Agricola, writing in France, and 

 putting all measures under four heads. 



J We hare found one, in the work of Neander (1555), in which the ratios of 

 the measures are represented by arbitrary lines. But as if to show what was 

 intended, the words next following the figured measures are " Hactenns 

 persecnti sumns nomina mcnsnranun," &c. 



ABTS A5D SCI. DIV. VOL. VIII. 



of 42 to 41. Other instances give smaller* amounts of shrinking : in 

 two different copies of one work we find the difference between two 

 impressions of the same foot agreeing within j^th of an inch in about 

 ten inches. It is very unlikely that, if the shrinking had been percep- 

 tible, two copies should have shrunk so equally. We adopt this ratio 

 of 42 to 41, and the more readily, because the larger allowance we 

 make the more is our final conclusion weakened : this final conclusion 

 being, that the geometers of the 16th century used a much shorter foot 

 than the Roman. 



That the mathematicians just named did use a set of measures 

 among themselves, in order to avoid the diversities of popular measures, 

 is established by the express assertion of Clavius, who died in 1612, 

 aged 75, and is therefore a contemporary authority. He says, in his 

 commentary on Sacrobosco, " Enumerandse sunt mensurse quibus 

 mathematici, maxime geometrse, utuntur. Mathematici entm, ne con- 

 fusio oriretur ob diversitatem mensurarum in variis regionibus (quselibet 

 namque regio proprias habet propemodum mensuras) utiliter excogi- 

 tarunt quasdam mensuras, quse certoe ac ratse apud omnes nationes 

 haberentur." He then gives the same table as that above. On looking 

 at some of the earlier writers of the 16th century, we find a foot which 

 is figured as ten English inches in length, after the shrinking of the 

 paper is allowed for. First, Fernel.t who measured a degree of the 

 earth, speaks of the foot which he used in two distinct works, the 

 ' Monalosphaerium ' (Paris, 1526) and the ' Cosmotheoria ' (Paris, 1528), 

 in which last the degree is described. In the first work he gives his 

 foot, or " figuratio pedis geometric!," which he says is to be chosen 

 with great care, on account of the great diversity of measures. This 

 paper-foot is now within a sixtieth of an inch of nine inches and two- 

 thirds (English), wftch, increased in the proportion of 41 to 42, is nine 

 inches and nine-tenths. In the second work, he says, that five of his 

 own paces, or those of ordinary men, make six geometrical paces. 

 Now the pace of an ordinary man, or two steps, is almost exactly five 

 English feet, which is the double of the regulation step of the army 

 in England. Paucton (p. 187), from actual experiment, gives what 

 amounts to 59 inches and 7-tenths English. At sixty inches per pace, 

 Kernel's foot is then ten inches (English) exactly ; at 59'7 inches it is 

 9'95 inches. The two descriptions agree so well, that Fernel's foot 

 may be considered as very well determined; nevertheless, Picard, 

 Caasini, Montucla, Lalande, and Delambre have all taken it for granted 

 that by a foot Fernel could have meant nothing but the Parisian foot 

 (12'8 English inches), and have therefore considered him as having (by 

 accident, they suppose), measured his degree with very great correct- 

 ness, whereas, in fact, he is fifteen miles wrong. Budieus (followed by 

 Glareanus and others) had, a few years before (1515), in his treatise, 

 ' De Asse,' the earliest work on Roman measures, &c., declared that the 

 Roman foot was the same as the Parisian ; and Picard, &c. seem to 

 have taken it for granted that Fernel followed Budseus. They might 

 have learnt from Lucas Ptetus that this foot of Budseus was " repro- 

 bated by all as having nothing in common with the Roman foot." 

 The treatise of StofBer, ' Elucidatio Fabricae Ususque Astrolabii ' 

 (Oppenheim, 1524), contains his configuration of the digit, palm, and 

 foot, separately, the foot being also divided into palms. These agree 

 exceedingly well with one another, and the foot on the paper is pre- 

 cisely nine inches and three-quarters (English). This increased in the 

 ratio of 41 to 42, gives 9'93 inches. The author speaks of the digit, 

 &c. as being the celebrated measures which are used by all or most, 

 and gives no hint whatever of his having made a measure for himself. 

 It may here be noted that the English writers of the period make little 

 mention of this book-system, and, when they do mention it, sometimes 

 confound it with the common and popular system. Thus Blundevil, 

 in his ' Exercises,' tells us that the German foot, according to Stoffler, 

 is two inches and a half less than ours ; alluding, no doubt, to the foot 

 we have just cited. 



Since the ' Penny Cyclopaedia ' appeared, we have examined several 

 other figured feet ; for some of which see De Morgan, ' Arithmetical 

 Books,' pp. 8, 9. The results accord very well with those given above ; 

 and the mean of the whole gives a foot of 9-85 inches. But Fernel and 

 Stoffler are the best authorities, because they are the best names, have 

 given the whole foot, and have taken the greatest pains with the sub- 

 divisions. The mean of their results, before allowance for shrinking, 

 is 97 inches : that of the barley, presently mentioned, is 9'8 inches. 

 The allowance for shrinking is, as above given, perhaps too great ; and 

 9*8 inches is, it may be, as good an estimate as can be given of this 

 once well-known measure. 



There is little reliance to be placed on the barley standard ; never- 

 theless, this addition to the Roman system of measures must have been 

 made by some who had tried it : we can hardly suppose that writers 



* We have taken the one which is most against us : in the ' Pathway to 

 Knowledge,' (1596; not the woik of Recorde under that name, but a trans- 

 lation from the Dutch, of which we can find no mention in bibliographers) a 

 line of six English inches, figured in the translator's preface, has shrunk only 

 by one part out of sixty. With reference to our frequent subsequent citations 

 from this ' Pathway,' we may observe that Jeakc, whose ample and laborious 

 accounts of weight! and measures (in his ' Aoyiffructi>i.oyla, or Arithmetick, 

 Survcighed and Reviewed,' London, 1696, but finished in 1674) makes him a 

 very respectable witness, considers it as a first-rate authority. 



t See a discussion on this case in various numbers of the ' Philosophical 

 Magazine' for 1841 and 1842. 



3o 



