174 REPORT—1857. 
On the Use of Prime Numbers in English Measures, Weights, and Coinage. 
_ By James Yates, I.A., F.RS. 
On examining the Tables of the measures, weights, and coins used throughout 
England, it is found that the prime numbers used in their composition and of the 
most frequent occurrence are 2, 3, and 5. Of these, 2 occurs as a factor by far the 
most frequently, indeed twice or thrice as often as either 3 or 5. 
Seven makes its appearance in the following weights and measures :— 
Avoirdupois Weight. 
7000 grains . Rete eee ce re onl fc == ie 
LCR Seah ORgOl AC REICI RCI a ere tbe rei okt. 
| Or ir i i Ce eM 
Wool Weight. 
7 lbs.=1 clove, whence 14 Ibs.=1 stone. 
Wine Measure. 
Rebeca ONS beta «1 cofompseeuys 4asds ved sory Wath sic eae oa. selene EL IE 
Gite PALL ONS Meter otek cle. ahi iat a Shcin =1 hogshead, 
Eleven is used in one case only, but that is an important one, viz. :— 
Long Measure. 
3 or 53 yards=1 rod or pole, from which is deduced 4 poles, or 22 yards=1 chain, 
The furlong, the mile, and the acre are also multiples of this fundamental number. 
Thirteen also comes in once as a factor, viz. in : 
Wool Weight. 
13 
7 or6ztods . - .~ 1 + ew ww eS) Wey, 
Wool weight is curiously compounded. No less than four primes, 2, 3, 7, 13, are 
used as factors, producing only six denominations, which are as follows :— 
Weclaverrs: | 21.01 s,, Saree su, Saake et aes | ekg Oe CRORES 
MUSEONE, Wi <p elateie: [oo trees take Ste) othe. a RON ENE 
US GOE oy as tee dis em Bomete sh Js torch topie a 2 Ake CONERA 
DEWEY, Heh vies ey Rags eto e¥i faerie osien'sat® Seb. OseOs ORO spa mens 
1 UC) SR Aa Re Pe er rN Me stents bee, 
Telaa tse Tecra. sg tetuve Reape epee ey) PA. 2y 
Only one other prime number requires notice, and that is found in a very conspi- 
cuous position, and where, perhaps, it was little to be expected, viz. in a recent Act 
of Parliament. The law now in force and known as the Weights and Measures Act, 
fixes the number of grains in the Ib. avoirdupois by the use of the number 7, and 
goes on to determine the relation of the pound troy to the standard linear measure 
by declaring, that a cubic inch of distilled water “is equal to 252 grains and 458 
thousandth parts of a grain.” If this number (~~) be divided by 2, it will be g 
1000 
found that a cubic inch of water weighs 126-229 five hundredth parts of a grain, the — 
numerator of this fraction, —— being a prime number. ! 
As the result of this analysis, it appears that the primes used in the English mea- — 
sures, weights, and coins are the following :— 
2, 3, 5, 7, 11, 13, and 126-229. ; 
I propose to offer a few remarks respecting the aptitude of these numbers for the — 
functions which they are appointed to perform. ; , ¥ 
The adoption of them does not appear to have been determined, in any case, so far 
as we can judge, by reason or principle, but to have arisen from accidental and arbi~ _ 
trary causes. There is no apparent benefit in connecting our highest coins by 2 and ; 
5, the intermediate by 2 and 3, and the lowest by 2 only. No advantage arises from — 
measuring land by elevens, and weighing wool by sevens and thirteens. No reason 
can be assigned why seven should be brought into avoirdupois weight and excluded — 
from troy weight; or why 3 should be excluded from avoirdupois weight, whilst it 
plays an important part in troy weight and apothecaries’ weight. -In short, all our — 
Tables present the appearance of an entire want of principle in their construction. — 
The introduction of an additional prime has the effect of making our weights and 
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