228 
BRITISH PHARMACEUTICAL CONFERENCE. 
value of the other. But supposing it was money, 3, 3, 3 expressed thus, the mid¬ 
dle digit has, in consequence of its position, ^ the value of the left-hand figure 
and 12 times the value of the right. Had it been the weight marked on a heavy 
package of goods, 3, 3, 3 might express 3 cwt. 3 qrs. and 3 lb., in which case 
position gives the middle figure \ the value of the left and 28 times the value of 
the right. These changes in the value given by the place which a digit holds 
are the cause of our requiring constant calculation to reduce numbers of one 
value to numbers of another; but the decimal arrangement, bringing weights 
and measures into accordance with the method of expressing number, does away 
with all this complexity, for in that case, whether it is weight, measure, money 
or number, the relative value of the places is the same, each being 10 times that 
of the place to the right of it. 
Had our arithmetic been duodecimal, 3, 3, 3 would have expressed 3 gross, 3 
dozen, and 3, and in that case duodecimal weights and measures would have 
brought our metrology into unison with our numeration ; and the same may, of 
course, be said of octavial arithmetic, and in either of these latter cases the 
adoption respectively of duodecimal or octavial metrology would have given us 
all the advantages which are now anticipated from the decimal system, and, in 
addition to these, various others, which, it may be, are of equal or of greater 
importance. 
The report on weights and measures presented to the American Pharmaceu¬ 
tical Association in 1859 contains a brief discussion, and Leslie’s ‘Philosophy of 
Arithmetic,’ 1817, contains a more elaborate discussion of the merits of various 
irithmetical scales, and of other matters, which, though of great interest, I do 
think desirable to include in the present paper. The former contains copious 
testimony, from high authorities, to show that the decimal scale is not a good 
one, either for abstract or practical purposes. I make use of its information 
and of some of its arguments, but as I do not quote the words, I must just make 
this passing acknowledgment that I am indebted to it. Like the authors of that 
report, I have come to the conclusion that an octonary scale is best, both for 
abstract and applied use; but I must satisfy myself with a brief statement of 
the grounds upon which I have come to that conclusion, together with a state¬ 
ment of what I consider the failings of their plan. 
The first consideration is the ready divisibility into the most useful fractions, 
together with gradations which are neither inconveniently long nor short. 
All scales will afford equal facility for obtaining increasing proportions to the 
unit in whole numbers; that is, supposing 1 to be the smallest number, the de¬ 
cimal or duodecimal scales would be as convenient as the octavial for providing 
us with the quantities 2, 4, 8, 16, or 32, but not for •§-, -/«, -gV ”, so with the 
octavial and duodecimal scale, we have not facility for obtaining the fractions 
h To: to: etc. ; and with the octavial or decimal scale we cannot produce a, a, -J-, 
etc. It is almost unnecessary to adduce evidence to show the greater utility of 
those fractions whose denominators are a power of 2. Evidence may be found 
in all directions ; I shall only draw attention to a few striking instances. 
We have a pound sterling consisting of 20 shillings ; £ and T V might have been 
expected consequently to appear as common fractions in the silver coins, but 
the A has never appeared and the only as the result of the recent attempt at 
decimal division ; those which sprang up spontaneously were the I, and a. 
The half sovereign is the only one of these which is commonly spoken of as a 
fraction of the pound, except where values are stated in pounds and fractions, 
such as, for example, share lists, where we find constantly the fractions i, and 
a or | and a, but rarely i or a, and never £ or T \y. 
Of old coins, the noble and the mark—I and f of the pound—have fallen out 
of use, while the angel has retained its value, but changed its name to ^ sove¬ 
reign. The angel and shilling were our only coins holding a decimal relation- 
