JANUARY 5, 1912] 
quantity expressed is less than unity, as it is 
about half the time. For then the exponent 
is negative, and the two numbers affect the 
resultant magnitude in opposite ways. 
For instance, suppose a galvanometer which 
requires 38 < 10° amperes to give unit deflec- 
tions: how will its sensitiveness compare with 
that of one for which both indicating numbers 
are numerically larger, say, 8.0X10° am- 
peres? The larger significant figure, 8.0, 
indicates a larger current, and therefore less 
sensitiveness, but the exponent, 9, though also 
larger, indicates greater sensitiveness. Really, 
the second is about four times as sensitive as 
the first, but this fact is far from evident on 
a first reading; yet this is a very simple case. 
If a reader should see an account of one of 
these instruments on a Friday, and of the 
other on, say, the next Wednesday, it would 
require unusually careful reading indeed to 
leave him with any definite idea of the rela- 
tive sensitiveness. 
The difficulty of this system can also be 
well stated as follows: When a number of 
magnitudes, say diameters of small rods, is 
stated, sometimes in centimeters and some- 
times in millimeters, it is evident that a good 
deal of unnecessary difficulty results, which 
can be avoided by sticking to one unit or the 
other. Now, between a millimeter and a 
centimeter there is the same difference as 
between any two consecutive powers of ten. 
An unrestricted system of notation by powers 
of ten, therefore, amounts practically to an 
unnecessary multiplication of the number of 
working units. 
The remedy is obvious—to diminish the 
number of units. This is realized in the 
other system, which proceeds by steps of 1,000, 
instead of 10. A further gain is sometimes 
secured by using prefixes instead of exponents 
to indicate the working units, since the com- 
bination of a word and a number is preferable 
to two numbers, each of which interferes with 
the apprehension of the other, and even more 
with its recollection. This system is perhaps 
seen at its best in the field of electricity, 
where, besides the units, ampere, ohm, volt, 
SCIENCE 39 
ete., the milliampere, millivolt, microampere, 
microvolt, kilowatt, megohm, etc., are in com- 
mon use, and have almost completely displaced 
the reckoning by powers of ten. The advan- 
tages of the system have been made available 
in stating galvanometer sensitiveness by the 
scheme proposed by Ayrton. The sensitive- 
ness is simply put equal to the deflection pro- 
duced by a unit current, usually the micro- 
ampere. According to this scheme, the sensi- 
tiveness of one of the galvyanometers men- 
tioned above is 125, of the other, 33. Here the 
difficulty of remembering or comparing the 
two quantities would seem to be reduced to 
the minimum. And this illustration gives a 
fair idea of the value of the general method. 
Under it, but one thing claims attention: a 
single number, which need never exceed 3 
digits unless the accuracy attained calls for a 
larger number of significant figures. Such a 
number is relatively easy to comprehend and 
to remember. The unit needs almost no at- 
tention, since all magnitudes between which a 
comparison is likely to be desirable will be 
expressed either in the same unit, or else in 
units so far apart that no confusion will occur. 
This choice of units is, of course, the essen- 
tial part of the method, and it, of course, can 
be realized under the form of the notation by 
powers of ten by those to whom that form 
seems desirable. All that is necessary is that 
those powers of ten shall be chosen which are 
also powers of 1,000, so that the use of 107, 
10°, 10°, 10’, 10°, ete., is to be discontinued. 
But the use of the prefixes to denote the units 
seems decidedly preferable. The electrician 
who should be advised to abandon his micro- 
volts and milliamperes, and go back to “ volts 
10°,” ete. would scarcely be profoundly 
impressed with the value of the advice. 
A, few special points seem worth noticing in 
this connection. 
A single prefix to denote 10° seems de- 
sirable. Until it appears, 10° amperes (for 
instance) should of course be ealled a mil- 
limicroampere. of course, 
means a millionth of a millionth, or 10%, 
and is illogical when used for 10°, besides 
“ Micro-micro,” 
