Biosophy 
to do with Christianity any more than with the rational 
ethics of any social reformer? Why abandon rational 
thought and why introduce the hysteria and emotionalism 
of the supernatural into the picture? Beverley Nichols 
is not behindhand in decrying Christianity when its 
hysteria takes the form of national patriotism; he should 
realise that supernaturalism and religious emotionalism 
' are false guides and dangerous in all circumstances. 
i CHAPTER V.—SCALE IN NATURE. 
182. In modern science accurate measurement 15 
of ever-increasing iniportance, and the dimensions dealt 
with range froin such extremes of inconceivable distance 
on the one hand to equally inconceivable minuteness on 
the other, that the choice of units and scales of measure- 
ment requires much consideration. 
The Centimetre Unit. 
183. Whatever measuring we may do we must have 
a unit to start from; the draper uses yards, the mechanic 
inches, the surveyor chains; but the measures which were 
in use in old days varied so much from country to 
‘country and from trade to trade, that their value in the 
international field of science was not great, and in most 
countries the international metric system is now com- 
pulsory even for commercial purposes; in the British 
Empire the metric system is a legalised optional alterna- 
tive to our usual commercial standards. Of the various 
decimal or metric measures, each of which is a multiple 
by ten of another in the system, the centimetre is the one 
generally selected as the scientific unit. Roughly 25 
centimetres make an inch (1 centimetre=0.3937 inch). 
In practice our metric measures are all derived as more 
or less accurate copies of a metre defined by two fine 
lines marked on a bar of iridio-platinum in the British 
Department of Standards; the centimetre, of course, 
being a hundredth part of this standard length. 
Multiples and Fractions of the Centimetre. 
184. When a scientific man is engaged on specialist 
work in which a rather limited range of dimensions is 
concerned, he often thinks and speaks in terms of some 
other unit within the metric system instead of in centi- 
metres. For example, in radio he thinks of his wave 
lengths in metres (100 cm.); whilst a bacteriologist 
thinks of his “germs” in microns (1/10,000th cm.). 
Here, then, is one way of visualising and speaking of 
very large or small dimensions, viz., by using large units 
for the former and small units for the latter. ‘The 
astronomer often uses as his unit the “light year," the 
distance which light travels in one year, which is about 
ten million million kilometres; the nearest star is over 
four "light years" away from us. To express such large 
dimensions as multiples of the centimetre would become 
increasingly cumbersome, and similarly to express the 
minute dimensions of atomic physics in decimals or 
fractions of the centimetre is almost equally cumbersome. 
The difficulty is accentuated when, as is often the case, 
yery large and very small dimensions are included in the 
Chapter V—Scale in Nature 
same paragraph, or in one mathematical formula or 
equation. 
Orders of Magnitude. 
65, The scientist avoids this difficulty, whilst 
retaining the centimetre unit for all measurements, by a 
very simple device. He expresses his figures in powers 
of ten; thus 1,000 is written 10°, 1,000,000 is written 
109; if the number were 1 with twenty-five noughts after 
it, he would write 102°. In the same way small fractions 
or decimals are written with a minus index corresponding 
to the number of noughts in the fraction, or to the places 
of decimals. Thus 1/100,000,000th or .000,000,01 is 
written 10-5. Three million is written 3 x 105, and the 
fraction, three millionths, or .000,003, is written 
3 x 10%, If more precision is needed, decimals may be 
added after the first figure; thus three and a quarter 
millionths or .000,003,25 is written 3.25 x 10-9. The 
saving of figures is not great when one is only dealing 
with millions, the last example: using five figures as 
compared with eight in the decimal notation; but the 
saving is great when very large or very minute magni- 
tudes are being considered. 
A Scale to Represent Orders of Magnitude. 
186. Usually, when we make use of a scale of any 
kind we consider equal divisions at one end of the scale 
as corresponding exactly to equal divisions at the other 
end. For example, a carpenter’s rule is divided equally 
into inches and eighths; we apply it to a piece of wood 
and find the thickness to be 14 inch, and if we apply the 
rule to a piece twice as thick it would read 24 inches. 
In this case the actual reading of the scale corresponds 
precisely to the thickness of the wood. We may also use 
the carpenter’s rule to draw a scale plan of a house, 
making $ inch on the rule correspond to one foot of the 
house; in other words, we are drawing a plan on the 
scale of 4 inch to the foot, or of one to ninety-six. We 
may similarly make an enlarged drawing of minute 
detail seen under the microscope, on a scale, for example, 
of ninety-six to one. In each of these cases, once the 
proportion of our scale is fixed, we treat any equal 
division at one part of the scale as exactly equivalent 
to an equal division at another part. 
187. The use of a scale in this way works well when 
we are dealing at one time with objects of the same 
order of magnitude. It is quite practicable to draw 
plans of a big house and a small house, both on a scale 
| of 4 inch to the foot, or half a dozen microscopic objects 
64 
on a scale of 100 to one. But we cannot use a single 
scale in this way when we wish to compare objects bigger 
than houses with objects smaller than can be seen under 
the microscope. 
188. The difficulty may be overcome by constructing 
a scale of orders of magnitude, as is shown in the accom- 
panying diagram on page 66. Here the large divisions, 
alternately black and white, are all equal, so far as the 
actual drawing is concerned, just as the divisions on a car- 
penter’s rule are all equal; but there resemblance ceases, 
and the “meanings” of the divisions are by no means 
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