AuGusT 17, 1899] 
NATURE 
395 
the more convenient, as the first decimal place is always suffi- 
cient. But in Europe and in North America, where the greater 
number of meteorological observatories is situated, the temper- 
ature falls every year below the freezing point of water. In 
some localities it passes quickly through this point and remains 
constantly below, often far below it, returning again in the 
spring and passing as quickly through it again in the beginning 
of summer, to remain constantly above it until it drops away 
again in the fall of the year In such places, where, however, 
the population affected is limited, the use of Celsius’ scale 
is not open to very much objection. With the exception of a 
few days in the fall, and again in the spring of the year, the 
temperatures are either continuously positive or continuously 
negative ; and during one-half of the year the observer reads 
his thermometer upwards, while during the other half of the 
year he reads it downwards. When he has got well into the 
one or the other half of the year, he will make no more errors 
than those that he is personally liable to under circumstances of 
no difficulty. But at and near the two dates when the temperature 
is falling or rising through that of melting ice the case is very 
different. If the rise or fall is rapid, his task is comparatively 
easy, and, after a few unavoidable mistakes, he has succeeded 
in inverting his habit of reading. But, in those parts of Europe 
and North America which carry nearly the whole of the popu- 
lation, the temperature in winter is frequently oscillating from 
one side to the other of the melting point of ice. If the observer 
is compelled to usea thermometer which he must read upwards 
when the temperature is on one side of that point, and down- 
wards when it is on the other side, and if he may be called on 
to perform this fatiguing functional inversion several times in one 
day, it is certain that he will suffer from exhaustion, and that 
the observations will be affected with error. 
Were there no other thermometric scale available but that 
of Celsius, we should simply have to put up with it, and endure 
the inconvenience of it; but, when we have another scale, one 
devised primarily for meteorological observations in the North 
of Europe, by a philosopher who constructed it with a single 
eye to its fitness for what it was to be called upon to measure, 
and when, in addition, this scale is still exclusively used in a 
large proportion of the meteorological observatories of the 
world, it seems almost incredible that amongst reasonable 
people, be they scientific or non-scientific, there should be a 
powerful agitation to abolish the scale which was devised for its 
work, which excludes error in so far as it can be excluded, and 
to replace it by one which, besides other defects, introduces, in 
the nature of things and of men, avozdadle errors, the elimin- 
ation of which is the first preliminary of the scientific treatment 
of all observations in nature. 
Every meteorologist in northern countries who makes use of 
the data which he collects knows that when his temperatures 
are expressed in Fahrenheit’s degrees, he can discuss them at 
much less expense both of labour and of money for computing 
than when they are expressed in Celsius’ degrees; yet such is 
the apprehension of even scientific men when brought face to 
face with the risk of being ruled ‘‘out of fashion,” that 
meteorologists who use Fahrenheit’s scale, though they fortun- 
ately do not give up its use, seem to be disabled from defend- 
ing it. 
What is this stupefying fashion, and can it not be made our 
friend ? 
Fahrenheit lived and died before the decimal cult or the wor- 
ship of the number ten and its multiples came into vogue ; but, 
whether in obedience to the prophetic instinct of great minds or 
not, it almost seems as if he had foreseen and was concerned to 
provide for the weaknesses of those that were to come after him. 
The reformers of weights and measures during the French 
revolution rejected every practical consideration, and chose the 
new fundamental unit, the metre, of the length that it is, 
because they believed it to be an exact decimal fraction one 
ten-millionth of the length of the meridian from the pole to the 
equator. Is it an accident that mercury, which was first used 
by Fahrenheit for filling thermometers, expands by almost 
exactly one ten-thousandth of its volume for one Fahrenheit’s 
degree ? 
Again, how did Fahrenheit devise and develop his thermo- 
metric scale? A native of Danzig and living the first half of his 
life there, he considered that the greatest winter cold which he 
had experienced in that rigorous climate might, for all the pur- 
poses of human life, be accepted as the greatest cold which 
required to be taken into account. He found that this temper- 
NO. 1555, VOL. 60] 
ature could be reproduced by a certain mixture of snow and 
salt. Asa higher limit of temperature which on similar grounds 
he held to be the highest that was humanly important, he took 
the temperature of the healthy human body, and he sub- 
divided the interval into twenty-four degrees, of which eight, 
or one-third of the scale, were to be below the melting point of 
pure ice, and two-thirds or sixteen were to be above it. 
Fahrenheit very early adopted the melting temperature of pure 
ice for fixing a definite point on his thermometer, but he recog- 
nised no right in that temperature to be called by one numeral 
more than by another. The length of his degree was one- 
sixteenth of the thermometric distance between the temper- 
ature of melting ice and that of the human body, and the zero 
of his scale was eight of these degrees below the temperature 
of melting ice, and not, as is often thought, the temperature 
of a mixture of ice and common salt or sal-ammoniac. 
Fahrenheit, as has been said, was the first to use mercury for 
filling thermometers ; and being a very skilful worker, he was 
able to make thermometers of considerable sensitiveness, on 
which his degrees occupied too great a length to be conveniently 
or accurately subdivided by the eye. To remedy this he 
divided the length of his degree by four, and the temperature 
from the greatest cold to the greatest heat which were of im- 
portance to human life came to be subdivided into 96 degrees. 
Had he lived in the following century he would have been 
able to point out that on his scale the range of temperature 
within which human beings find continued existence possible is 
represented by the interval o to 100 degrees, and there can be 
little doubt that this would have secured its general adoption. 
Its preferential title to the name Centigrade is indisputable. 
Perhaps this may be an assistance to its rehabilitation as the 
thermometer of meteorology. J. Y. BUCHANAN. 
Cambridge, August 4. 
On the Deduction of Increase-Rates from Physical 
and other Tables. 
Tue problem treated by Prof. Everett in your issue of 
July 20, p. 271, allows a somewhat simpler solution. Take 
d) 
the example given by Prof. Everett. To find the value of “ 
at the temperature 105°, we have only to consider the columns 
for Af, O*f, A°P, &c. In each of these columns there are two 
numbers, one just above and one just below the horizontal line, 
corresponding to the value @=105°. In the column for A¢, for 
instance, these two numbers are 408 and 470, in the column for 
A*p they are 5and8 _ If now 7, 723, 25, &c., are the means 
of each of these two numbers, so that in this case 77,=439, 
m3,=6.5, we have: 
hdp Nhs ms sone 
de BBB 23-45 2.3.4.5.6.7 
If be capable of being expressed in the form A+ Bé+Cé 
only the first term wz, is required ; if 
p=A+ Be +Co?+ Doe* + Eat 
My, 
=m, — eRe raneeae 
Ms . 
only the first two terms 7, — = are required, and so forth. In 
Dae 
these cases the solution is exact, whereas in general the method 
gives only approximations closer and closer the more terms are 
added. 
The difference between my solution of the problem and Prof. 
Everett's is only formal. It may readily be seen that in Prof. 
Everett’s notation 
21 =A, +l, 2tz=Ay— ty, 215= (ils + My) — (4p — Ua), 
which makes his equations special cases of my expression for 
s The proof of my expression may be given by the cal- 
culus of finite differences. For simplicity let us write 
x =0@-—105', and let us develop the function / in the form: 
ay a, 
p= Ht agx+s x( v—-h)+ 
(xath)x(x-A)+... 
Drs) 
General terms: 
on 
aa k ait + (22 = 1)h) ete tole” 
. « (w-7h) 
(eek). 2 we. (Suh) 
