Oct. 29, 1885 | 
NATURE 
627 
frame, say an eighth of an inch, separated the two plates from 
each other. 
On taking them out of the case the other day I noticed the 
pattern on the glass clearly and sharply imprinted on the 
ebonite ; every little circle well marked. Dust had been plenti- 
fully deposited on all parts not screened by the tinfoil spots, and 
the striking clearness of the impression was mainly due to this 
local absence of dust ; but even on wiping off some of the dust 
the pattern could still be detected, owing to some difference of 
surface between the exposed and the shaded portions. 
It evidently is another illustration of Prof. McLeod’s observa- 
tion of the effect of light on ebonite, the modified surface afford- 
ing an easy lodgment for dust. In case there be anything more 
in the matter it is proposed to replace the same or similar 
plates, and observe at intervals. 
Epwarp E, Ropinson 
Lecture Assistant to the Professor of Physics in 
University College, Liverpool 
TIED SIPIDIE JROILAS 
e is a perpetual source of amazement to those who 
are familiar with this instrument that its use is not 
almost universal. People of every class have to make 
simple calculations, while those engaged in scientific 
work, in designing apparatus, or in invention perpetually 
cover sheets of paper with figures, all of which trouble 
and the loss of time which it involves might be saved by 
the intelligent use of a good slide rule, and yet, for 
reasons difficult to find out, the habitual use of this instru- 
ment is limited to a very small proportion of the calcul- 
ating community. 
Most people know that the scales are logarithmically 
divided—that is, that the distance between the divisions 
marked 1 and 10 being in imagination divided into 10,000 
parts, the division marked 2 is at the 3o010th of these parts, 
the division marked 3 is at the 4771Ist of these parts, and 
sO on, 3010 being the log. of 2, 4771 the log. of 3, and 
so on; and further, that the spaces between these whole 
numbers are similarly divided into fractional parts, thus 1°1 
is at the 414th of the imaginary parts and r’o1 at the 
43rd of these parts, 414 and 13 being the logs. of 11 and 
rol. This is very generally known, but it is more gener- 
ally believed that to use the rule involves so much 
thought and anxiety that it is far simpler to work out 
results in the usual way, or at any rate that the rule can 
only be of any real assistance when a great number of 
similar calcuiations have to be made; and further that, 
as the results to be obtained are not absolutely correct, 
that as an extreme error of 1, 1-10th, or 1-100th per cent. 
is possible, according to the nature of the instrument, it is 
not really to be trusted. These objections are easily 
answered. As soon as the slight difficulty of reading the 
rule has been overcome—a difficulty due to the fact that in 
ascending the scale the divisions become closer, so that 
if there is room for ten subdivisions between ro and 11, 
there are only five between 20 and 21, and two between 40 
and 41—a difficulty which once overcome never recurs— 
then the simpler calculations, such as multiplication, 
division, and simple proportion, can at all times without 
an effort or a thought be instantly performed, while those 
involving proportions in which some of the terms are 
squares, cubes, roots, sines, or tangents can, after a 
moment’s reflection, be as easily completed, so that even 
in the case of single operations time is saved. It 
is true when many calculations of the same kind present 
themselves, especially if some of the terms in the series 
are identical, that the use of the rule is specially advant- 
ageous; but in any case mental labour and time are 
saved. 
As to the probable accuracy of results obtained by the 
use of the rule, they are in general superior to the 
accuracy with which the figures which require reduction 
have been determined, or, if this is not the case, they are 
in general so nearly correct that the error is of no con- 
sequence. For instance, if the marks obtained by several 
examinees are to be reduced to correspond to a total of 
100, the commonest rule, which gives an accuracy of 
1-300th part, is sufficiently good; for the nearest whole 
number only, and the right order are all that are needed. 
It would be absurd to doubt the accuracy of the instru- 
ment because it cannot be trusted to give figures correct 
to one part ina thousand. Or, again, if the weight of a 
piece of metal has to be determined from its dimensions, 
a good rule trustworthy tor part in 1000 will in almost every 
case be more than good enough ; for, even if the specific 
gravity of the material be known so truly, it is not often 
that the piece can be made so near the specified size that 
the discrepancy which may ultimately be observed will be 
due more to the error of the rule than to the inaccuracy of 
construction. In sucha case it would be as absurd to 
discard the rule as untrustworthy as it is to use 7-figure 
logarithms for the calculations of an ordinary chemical 
analysis. There are cases, of course, where observations 
can be made with a degree of accuracy beyond that which 
is obtainable by any rule—for instance, determinations of 
mass, length, angles, and time can all be made with extra- 
ordinary precision. Where, then, uncertainty is not intro- 
duced by observations of another kind, where the entire 
precision to be obtained in any such observations may be 
expected in the result, as, for instance, in the determina- 
tion of the refractive index of the glass of a prism, in such 
cases the slide rule is unsuitable, and tables of log- 
arithms furnish the most obvious means of making the 
calculations. Or, again, when pounds, shillings, and pence 
are involved, a result correct to the nearest farthing is 
generally desired to make accounts come right, and so, 
unless the sums dealt with are moderate, the slide rule is 
again unsuitable. However, the calculation of interest 
furnishes a good example of proper and improper use of 
the rule in making calculations. If it is required to find 
what a certain sum (s) will be worth at the end of a 
year at so much (*) percent., the result might be found 
from the proportion 100: 100 +7:: 5: 4. Here 
the amount 2 would be determined with an accuracy 
of say 1-roooth part, so that if 1000/. were involved, an 
error of 17. might arise. This is an improper use of the 
rule. A greater degree of accuracy would be ob- 
tained by the proportion 1oo : ~::s: the increase of s. 
Here the interest is found to the same proportionate 
accuracy, and so in such a case the greatest possible 
error could only be one shilling, if the rate is 5 per cent. 
This example, though obvious, is given because it cor- 
responds exactly with cases that arise in the laboratory, 
where the rule, if used properly, is of service, but, if im- 
properly, is useless. 
Calculations involving only the simple arithmetical 
rules, when extreme accuracy is required, are best per- 
formed by the help of a table of logarithms, or with an 
arithmometer ; in fact with an arithmometer a far greater 
degree of accuracy can be reached than with ordinary 
7-ficure logarithms, and though they are also suitable for 
calculations in which only three or four significant figures 
are required, their great size and expense compare un- 
favourably with the portability and cheapness of the 
rule, and, moreover, trigonometrical and logarithmic 
functions cannot be found with them. These machines 
are shown at the Inventions Exhibition by Tate and 
Edmonson, and are worth examining. There is another 
calculating machine close to Tate’s, by which the interest 
on any sum at any rate per cent. for any time may be 
found to the nearest halfpenny in an incredibly short 
space of time, worthy of the attention of those who have 
to calculate interest. But, to return to the slide-rule, it is 
astonishing that an instrument like Gravet’s, ro inches 
long only, with which all calculations, arithmetical, trigo- 
nometrical, and logarithmic, can be worked out so easily 
and with an accuracy of from 1-500 to 1-1000, according 
to the nature of the calculation, should be so little used: 
