98 
of logarithmic tables was’ invented and drawn 
up almost contemporaneously with Napier’s work 
by Jost Burgi, a Swiss. A brief note deal- 
ing with Burgi’s work is contributed to the 
Mitteilungen der naturforschenden Gesellschaft in Bern | 
for 1914 (p. 318) by Dr. A. Bohren. Burgi was born 
at Lichtenstein, in Toggenburg, about the year 1552, 
but of his early life little is known. He was originally 
a clockmaker by trade, but developed .a talent for 
astronomical work, and, under the patronage at first 
of the Landgraf Wilhelm of Hesse, and _ later 
of Rudolf II. of Bohemia, he not only invented new 
astronomical instruments, but greatly assisted Kepler 
with his observations. His treatise on logarithmic 
methods described under the title ‘‘Arithmetical 
and Geometrical Progression-Tables"’ first saw the 
light in 1620, but it'is certain that the tables were 
calculated and used by him long before that date, and 
their publication had been ‘delayed by the war in 
Bohemia. Probably for the same reason the instruc- 
tions which were to accompany the tables were never 
published, and in consequence they failed to come 
into general use. Both Biirgi and Napier built up 
their tables by forming successive positive integral 
powers of anumber differing from unity by a very small 
decimal, but Biirgi’s tables are based on the relations 
x=10n, and y=108 (1-0001)", while Napier calculated 
his logarithms from the successive powers of 1—10~’. 
It would thus appear probable that Biirgi was the 
first to use a base greater than unity, and so to obtain 
a scale more suitable for use with integral numbers. 
Whether Napier was acquainted with Biirgi’s work 
is considered doubtful. Possibly Napier may have got 
the idea from Biirgi, and his choice of a system the 
base of which is less than unity may have been in- 
tended as an improvement to facilitate the use of the 
tables in trigonometry. 
CrrcuLar No. 58 of the Bureau of Standards con- 
tains much valuable information as to the properties 
of invar and related nickel steels. Invar is a nickel 
steel containing about 36 per cent. of nickel, together 
with small amounts of carbon and manganese, 
and metallurgically negligible amounts of sulphur, 
phosphorus, and other elements. It melts sharply at 
about 1425° C. Above 200° C. to its melting point it 
may be considered to consist of a homogeneous solid 
solution of the above elements. Below 200° C., and 
at a temperature dependent on its history and exact 
composition, it undergoes a reversible transformation 
of such a nature that for any sample the transforma- 
tion may be incomplete. This condition of thermo- 
chemical instability gives rise to both slowly and 
quickly changing values of its physical properties— 
changes which are particularly manifested in the ex- 
pansion. It can be rolled, forged, turned, filed, and 
drawn into wires, and it takes a beautiful polish, giving 
an excellent surface on which fine lines may be ruled. 
It will withstand without spotting the corrosive action 
of water, even when immersed for several days. Its 
electrical resistivity is about eight times that of pure 
iron, and its temperature-coefficient of electrical resist- 
ance about o-o012 per degree Centigrade. It is ferro- 
magnetic, but becomes paramagnetic in the neigh- 
bourhood of 165° C. The mean ,coefficient of linear 
expansion between 0° and 4o° C. is for ordinary invar 
of the order of one millionth, and samples have been 
prepared with even small negative coefficients; the 
amounts of carbon and manganese appear to exercise 
considerable influence on the expansion. Above 
200° C, its expansion is nearly the same as that of 
ordinary Bessemer steel. It is subject to changes in 
length due to “‘after effects”? following cooling from 
a high temperature, and even following slight altera- 
tions in temperature. A mathematical formula, 
NO. 2449, VOL. 98] 
- NATURE 
[Ocroser 5, 1916 
Ah/h=—0-00325 . 107 "t*, 
holds for. temperatures . be- 
tween 0° and 100° C, ! ; 
Tue results of the measurements of the rate of 
vaporisation of platinum yessels raised to high tem- 
peratures which have been made at the U.S. Bureau 
of Standards by Messrs. Burgéss and’ Waltenberg are 
given in Scientific Paper No. 280, recently issued by 
the bureau. At temperatures below goo° C. there is_ 
no appreciable vaporisation, whatever be the composi- 
made. At 1000° C., however, the loss from 100 sq. cm. 
of a vessel of pure platinum is 0-08, and at 
1200° C. 0-81 milligram per hour. For an alloy con- 
taining 1 per cent. iridium the corresponding rates are 
at 1000° C. 0:30, and at 1200° C, 1-2 milligrams per 
hour. For a 2-5 per cent. iridium alloy they are at 
tooo? C. 0:57, and, at 1200° C. 2-5 milligrams per 
hour. Rhodium alloys, on the contrary, vaporise at 
lower rates. For an 8 per cent. rhodium alloy the 
rates of loss are at 1000° C. 0-07, and at 1200° C. 
0:54 milligram per hour. 
Sivce the appearance three years ago of the last 
edition of Prof. G. Lunge’s ‘The Manufacture of 
Sulphuric Acid and Alkali,” vol. i., many additions to 
the subjects treated of have been made. To deal with 
the new developments, Prof. Lunge has prepared a 
supplementary volume, which Messrs. Gurney and 
Jackson announce for publication this autumn. 
Mr. F. Epwarps, of High Street, Marylebone, 
announces for early publication ‘‘The Fauna and 
Ethnology of New Guinea,” being the official records 
of the collections formed by the British Ornithologists’ 
Union Expedition, 1909-11, and the Wollaston Expedi- 
tion, 1912-13, in Dutch New Guinea. The work will 
be in two volumes, and the edition limited to 150 
copies. : 
OUR ASTRONOMICAL COLUMN. 
Tue AstronomicaL Compass.—The utilisation of the 
heavenly bodies as a means of determining direction 
has attracted considerable attention since the outbreak 
of war, and various attempts to simplify the problem 
for general use have been made. Simplified azimuth 
tables, in conjunction with maps of the stars, have 
mostly been employed, but it is evident that such tables 
may be replaced by graphical projections of the circles 
of the celestial sphere. Under the title of the ** Rev. 
William Hall’s Visible Astronomical Compass,” an 
arrangement for the direct solution of the chief 
problems depending upon the diurnal motion of the 
heavens has been published by Mr. J. D. Potter, 145 
Minories, E.C. (price 1s. net, post free). A circle 6 in, 
in diameter, on a card ro in. x8 in., contains a stereo- 
graphic projection on the plane of the horizon, for 
latitude 50° N., showing the circles of each even 
degree of declination, and ’hour circles at intervals of 
ten minutes. Circles of azimuth and altitude are not 
drawn, but the outer edge of the horizon circle is 
graduated for true bearings, and altitudes may be read 
off on a scale provided, after measurement with dividers 
along a travelling thread fixed at the zenith point. 
Given the time, or an approximate measurement of 
altitude, the bearing of any object is, of course, readily 
determined, and the ‘‘compass’’ can then be adjusted 
so as to show true directions. No new principle is 
involved, but the arrangement provides a stereographic 
projection in a convenient form, and the necessary 
instructions for its use are given. It should be under- 
stood, however, that a star map and an almanac are 
also requisite, and that some means of measuring 
altitudes would greatly extend the usefulness of the 
| projection. i 
tion of the platinum alloy of which the vessel is 
