We 
NATURE 
[ JULY. 30, 1914 
base extension is discussed, and the conclusion is 
reached that it was probably due to lateral refraction 
caused by a cairn near to which the doubtful ray 
passed. 
The alterations which this check triangulation would 
produce in the sides which were revised were from 
I in 39,000 to I in 94,000, and the angular corrections 
from 0-989" to 1-066". 
Captain H. Winterbotham proceeds to discuss the 
accord between the bases which have been measured 
at Salisbury Plain, Lough Foyle, Lossiemouth, and 
the French base at Paris, calculated through the side 
Cassel les Harlettes, and investigates the accuracy of 
the triangulation as shown thereby. Four other bases 
which were measured with Ramsden’s steel chains at 
the beginning of the eighteenth century are also com- 
pared, though they were not used in the reduction of 
the triangulation, and are in good agreement with 
the other results. 
The general result is to show that the alteration 
which would probably be caused by the re-measure- 
ment of an arc in the United Kingdom would be small, 
and that the agreement between the calculated and 
computed lengths of the Salisbury Plain and Lough 
Foyle bases was not accidental, since the other bases 
here used indicate an accuracy of triangulation of the 
same order. 
THE BONAPARTE FUND. 
puke Committee appointed by the Paris Academy 
_of Sciences to allocate the amount placed at 
its disposal by Prince Bonaparte, makes the following 
proposals for grants during 1914. 
_ 2000 francs to Dr. Pierre Breteau, for the con- 
tinuation of his researches on the use of palladium 
in analysis and organic chemistry; 2000 francs to 
M. Chatton, to enable him to continue his researches 
on the parasite Peridinians; 3000 francs to Dr. Fr. 
Croze, for the purchase of a concave diffraction 
grating and a 16 cm. objective, to be used in work 
on the Zeeman phenomena in line and band spectra ; 
6000 francs to Dr. Hemsalech, for the purchase of a 
resonance transformer and battery of condensers, to 
be used in his spectroscopical researches; 2000 francs 
to P. Lais, for assisting the publication of the photo- 
graphic star map; 2000 francs to M. Pellegrin, to 
assist him in pursuing his researches and continuing 
his publications concerning African fishes; 2000 
francs to Dr. Trousset, to assist him in his studies 
of the minor planets; 2000 francs to M. Vigouroux, 
to enable him to continue his researches on silicon 
and its different varieties; 3000 francs to M. A‘luaud, 
to assist the publication (with Dr. R. Jeannel) of the 
scientific results of three expeditions to eastern and 
central Africa; gooo francs divided equally between 
MM. Pitart, de Gironcourt, and Lecointre, members 
of the Morocco expedition, for scientific study, 
organised by the Société de Géographie; 2000 francs 
to M. Vasseur, for the continuation of his geological 
excavations in a fossil bearing stratum in Lot-et- 
Garonne; 3500 francs to Dr. Mauguin, for the con- 
tinuation of his work on liquid crystals and the re- 
markable phenomena presented by these bodies when 
placed in a magnetic field; 2000 francs to Dr. Anthony, 
to defray the cost of his researches on the determinism 
of morphological characters and the action of primary 
factors during evolution; 4000 francs to M. Andover, 
to assist the publication of his new set of trigono- 
metrical tables; 4ooo francs to M. Bénard, to enable 
him to continue, on a larger scale, his researches on 
experimental hydrodynamics; 2000 francs to Dr. 
Chauvenet, for the continuation of his researches on 
NO, 723355 VOlMmOg| 
zirconium and the complex combinations of that ele- 
ment; 2000 francs to Frangois Franck, for the chrono- 
graphic study of the development of the embryo, with 
special examination of the rhythmic function of the 
| heart; 2000 francs to M. Sauvageau, for the pursuit 
! 
| 
| 
of his studies on the marine alge. 
The Committee recommends these eighteen grants 
after considering close upon sixty applications for 
assistance. The amount allocated for the year is 
54,500 francs. 
NAPIER TERCENTENARY CELEBRATION. 
pes Tercentenary Celebration of the publication 
of Napier’s Description of the Wonderful Canon 
of Logarithms opened formally on July 24 under the 
auspices of the Royal Society of Edinburgh. On 
Thursday at two o’clock, however, the Committee 
was able to open to the members of the congress the 
exhibition of books, calculating machines, mathe- 
matical models, relics of Napier, portraits, and other 
objects of mathematical interest. A fair number of 
visitors had already arrived in the city, and on the 
Friday morning the examination room of the Uni- 
versity, in which the exhibition was arranged, was a 
lively scene. The tide-predicting machine under the 
charge of Mr. Edward Roberts attracted a large 
amount of attention. Many forms of arithmometers 
and calculating machines, from the abacus of the 
East and Napier’s ‘‘ Bones’? down to the beautiful 
instruments of the present day occupied a large part 
of the hall. Each member received, along with his 
membership card, the handbook of the exhibition, a 
large octavo of 340 pages, which contained, not only 
a descriptive catalogue of. what was on exhibition, 
but also sustained scientific articles on sun-dials, slide 
rules, integraphs, planimeters, harmonic analysers, 
nomograms, mathematical models, etc., etc. The 
articles were contributed mainly by members of the 
mathematical departments of the Universities of 
Edinburgh and Glasgow, under the editorship of 
E. M. Horsburgh. 
The opening meeting of the congress was held in 
the debating hall of the University (Students’) Union. 
The Lord Provost of Edinburgh occupied the chair 
and introduced Lord Moulton in a brief speech, re-- 
calling the main facts of Lord Moulton’s mathematical 
career. Among the audience which filled the fine hall 
may be mentioned Prof. Andoyer, Prof. Bauschinger, 
Prof. Cajori, Sir William Bilsland, Dr. Dugald Clerk, 
Prof. Conway, Dr. Glaisher, Dr. J. P. Gram, Prof. 
Hill, Prof. Hobson, Prof. Macdonald, Major Mac- 
Mahon, Dr. Conrad Miller, Sir Alexander Napier, 
Prof. Nielsen, Prof. d’Ocagne, Prof. Putnam, Berke- 
ley, Cal., Dr. Sheppard, Prof. Stekloff, limiting the 
list to a few of the representative men from a 
distance. 
Lord Moulton, in his inaugural address, endeavoured 
to trace the origin and growth of the ideas which 
finally took form in Napier’s Descriptio. Emphasis 
was laid upon the fact that Napier’s first table is a 
table of logarithms of sines. This seemed to indicate 
that Napier’s intention was to facilitate trigono- 
metrical calculation, although in the Descriptio itself 
this limitation soon disappears from view. Lord 
Moulton divided what he judged to be the course of 
discovery into three stages. The first stage was to 
create tables which would enable numbers to be 
multiplied together without actually performing the 
calculation. For this purpose they must proceed in 
an order resulting from continued multiplication. 
The word logarithm seems to preserve the trace of 
this stage. for there can be little doubt that the word 
means ‘‘the number of the ratio.’? The second stage 
