400 REPORT—1883. 
quickened and elevated and his faith awakened by early initiation into the ruling 
ideas of polarity, continuity, infinity, and familiarisation with the doctrine of the 
imaginary and inconceivable. It is this living interest in the subject which is so 
wanting in our traditional and medizval modes of teaching.’ 
If from this point of view we now look towards the work of the Association 
for the Improvement of Geometrical Teaching, the result is not so satisfactory as 
might have been wished. There is very little of the influence of modern ideas to 
be found in the different syllabuses which have been published. Even in the one 
headed ‘Modern Geometry’ there is nothing of the genius of modern thought. 
The subject-matter is partly taken from modern geometry, but for modern methods 
one looks in vain. In the geometrical conics, too, one would like to see Steiner’s 
generation of conics, but of these there is no trace. 
Nevertheless, it is satisfactory to see that the use of the syllabus on plane 
geometry has spread pretty widely, and it is to be hoped that it will continue to do 
so. A thorough reform, in the direction indicated, will be a difficult task, and it 
will perhaps be a long time before it is possible. At present it has not even 
been settled which series of axioms will ultimately be adopted. Of the 
various systems which have been proposed since the investigations of Riemann 
and Helmholtz, I may mention here Clifford's suggestion to replace Euclid’s axiom 
about parallels by the new one, which maintains that in a plane similar figures 
exist, or, more completely, that at any part in a plane a figure is possible which is 
similar to any given figure in that plane. This axiom is somewhat startling as 
long as we have the usual theory of similar figures in our mind. But the notion 
of similar figures is truly axiomatic, and it has lately become my conviction that 
this axiom may be extremely fruitful, and the working out of a syllabus of plane 
geometry based on it would be very desirable. 
Possibly many such attempts have still to be made before a new Euclid finds 
the materials sufficiently prepared for him to raise the hoped-for edifice. 4 
The following Report and Papers were read :— 
1. Third Report of the Committee on Meteoric Dust.—See Reports, p. 126. 
2. On some Spectroscopic Appliances. 
By Professor ArTHuUR Scuuster, F.R.S. 
The author exhibited a rotating spark-holder which could be adjusted by the 
observer at the eye-piece of the spectroscope, and thus allowed spectra of different 
bodies to be brought into the field of view in rapid succession. 
He also exhibited a modified simple form of Mermet and Déchanel’s fulgurator 
for the examination of spectra of liquid bodies. 
3. On the Absorption Spectrum of Didymium Chloride. 
By Professor Arruur Scuuster, F.R.S., and T. G, Bamey. 
The authors have examined the absorption-spectrum of crystals of didymium 
chloride by polarised light, and have found differences similar to those which 
Bunsen discovered in the sulphate. They propose to extend their observations to 
other didymium sulphate, and defer a full discussion of the comparison of the 
different spectra until more material has been collected. 
4. On the Cause of Crystalline Form. By G. Jounstone Sroney, F.R.S. 
5. A specimen of the Work of the new Chronograph at Dunsink Observatory. 
By Professor Roserr 8. Batt, LL.D., F.R.S. 
