Intelligence and Miscellaneous Articles. 469 



change, if effected, will be for the worse, even if books as good as 

 Mr. Wright's are adopted. We think that an advocate for the use of 

 Euclid's 'Elements' might fairly urge — 



(1) That, on the whole, the first and third books of Euclid would 

 prove easier to a learner than Mr. Wright's first and second books. 



(2) That the arrangement by which theorems are treated first and 

 problems afterwards is calculated to weaken the learner's perception 

 of the conditions of proof, and that it might in many cases lead to 

 an unnoticed failure of proof. And he might urge that most learners, 

 particularly boys, more readily understand a reason for a thing done, 

 than a reason for an abstract truth of which they do not see the 

 use. 



(3) That to look at truths so elementary as Euclid 35. I., and 

 the propositions of Book II., through the medium of numerical mea- 

 sure is to take unnecessarily a very artificial view of those questions, 

 although its artificial character may be disguised by familiarity. 



(4) That, as a matter of science, Euclid's treatment of proportion 

 has the advantage of being perfectly rigorous and extremely elemen- 

 tary, Euclid's definition embodying perhaps the most elementary 

 conception that can be formed of equality of ratios. 



(5) That, from a teacher's point of view, it is possible to make 

 most boys understand the sixth book, and then to lead them on suc- 

 cessively to geometrical limits and to numerical measures, when the 

 question of incommensurability can be faced ; but that to try to 

 master all three difficulties at once is to undertake a nearly hopeless 

 task ; and that practically few, if any, learners would get any deeper 

 notion of ratio than that of commensurable magnitudes, at least until 

 they looked back to their elementary work after having pursued 

 their studies into the higher branches of mathematics. 



LIX. Intelligence and Miscellaneous Articles. 



ON THE CONDUCTIVITY OF SOME LIQUIDS FOR HEAT. 

 BY A. PAALZOW. 



AS far as I am aware, there are no statements respecting the con- 

 ductivity of liquids for heat besides those of Despretz*. Occu- 

 pied with investigations on the conducting-power of liquids for 

 heat, I was interested, for theoretical reasons, with the question 

 whether in liquids also there is a connexion between the conduction 

 of heat and the conduction of electricity. Hence I instituted the 

 experiments I am about to describe, only with the view of acquiring 

 a general knowledge of the phenomenon in question, and not with 

 the view of acquiring accurate numbers ; for I did not possess the 

 necessary means of solving such a problem. 



I used for the experiments a cylindrical glass vessel of 60 millims. 



* Ann. de Chim. et de Phys. vol. lxxi. p. 216. 



