460 REPORT— 1873. 



independent of one another. For example, if the two assumptions were made 

 that two straight lines cannot enclose a space, and that a straight line is the 

 shortest distance between any two of its points. It appears to the Committee 

 that it is not advisable to introduce redundant axioms, but that all the as- 

 sumptions made should be necessary for demonstration of the propositions 

 and independent of one another. 



It appears that the Principle of Superposition might advantageously be em- 

 ployed with greater frequency in the demonstrations, and that an explicit 

 recognition of it as an axiom or fundamental assumption should be made at 

 the commencement. 



The Committee think also that it would be advisable to introduce explicitly 

 certain definitions and principles of general logic, in order that the processes 

 of simple conversion may not be confounded with geometrical methods. 



3. The Syllabus of the Geometrical Association. 



The Association for the Improvement of Geometrical Teaching has issued 

 (privately) a syllabus covering the ground of the first three books of Euclid 

 and the doctrine of proportionals. The Committee are of opinion that this 

 Syllabus is decidedly good so far as it goes, but they do not wish to make a 

 detailed report upon it in its present incomplete state. AVhen it is finished, 

 however, they will be prepared to report fuUy upon the merit of its several 

 parts, to make such suggestions for revision as may appear necessaiy, and to 

 discuss the advisability of giving to it the authority of the British Association. 

 For this purpose the Committee request that they may be reappointed. 



Interim Report of the Committee apjjoiiited for the purpose of making 

 Experiments on Instruments for Measuring the Speed of Ships, ^-c. 



Your Committee have to report that, owing to the various engagements of 

 the members, it has been possible to hold only one meeting during the past 

 twelve months. 



At this meeting it was resolved to request the loan of instruments of 

 each of the pressure and other logs to be experimented with, and also to 

 endeavour to obtain the use of a vessel whereon to carry out the expe- 

 riments. 



Your Committee have much pleasure in stating that three instruments 

 have now been kindly placed at their disposal, as well as a steam-launch 

 for conducting the experiments. 



Your Committee, if reappointed, trust that some actual results may be 

 anticipated during the next twelve months. 



No expense has been incurred, and no part of the grant of .£50 has 

 been drawn. 



