38 SIXTH REPORT — 1836. 



forte and organ as now tuned, they are altogether rejected, and pro- 

 nounced discordant, although in fact they would occasion no beating in 

 an organ perfectly tuned. 



The object of this paper was to show that they are improperly discarded, 

 and that as they characterize the sweetest concords, as they are there- 

 fore required by the ear, and are constantly practised by the best voices, 

 it is worth while to inquire more into the consequence of adopting them 

 wherever it is possible, and of teaching their extensive use in every 

 school of Music. 



Plutarch, Boethius, and all the authors whose writings are collected 

 by Meibomius, viz., Aristoxenus, Euclid (Introductio Harmonica), Ni- 

 comachus, Alypius, Gaudentius, Bacchius, Aristides, Quintilianus, and 

 Martianus Capella. explain none of these higher orders, but Ptolemy in 

 his Harmonics proves that Archytas, Eratosthenes, and Didymus, as 

 well as himself, used them continually. 



Far from agreeing with Dr. Burney that two tones and two semitones 

 are all that are useful, and that eleven ancient intervals are impracticable. 

 Dr. Rootsey endeavoured to show that 30 intervals, namely 8 tones and 

 22 semitones, are required by a modern ear, and are daily practised on 

 the voice and violin ; they ought therefore to be universally understood 

 and appreciated by all contrapuntists and professors of the science of 

 music. 



On Mnemonical Logarithms. By Samuel Rootsey, M.D. 



In this communication the author described and exemplified the use 

 of certain low numbers, which serve to compare the simpler ratios with 

 sufficient accuracy for many purposes, and thus, when fixed in the 

 memory, to supply occasionally the want of a table of logarithms. 



Experiments on the Weight, Height, and Strength of Men at different 

 Ages. By Professor Fokbes. 



These experiments, on above 800 individuals, students in the Uni- 

 versity of Edinburgh, were entirely made personally by the author, with 

 a view to the extension of M. Quetelet's general results and to the 

 comparison of the physical development of different nations. Of the 

 persons measured, (who were chiefly between the ages of 15 and 25,) 

 nearly two thirds were natives of Scotland, and in the calculation of 

 averages these were kept apart, as were the English and Irish. The 

 leading results were these : 



1 . The form of the curves indicating the law of development with 

 age, remarkably coincide with those of M. Quetelet. The attainment 

 of full growth seems (as in his experiments) to be scarcely complete 

 even at the age of 25 . 



2. The development of the Scotch in the particulars of weight, height. 



