PROCEEDINGS, SEPTEMBER, XXVii 



double star measurements." The author referred to the fact that some 

 of the grandest achievements of science were due to workers who had 

 had to content themselves with very simple and perhaps roughly 

 constructed apparatus, the outcome of their own ingenuity, called 

 forth by the necessities of the case. The writer claimed the applicability 

 of these remarks to his own case only so far as they related to the 

 necessity of trusting mainly to his own resources in his very limited 

 field of scientific work. The instrument, of which he furnished a 

 description, had been in this way the outcome of his necessity ; its 

 special function being the measurement of very minute angular distances, 

 such as those of double stars, giving at the same time the angle of 

 position with reference to the meridian. 



PYRAMIDAL NUMBERS. 



Mr. Johnston read a paper on a discovery made respecting pyramidal 

 numbers, suggesting that these might have formed the original 

 selections of sub-divisions of time, space, weight, coinage, etc. 



Mr. Johnston suggested that as the Egyptian pyramid builders were 

 great geometricians, the peculiar combinations of numbers in models of 

 simple pyramids of odd, even, and mixed numbers would be familiar to 

 them ; and that the square pyramid of even numbers with 12 as base and 

 the odd and even square pyramids with a base of twice 7, or 14, might 

 be seized upon by them for typifying astronomical facts, in conjunction 

 with some great fixed standard of measurements. The selection of 

 these types might be supposed reasonable, as the aggregates or squares 

 of cubes in their principal divisions coincide exactly with the known 

 days of year, month, week, etc. ; their simple multiples also coincide 

 with the principal dimensions of the Great Pyramid of Egypt, and with 

 the length of the Egyptian cubit ; while many of the natural sequences 

 of related layers of cubes such as 4, 12, 20 ; 28, 56, 112 ; 44, 220, 440 ; 

 12, 24, 36, 144 — are very suggestive, as accounting for the origin of 

 many of our more important existing sub- divisions of time, space, 

 weight and money. 



Mr. Taylor said it would be almost impossible to discuss such a 

 paper. He suggested the advisableness of dividing the work of the 

 Society into difierent branches. They might form a Philosophical 

 Society to deal with subjects apart from the scientific subjects now 

 dealt with by the Society. Many subjects would, he thought, be dealt 

 with under such an arrangement. 



Mr. Morton said the Society was always ready to discuss papers on 

 any subject. They were too small to have these sub-sections. This 

 had been done in the past, and lasted but a very short time. The 

 Council had considered the matter some three years since, and decided 

 that the Society was too small to thus sub-divide themselves. The 

 papers of late years had been most varied, and had always been ably 

 dealt with. He drew attention that a member of the New South Wales 

 Society had congratulated them on the fact that the Royal Society 

 of Tasmania in the thoroughness of its work had only one contemporary 

 society in the colonies that held higher position than them, viz., the 

 Linnffian Society of Sydney. 



COMPLIMENTARY. 



The President in moving the usual complimentary vote to contributors 

 of papers, said he thought the Society specially indebted to Mr. Barnard 

 for his paper. The records of the Society were for all time, and it 

 would be to these records that reference would be made for authentic 

 information on a matter of this sort. He thought the paper would 

 help much toward the settlement of the question as to the last of the 

 Tasmanian aboriginals, seeing that it adopted the scientific method of 

 taking nothing for granted, but giving data for all his conclusions. 



