Kansas A cademy of Science. 



ABSTRACT AND CONCRETE NUMBERS. 



Perhaps the frequent occurrence of these terms forms a sufficient reason for noticing 

 them in this connection. Number in its very nature is abstract, and it is an obvious mis- 

 nomer to call it concrete in any case. Twfi means two things, and though the kind of 

 things is not explicitly named, the essential character of number is not affected. The 

 statement "two and three are live," means merely '"two things and three things counted 

 together, are five things." It may be mentioned in passing, that since the office of num- 

 ber is exclusively that of fixing a limit of " how many," the greater or less extent of 

 " how many," does not at all affect the character of the number applicable to the partic- 

 ular case. Thus the number two or three, possesses as completely the character of num- 

 ber as a thousand or a million. It follows then that zero or naught, wlien used, as it often 

 is, to designate the limit of " how many," is i)roperly included under the name number. 

 It is believed that this consideration is not only logically consistent, but that it simplifies 

 the use of naught, as well in arithmetic as in algebra, where it often appears as the root 

 of an equation, and in many instances performs as conspicuous and important services 

 as are assigned to any number. 



The necessarily brief limits of the present paper do not permit a further examination 

 of these questions at this time ; but it is believed enough has been said to show that a 

 thorough revision of the fundamental theory of number is required in order that this) 

 branch of instruction should not fall behind in the developments of the day. 



ANALYSIS OF CLAYS. 



The following brief notes of qualitative and quantitative analyses, taken from my 

 laboratory record, will be of interest to some, and give a general idea of the chemical 

 composition of some of the clays found in so great abundance in this State. 



In this form of mineral wealth, Kansas is rich, the list embracing every variety in 

 inexhaustible quantities, from pure white porcelain clay to common marl, and in time it 

 must develop a large and varied manufacturing industry. 



Many of you have lieard of the Osage City ochre, which is found in an immense bed, 

 varying from twelve to twenty-four feet in thickness. Its composition is — 



Silicate of Alumina Neaily 98 per cent Silicate of Magnesia Trace 



Silicate of Lime Small amount ■ Scsqui-oxicle of Iron Small amount 



In that portion of the bed worked at the present time, the percentage of oxide of iron 

 is a little larger than the sample gave from which the analysis was made. 

 At Council Grove is found an ochre with the same constituents: 



Silicate of Alumina Large amount I Silicate of Magnesia Trace 



Silicate of Lime Small amount I Sesqui-oxide of Iron Moderate amount 



This ochre has exactly the shade of the Spanish hroum largely used as a mineral paint, 

 and is in every way equal to it. 



The extent of the deposit, its geological position, and its physical characters, I do not 

 know. 



Over the eastern half of the State are distributed strata of a light, bluish clay, varying 

 from one to two feet in thickness, lying immediately over or under the coal, commonly 

 called fire clay, but none that I know of are sufficiently pure to furnish first-class refrac- 

 tory fire brick, suitable for furnace linings. Some sufficiently pure, however, will, I 

 believe, eventually be found. Clays sufficiently pure for the manufacture of stone-ware, 

 and other articles that are not required to resist an intense and prolonged heat, are 

 known. 



A so-called fire clay found at Council Grove, contains — 

 Silicates of Alumina and Iron. | Carbonate of Lime. | Sulphate of Lime. | Chloride of Calcium, 



Carbonate of Magnesia. 



