- Long, which after leaving Lake of the Woods
**dashes**with its clear water over many cascades, and traverses very beautiful scenery. - The valency of an element is usually expressed by
**dashes**or Roman numerals placed on the right of its symbol, thus: H', O", B"', C I ", P", mow; but in constructing graphic formulae the symbols of the elements are written with as many lines attached to each symbol as the element which it represents has units of affinity. - Two relations R and R' are said to be ordinally similar, if a one-one relation holds between the members of the two fields of R and R', such that if x and y are any two members of the field of R, such that x has the relation R to y, and if x' and y are the correlates in the field of R' of x and y, then in all such cases x has the relation R' to y', and conversely, interchanging the
**dashes**on the letters, i.e. - Their colour is usually some tone of yellow with
**dashes**of red, brown and green, and they frequently emit a pungent odour. - If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double
**dashes**to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the**dashes**we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.

» more...

Create and save customized word lists. Sign up today and start improving your vocabulary!