 ... from 0 to oo , we see that while X is increased from - 1 to 0 the first member of (50) passes an infinite number of times continuously through all real values from - oo to + oo : and that it does the same when X is diminished from + 1 to 0. Hence...  Philosophical Magazine - Page 1631880Full view - About this book
 | Royal Society of Edinburgh - Science - 1880 - 864 pages
...the same when X is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in A, has an infinite number of roots between — 1 and...its second member is clearly positive, whatever be tiia ; and its first member is essentially real and negative for all real values of X except between... | |
 | William Thomson Baron Kelvin - Mathematics - 1910 - 581 pages
...the same when X is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in X, has an infinite number of roots between — 1 and...1 and + 1, as we see by remarking that when X2>1, — g2 is real and positive, and —Ji(q)/qJi(q) is real and > i/(— qz) ; while i/q2\ whether positive... | |
 | William Thomson Baron Kelvin - Mathematics - 1910 - 588 pages
...the same when X is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in X, has an infinite number of roots between — 1 and...between — 1 and + 1, as we see by remarking that when X" > 1, —g* is real and positive, and —Ji'(q)/qJi(q) is real and > i'/(— q*) ; while i/q'\, whether... | |
 | William Thomson Baron Kelvin - Mathematics - 1910 - 588 pages
...the same when X is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in X, has an infinite number of roots between — 1 and...between — 1 and + 1, as we see by remarking that when X* > 1, —q* is real and positive, and —Ji'(q)/qJi(q) is real and > i/(— q*) ; while i/^X, whether... | |
 | Royal Society of Edinburgh - Science - 1880 - 874 pages
...the same when X is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in X, has an infinite number of roots between — 1 and...remarking that when X2>1,— q2 is real and positive, and - J'i(q)/q3i(q) is real and > i/( - qz), while i/qz\, whether positive or negative, is of less absolute... | |
 | Royal Society of Edinburgh - Science - 1880 - 850 pages
...the same when X is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in X, has an infinite number of roots between - 1 and 0...clearly positive, whatever be ma; and its first member i? essentially real and negative for all real values of X except between - 1 and + 1 , as we see by... | |
 | English periodicals - 1880 - 552 pages
...the same when A, is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in X, has an infinite number of roots between — 1 and...between — 1 and + 1, as we see by remarking that when \J>1 — g* is real and positive, and ~3't(q)iq3i(q) is real and >i/(—qi)', while HcfK, whether positive... | |
 | Sir Joseph Larmor - Electric power - 1929 - 596 pages
...the same when X is diminished from + 1 to 0. Hence (50), regarded as a transcendental equation in X, has an infinite number of roots between — 1 and...between — 1 and + 1, as we see by remarking that when X'->1, —*/-' is real and positive, and —</,•'( </)'</ </<(</) is real and > /•'(— </') ;... | |
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