Titanium-Oxygen Bond Length -Bond Valence Relationship

A bond length–bond valence correlation is a simple method of checking and evaluating molecular structures and is of great interest in chemistry, biology, geology, and material science. Recently, we used quantum-mechanical arguments to derive Pauling’s bond length-valence relationship and to define the adjustable fitting parameter b in terms of atomic-orbital exponents. Improved orbital exponents were generated for elements 1-103 using published atomic radii and single-bond covalent radii as well as a continuous function for effective principal quantum number. In this study, we use orbital exponents for titanium (Ti) and oxygen (O) to generate a bond length-valence relationship for Ti-O bonds. Recent crystallographic Ti-O bond lengths from 32 environments were collected and converted to Ti-O bond valences to check the reliability of the bond length-valence relationship where Ro was found (bond length of unit valence). This relationship is expected to apply to any Ti-O bond regardless of environment, physical state, or oxidation number

Extra-Constitutional Limitations upon Legislative Power

THE appearance of Professor Haines\u27 volume on The Revival ofNatural Law Concepts and the recent decision of the SupremeCourt of Oklahoma in Thomas v. Reid, present anew the issuewhether state legislatures are limited in their powers by restrictionsnot found in the text of written constitutions. In the caseof Thomas v. Reid the court held invalid a legislative act requiringa vote of sixty per cent of the qualified voters to authorizethe sale of a municipally-owned public utility, saying that majorityrule is one of the foundation stones of our government and that the legislature is powerless to take away the right oflocal government existing in the several municipalities at thetime of the adoption of the state constitution

The Constitution-1787 and Today

An Address given before Indianapolis Bar Association, September 6, 1944

State Constitutional Conventions and State Legislative Power

The State of Tennessee faces a serious problem in that it badly needs changes in its Constitution of 1870 and finds it substantially impossible to make such changes by means of proposed amendments by the two houses of its General Assembly. The requirements (1) that legislative proposal be by a majority of all members of the two houses and that it be agreed to by two thirds of the General Assembly then next chosen, and (2) that approval of a proposed amendment be by a majority of all the citizens of the State, voting for Representatives, \u27 substantially defeat possibility of change, as has been found with respect to such requirements in other states. The further requirement that amendments are not to be proposed oftener than once in six years materially restricts legislative proposals, and such proposal if made has little chance of adoption. In the State of Tennessee there appears to be no possibility that the General Assembly should submit a revised constitution to popular vote as was done in the State of Georgia in 1945