Indirect estimation methodologies of the total fertility rate (TFR) have a long history within demography and have provided important techniques applied demographers can use when data is sparse or lacking. However new methodologies for approximating the total fertility rate have not been proposed in nearly 30 years. This study presents a novel method for indirectly approximating the total fertility rate using an algebraic rearrangement of the general fertility rate (GFR) through the known relationship between GFR and TFR. It then compares the proposed method to the well-known Bogue-Palmore method. These methods are compared in 196 countries and include overall errors as well as characteristics of the countries that contribute to fertility behavior. Additionally, these methods were compared geographically to find any geographical patterns. We find this novel method is not only simpler than the Bogue-Palmore method, requiring fewer data inputs, but also has reduced algebraic and absolute errors when compared with the Bogue-Palmore method and specifically outperforms the Bogue-Palmore method in developing countries. We find that our novel method may be useful estimation procedure for demographers.

The natural rates of occurrences in the gases He, N, Ne, and A, of nuclear interactions of the cosmic --ay N-ccmponent in which more than 8 Mev are given to charged secondary particles, have been measured* The rates per gram atom of the four gases are in about the same ratio as their geometric nuclear cross sections. An integrated flux of N-rays of 6.0 x JO" 3 cm* 2 sec' 1 would produce the observed rates of occurrence of nuclear interactions if the cross section were geometric. The rates in argon, measured at sea level and 10,600 ft. elevation, correspond to an absorption mean free path in air of 132 £ 4 g cm* 2 for the total flux of N-rays. The interactions, 2783 in total, were observed in the gas of a cloud chamber filled to 5 atmospheres pressure. Inside the cloud chamber was placed a system of wires forming an ionixation chamber. An expansion was initiated whenever a pulse from the ionixation chamber corresponding to an energy release of more than 8 Mev (1.5 Po alpha) occurred. Fast reduction of the high voltage after electron collection was over permitted track formation on the positive ions. Of the nuclear interactions produced in argon about 20% are produced by charged particles at the higher elevation, and about 15% at sea level.

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In 4949 photographs of cosmic-ray phenomena, not associated with dense air showers, occurring in a counter controlled cloud chamber surrounded by lead, the numbers of nuclear interactions in which secondaries were produced and observed to occur in and above the chamber were 182 and 223, respectively. The mean free path for nuclear interaction of the penetrating particles produced in these nuclear interactions is 316=fc70 g/cm 2 of lead, while for nuclear scattering (large angle scattering without the production of secondaries) it is at least 4 or 5 times this value. The projected zenith angular distributions of the secondaries from these interactions are given. The lightly ionizing secondaries going in the forward direction have an angular distribution ^cos 3 0, while those in the backward direction from nuclear interactions occurring in the chamber have a uniform distribution.

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