In Chapter 1 we introduce the basics of pulsar history, observations and terminology. The identification of pulsars with neutron stars is explained, then the various observational means of determining pulsar properties are dealt with. Next the nature and importance of selection effects are explained in turn, before an overview of the main observational data and a discussion of the outstanding features of these data. The standard models for pulsar evolution are introduced in Chapter 2. This puts into context the nature of and difficulty with pulsar evolutionary problems. Chapter 3 begins with a justification for the time-dependent nature of our work, which is jointly a criticism of the inadequacies of the time-independent argument, and an exposition of the potential merits to be gained from abandoning the ubiquitous notion of stationarity. Then the continuity equation method is introduced and the means of solution described. The technique is next demonstrated by developing four simple models in the time-dependent approach, two with and two without field decay. These show the power of the method, the critical influence of selection effects and challenges some preconceived notions concerning the steady-state ideas. This work is not intended to reproduce the observational data but to be primarily demonstrative. It is also shown in Chapter 3 how interesting inverse problems arise from the application of our method to simple models, and these can in principle be solved to yield information on the source distribution of intrinsic pulsar properties. Thus it is possible to treat the first major model in Chapter 4. This is a model with no field decay and no alignment. Using the time-dependent method, we derive the P,P distribution predicted by this model. This is then compared with the observed P,P diagram using the chi-squared goodness-of-fit test. This test will be applied to all models in turn. This is similar to the work of Cheng (1989) but more analytically explicit. The flaws of not treating the data in this fashion can be exposed with this first model. This fails to provide a satisfactory fit to the joint P,P distribution but can account for the period histogram alone. Thus accepting a model on the basis of the good fit to the P distribution would be fallacious, since it cannot explain the more important joint distribution. The field-decay type of model is examined in Chapter 5. Exponential decay of the magnetic field is the 'standard' explanation of pulsar evolution by most authors. In our model, it is found that an acceptable fit can be made to the P,P diagram. A discussion of magnetic field decay of a neutron star is also included. In Chapter 6 an alignment model is presented. By alignment, it is conventional to refer to the scenario where magnetic and rotation axes tend to align as time passes (alignment angle tends to 0
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