Using the Sunyaev-Zel'dovich effect.

This work is concerned with the Sunyaev-Zel'dovich (S-Z) effect in clusters of galaxies and its use in cosmology. In Chapter 2, I consider possible causes of error in the determination of H0 from the uncertain geometry of clusters and complications such as lack of virialisation. From numerical simulations, I find that with 20 clusters, the resultant error is 8%. Chapter 3 details and tests a new maximum likelihood algorithm for the removal of contaminating radio sources. Two new estimates of H0 are presented, 78+26-20 km s-1 Mpc-1 for 0016+16 and 48+14-11 km s-1 Mpc-1 for A611. In chapters 4 and 5 I describe a search for new clusters via extended steep-spectrum radio emission due to merger events or head-tail sources. A candidate sample of possible high-redshift clusters is produced based on S326MHz > 65 mJy and a1.4GHz0.3GHz > 1.5. Six of these were then used as targets for S-Z observations; no unequivocal detection was found implying each cluster has a total mass <~ 10^15 Msun. Optical V, Rs and I follow-up in two of the fields shows two galaxies in each field with V - Rs ~ 3 and Rs ~ 20; similar observations of blank fields show no such galaxies and hence these are good candidate cluster members at z = 0.5-0.6