  We present an extensive comparison of models of structure formation with
observations, based on linear and quasi-linear theory. We assume a critical
matter density, and study both cold dark matter models and cold plus hot dark
matter models. We explore a wide range of parameters, by varying the fraction
of hot dark matter $\Omega_{\nu}$, the Hubble parameter $h$ and the spectral
index of density perturbations $n$, and allowing for the possibility of
gravitational waves from inflation influencing large-angle microwave background
anisotropies. New calculations are made of the transfer functions describing
the linear power spectrum, with special emphasis on improving the accuracy on
short scales where there are strong constraints. For assessing early object
formation, the transfer functions are explicitly evaluated at the appropriate
redshift. The observations considered are the four-year {\it COBE} observations
of microwave background anisotropies, peculiar velocity flows, the galaxy
correlation function, and the abundances of galaxy clusters, quasars and damped
Lyman alpha systems. Each observation is interpreted in terms of the power
spectrum filtered by a top-hat window function. We find that there remains a
viable region of parameter space for critical-density models when all the dark
matter is cold, though $h$ must be less than 0.5 before any fit is found and
$n$ significantly below unity is preferred. Once a hot dark matter component is
invoked, a wide parameter space is acceptable, including $n\simeq 1$. The
allowed region is characterized by $\Omega_\nu \la 0.35$ and $0.60 \la n \la
1.25$, at 95 per cent confidence on at least one piece of data. There is no
useful lower bound on $h$, and for curious combinations of the other parameters
it is possible to fit the data with $h$ as high as 0.65.
