  We compare four sunspot-number data sequences against geomagnetic and
terrestrial auroral observations. The comparisons are made for the original
SIDC composite of Wolf-Zurich-International sunspot number [$R_{ISNv1}$], the
group sunspot number [$R_{G}$] by Hoyt and Schatten (Solar Phys., 1998), the
new "backbone" group sunspot number [$R_{BB}$] by Svalgaard and Schatten (Solar
Phys., 2016), and the "corrected" sunspot number [$R_{C}$] by Lockwood at al.
(J.G.R., 2014). Each sunspot number is fitted with terrestrial observations, or
parameters derived from terrestrial observations to be linearly proportional to
sunspot number, over a 30-year calibration interval of 1982-2012. The fits are
then used to compute test sequences, which extend further back in time and
which are compared to $R_{ISNv1}$, $R_{G}$, $R_{BB}$, and $R_{C}$. To study the
long-term trends, comparisons are made using averages over whole solar cycles
(minimum-to-minimum). The test variations are generated in four ways: i) using
the IDV(1d) and IDV geomagnetic indices (for 1845-2013) fitted over the
calibration interval using the various sunspot numbers and the phase of the
solar cycle; ii) from the open solar flux (OSF) generated for 1845 - 2013 from
four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys., 2014)
and analysed using the OSF continuity model of Solanki at al. (Nature, 2000)
which employs a constant fractional OSF loss rate; iii) the same OSF data
analysed using the OSF continuity model of Owens and Lockwood (J.G.R., 2012) in
which the fractional loss rate varies with the tilt of the heliospheric current
sheet and hence with the phase of the solar cycle; iv) the occurrence frequency
of low-latitude aurora for 1780-1980 from the survey of Legrand and Simon (Ann.
Geophys., 1987). For all cases, $R_{BB}$ exceeds the test terrestrial series by
an amount that increases as one goes back in time.
