# Dimensionless units

Martin Hill mchill at dial.pipex.com
Fri Feb 18 08:27:24 PST 2005

```David Berry wrote:
> But the scaling factor as I understand it is just the ratio of the units
> you want, to the SI units implied by the dimensional analysis. That is,
> The DIMEQ for "Jy" is "MT-2", implying SI units of kg/s/s, and the
> corresponding SCALEQ value of 1.0E-26 means that 1 Jy is 1.0E-26 kg/s/s/.

I don't actually think the scaling factor has to make the dimension
equation match SI units, or indeed any other.  It just exists so that we
can convert between the various values *in that context*.  Although SI
might be a sensible convention.

> But since angle does not enter into the dimensional analysis, neither will
> it enter into the scaling factor. So I would expect Jy/sr and Jy/arcmin**2
> to have the same scale factor.

But an angle is a ratio, so isn't the scaling factor the inverse of that
ratio?  Similarly with any other ratios?  Minutes/Seconds have a ratio
which goes into the scaling factor; they just happen to have a dimension
too.

>>However you can, in principal, ask a dimension-based unit converter to
>>convert from Jy/sr to Jy, and it will not be able to tell you that this is,
>>at first glance, just silly.
>
> Is this progress, given that a straightforward string parsing system could
> tell you this?

"Progress?" No! Dimension analysis has been around since well before I
was at school which was a good (mumble mumble) years ago. Dimension
analysis gives us an old, simple, easily-parsed way of comparing like
with like.  I don't think dealing with the massive range of different
units in all their different combinations is straightforward at all...
But then I am just a wimp.

Martin

--
Martin Hill
AstroGrid Software Engineer @ ROE
07901 55 24 66

```