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Ες implies that our system alignment was not perfect.	This implies that our system alignment was not perfect.
Fhis is not surprising eiven that this was the first time that TIIUMPIER had been mounted on JCNM'T and this was the first-light astronomical Image,	This is not surprising given that this was the first time that THUMPER had been mounted on JCMT and this was the first-light astronomical image.
The flux density of Jupiter at this wavelength can be predicted. from. planetary modelling (Griffin ct al..	The flux density of Jupiter at this wavelength can be predicted from planetary modelling (Griffin et al.,
. 1986: Orton οἱ al..	1986; Orton et al.,
1986: Grillin Orton 1993).	1986; Griffin Orton 1993).
Based on this. we expect the peak flux density of Jupiter to be 34 kJv/beam.	Based on this, we expect the peak flux density of Jupiter to be 34 kJy/beam.
During the observations the measured. value. of. 3c: was 0.0625.	During the observations the measured value of $\tau_{225 GHz}$ was 0.0625.
Using our relation above. between 1.5TLHz and 225Cllz. this corresponds to a value of Tyrg: of 75.95.	Using our relation above, between 1.5THz and 225GHz, this corresponds to a value of $\tau_{1.5 THz}$ of $\sim$ 5.95.
Therefore the observed. Hux density at. the telescope is predicted to be 21 Jv/beam.	Therefore the observed flux density at the telescope is predicted to be 21 Jy/beam.
The total integration time per point of the two co-acded maps was LOO seconds.	The total integration time per point of the two co-added maps was 100 seconds.
The peak was detected at à. level of 73.3. a.	The peak was detected at a level of $\sim$ 3.3 $\sigma$.
Pherefore we calculate from. the Jupiter data that the noise equivalent lux density (NEED) of the JCALT-PIUAIPER. combination is 63::10 Jv (lo Is).	Therefore we calculate from the Jupiter data that the noise equivalent flux density (NEFD) of the JCMT-THUMPER combination is $\sim$ $\pm$ 10 Jy $\sigma$ 1s).
We note that our detection is not at the 5-7 level.	We note that our detection is not at the $\sigma$ level.
llowever. we believe it is a real detection for a number of reasons: the source was seen in several pixels simultaneously: the structure in the two maps that we took was the same: the source appeared in the same place in both maps: and the NEPD we caleulate from the measurements is consistent with that. predicted. from laboratory measurements of the detector svstem.	However, we believe it is a real detection for a number of reasons: the source was seen in several pixels simultaneously; the structure in the two maps that we took was the same; the source appeared in the same place in both maps; and the NEFD we calculate from the measurements is consistent with that predicted from laboratory measurements of the detector system.
In re-gridding the map onto an RA-Dec evicl as shown in Figure 7— some smoothing naturally. occurred. as a pixel scale of 5 aresec was adopted.	In re-gridding the map onto an RA-Dec grid as shown in Figure \ref{jupiter} some smoothing naturally occurred, as a pixel scale of 5 arcsec was adopted.
The full-width at half-maximum (ENLIIM) of Jupiter in our map is 46. 38 (+S) aresec.	The full-width at half-maximum (FWHM) of Jupiter in our map is $\sim$ $\times$ 38 $\pm$ 8) arcsec.
At the time of the observations. the diameter of Jupiter was 42 arcsec.	At the time of the observations, the diameter of Jupiter was 42 arcsec.
When convolved with our ld-arcsec beam. this becomes 44.2 arcsec.	When convolved with our 14-arcsec beam, this becomes 44.2 arcsec.
Llence our observations are consistent with this.	Hence our observations are consistent with this.
Llowever. the non-circularity. visible in the map shows that we are also detecting part of the telescope error beam. which is predicted to be significant at this wavelength.	However, the non-circularity visible in the map shows that we are also detecting part of the telescope error beam, which is predicted to be significant at this wavelength.
We could not trace the error beam further in these data due to their low signal-to-noise ratio.	We could not trace the error beam further in these data due to their low signal-to-noise ratio.
Lt is also possible that if we did not have the instrument exactly in focus then this would also contribute to the apparent non-cireularity of the beam.	It is also possible that if we did not have the instrument exactly in focus then this would also contribute to the apparent non-circularity of the beam.
We focussed. the instrument using our model of the telescope and our calculation of the optimal focal position.	We focussed the instrument using our model of the telescope and our calculation of the optimal focal position.
Llowever. we cid not have time to check the focus on-source before Jupiter began to set.	However, we did not have time to check the focus on-source before Jupiter began to set.
Later in the night5 we imaged.5 Mars as it was rising.5 from airmass 1.30 to 1.29.	Later in the night we imaged Mars as it was rising, from airmass 1.30 to 1.29.
Figure S shows our map of Mars.	Figure \ref{mars} shows our map of Mars.
Once again5 the source is not centred. although5 we have managed to improve the alignment in IX. at least.	Once again the source is not centred, although we have managed to improve the alignment in R.A. at least.
The Hux density of Mars at this wavelength can be predicted from planetary moclelling in the same way as that of Jupiter	The flux density of Mars at this wavelength can be predicted from planetary modelling in the same way as that of Jupiter
points s;. determined by the recurrent sequence (see Paper 11) llere is the correlation function anc € is a random number picked from a normal distribution with (£?=0 ancl Var(£) —].	points $s_j$, determined by the recurrent sequence (see Paper II) Here is the correlation function and $\xi$ is a random number picked from a normal distribution with $\langle \xi \rangle = 0$ and $\xi$ ) = 1.
For a chosen 6 and velocity field clistribution the objective function £ is caleulated according to where r(A;) isthe simulated random intensity. eq.(19) in Paper 7(A;) the observed normalized intensity within the Ah pixel of the line profile. 0; an estimate of the experimental error. and vy=mon the degree of freedom. (m ds the number of data points anc n is the number of fitted physical parameters. n—5 in our case)	For a chosen ${\hat \theta}$ and velocity field distribution the objective function ${\cal L}$ is calculated according to where $r(\lambda_i)$ isthe simulated random intensity [eq.(19) in Paper $I(\lambda_i)$ the observed normalized intensity within the $i$ th pixel of the line profile, $\sigma_i$ an estimate of the experimental error, and $\nu = m - n$ the degree of freedom $m$ is the number of data points and $n$ is the number of fitted physical parameters, $n = 5$ in our case).
Phe minimization of X is the main goal of the procedure.	The minimization of $\chi^2$ is the main goal of the procedure.
Any parameter configuration with X71 has to be considered as a physically reasonable model for the interpretation of the observational data.	Any parameter configuration with $\chi^2 \sim 1$ has to be considered as a physically reasonable model for the interpretation of the observational data.
The computational IUMC procedure is split into two steps.	The computational RMC procedure is split into two steps.
At first. random values for the physical parameters are chosen. ic. the vector @	At first, random values for the physical parameters are chosen, i.e. the vector ${\hat \theta}$.
Secondly. an optimal velocity icld configuration is estimated. for these parameters.	Secondly, an optimal velocity field configuration is estimated for these parameters.
The current N value is computed and if it is larger than X7. (which is the value of 42 for a given credible probability Po=1 a) the whole procedure is repeated.	The current $\chi^2$ value is computed and if it is larger than $\chi^2_{\nu,\alpha}$ (which is the value of $\chi^2_{\nu}$ for a given credible probability $P_{\alpha} = 1 - \alpha$ ) the whole procedure is repeated.
La principle. o choose the vector @ in the physical parameter subspace we could use any of the common optimization methocls (like e.g. nonlinear simplex) but we apply the same stochastic RAC ocedure Lor both stages of the computational scheme.	In principle, to choose the vector ${\hat \theta}$ in the physical parameter subspace we could use any of the common optimization methods (like e.g. nonlinear simplex) but we apply the same stochastic RMC procedure for both stages of the computational scheme.
In cletail it is clescribed as follows. 1)	In detail it is described as follows. )
) X simulation box in the parameter subspace is specified by fixing the parameter boundaries.	A simulation box in the parameter subspace is specified by fixing the parameter boundaries. )
2)) @ is chosen arbitrarily in the simulation box.	${\hat \theta}$ is chosen arbitrarily in the simulation box.