328 B. A. Gould—Number and Distribution 
expressions of the form ab” can be found which will represent 
all the values to the 8! magnitude inclusive, with an essentially 
better accordance. The numerical values of the residuals 
18 times, that of a star of the first magnitude. 
he Uranometria Nova of Argelander, which gives the care- 
fully observed magnitudes of all the stars which he could dis- 
tinguish with the naked eye, afforded the standard for the 
magnitudes of the Durchmusterung ; yet the first glance makes 
manifest large discrepancies between the rapidly made estimates 
in the latter work and the sharp determinations of the former. 
The recently published revision and extension of the Uranome- 
tria by Professor Heis of Aachen, assigns the magnitude to the 
nearest third of a unit for every star which he could discern, 
the lowest being 64, or one-third of a magnitude fainter than 
Argelander’s inferior limit. The far greater precision of these 
determinations would give a more trustworthy basis for our 
inquiries than the Durchmusterung affords, were the numbers 
large enough to eliminate such irregularities as may justly be 
treated as accidental ; but this seems not to be the case. 
The completion of our Argentine Uranometry now augments 
the number of accurately determined stars, and renders it possl- 
ble to assign the actual magnitudes for all stars throughout the 
heavens which are easily visible to the naked eye. I have 
taken much pains to secure an accordance between the adopte 
scale of magnitudes and that employed by Argelander in his 
Uranometry, and regard it as unlikely that the probable error 
of our individual magnitudes exceeds one-tenth of a unit. 50 
does Heis seem to have omitted no efforts for securing a0 
accordance of his work with the same standard, and it is im- 
probable that any essential error can exist in these estimates, 
: aoe as they are by an astronomer of exceptional keenness 0 
