CclxXX DIAMETERS. 



i 



Assuming the value of t to be identical for the two planets, and combining the results 

 with regard to their probable errors, Professor Peirce obtained the final determinations : 



t = 0."565 O."121 f = 5."055 O."101 for Mars 



e = 8."546 O."086 for Venus 



The discordance between these results and those deduced from Konigsberg observations cannot 

 fail to attract attention. 



I had hoped that the large number of observations now under discussion would throw much 

 light upon the source of these discordances, and did not consider it permissible, under the 

 circumstances, to omit terms containing the two unknown quantities t and u from the 

 equations of condition. One of these, t = i x + q, depends upon such influences as are 

 peculiar to the observer and the instrument, comprising such portion of the irradiation as is 

 constant, as also the personal error of the observer in setting, and any error in the assumed 

 thickness of the threads. The other, u = t>( + i a} is simply the correction to the assumed 

 semidiameter, and consists of the correction proper, together with such irradiation as may be 

 practically inseparable from it when illuminated limbs are observed, or that which varies with 

 the amount of light. These two terms are not strictly merged, the influence of one varying 

 inversely with the distance from the earth, and that of the other being dependent on the 

 brightness, and consequently on the radius-vector also. But in the entire absence of any proba- 

 bility of trustworthy results should these be separated, both were brought into one term, having 

 a coefficient inversely proportional to the distance from the earth. 



The earliest tentative solutions, in which these quantities were placed on the same footing 

 with the others, suggested grave doubts as to the practicability of deducing satisfactory results 

 even for t and u. It has been seen that in the subsequent solutions these doubts were too 

 well confirmed ; so that it became necessary both to ignore one of the terms, by assuming one 

 unknown quantity as inappreciable, and then to call the measured semidiameters to our aid for 

 freeing the fundamental equations from the influence of the other one. For various reasons it 

 appeared advisable to discard u rather than t, especially, since the variety of instruments and 

 observers seemed to offer more opportunities for the elimination of the latter than the compara- 

 tively small variation in the distance during the period comprised by any one of the four 

 planet-series permits for the former. 



The deduction of any satisfactory values of the semidiameters from the Fundamental 

 Equations being entirely abandoned, our only remaining reliance must be upon what were 

 called in 11 " Additional Equations," i.e., those derived from actual measurement of the 

 diameters ; these measurements having been in a few cases direct, and in the others affected by 

 the motion of the planet and by changes of parallax and refraction. But here, also, as has been 

 already stated, the attempt to separate the two unknown quantities was unavailing ; and the 

 only course is, here upon a small scale as in the whole investigation upon a larger one, to 

 deduce from the materials before us such results as they are competent to furnish, and therewith 

 to be for the present content. 



