,._ ,;. A. BAUFBOfl 



O v 



,,., t:iu i,s that d^nd "M "Equity, I shall take as standard 



= -01 = tan' 1 34' 22"'6, 



,,, sl,,l! ,1s,, ,iv,- the -suits for = tan 30', and = tan ('. We have then for the 

 radius of the <;nat!c circle 



fl- tan 30'. = tan 34' -4. = tan 60'. 



_0"-0042 -0"X)048 -O'"0083. 



I-',,,- tli,- /./</;* of the focal cir-l'- 



0-taiiSO 1 . = tan 34' -4. = tan 60'. 



+ 0'"282 + 0"'370 + 1"'127. 



P the m<//* '!/'/" wnwtore ,,f the field, -1G2'817 ; and hence for the displace- 

 ment ,,f the f.K-al circl. IV. .11 1 the plane through the axial principal focus 



/3 = tan30'. = tan 34' -4. = tan 60'. 



- -000006 -'000008 -'000024. 



Finally. i>r the distortional displacement 



ft = tan 30'. ft = tan 34'-4. ft = tan 60'. 



+ 4"'48 4-6"75 +35'"89. 



It will he recalled that the linear unit is supposed to be 100 inches.* 



We conclude that spherical aberration, coma, and curvature of the field are now 



completely insensible, and that stars would be represented by strictly circular images 



of diameter 0'56 seconds at a distance of 30 minutes from the centre of the field, and 



2'25 S.M-.. in Is at 1 degree distance. No images at present obtained with any telescope, 



at the middle of the field, where all obliquity-faults are absent, are sensibly less than 



1 Beoond in diameter. Hence this also is completely satisfactory up to a diameter of field 



of l degrees, or even more. There remains distortion, which requires examination. 



This can !* calculated precisely and applied as a correction to measures made, along with 



difl'i'tvntial ivt'raotion and other unavoidable corrections. Hence, even if its amount 



is very considerable it can be dealt with in a way that will not vitiate the use of the 



telescope. It is possible, indeed, that a correction for distortion requires to be applied 



toother 1'-l-M-"|x-s now in use, especially those in which the lenses of the object-glass 



are aepurati-d. It is instructive to look into the contributions of the different surfaces 



t< tin- t,.tal <(', Ml. Tin- most remarkable is 132'4 units from the surface (6) which 



is nearly a plain- surface. This is an obliquity-constituent, and would be present if 



tin- surface were a perfect plane. We see by examining the normal scheme next 



preceding the surface (6) that the original obliquity, /3, of the ray is increased nearly 



iililnl Mmrh .v, IHI.i. It is of interest to add that these conclusions have been checked by 

 trigonometrical calculations also, made by Mr. A. E. CONRADY at the instance of one of the Referees.] 



