AUBURNDALE, MASS., Jan. 9, 1889. 



Dear Sirs : For many years I have been of the opinion, reasoning " priori, that 

 the limit of precision attainable in tin- ordinary Held operation-, of the civil en- 

 gineer might, ho attained, other things equal, as well with a small as with a large 

 instrument . 

 This opinion is continued by the results of some recent experiments with in- 



:,ent- of your make, to which 1 shall now call your attent ion. 



For several weeks I have been engaged in the design and const ruction of an ap- 

 is for determining the exact equivalent foci of lenses. This apparat n- in- 

 cludes a collimating telescope, in the principal focus of which arc two vertical lines ; 

 and the accuracy of the results obtained with it depends upon the accuraey of the 

 irement of the angular distance between these linos a^ viewed through Hie 

 collimator objective. 



lir-t series of measurements of this angle was made with my 4-in. theodolite 

 liuili by you several years ago. This instrument, described in your catalogue as 

 N<>. la.' ha- a horizontal circle graduated to be read to I 7 of arc by two equidis- 

 tant verniers; but it is easily read to 30" by estimation. As to its general design 

 and workmanship, there are no changes I should wish to have made 1 . 



The lir-t series of measurements of the "collimator angle" wore made in the 

 foil'. wing manner: vernier A was set at the graduation of the limb, and twenty 

 f twelve repetitions each (six direct and six reversed) were taken in the direc- 

 tion of increasing readings. This covered the limb up to 298, arid the resulting 

 mean angle was 1 14' 27.49" 



liy the second series, the collimator angle was again determined by precisely 

 similar measurements using the 8-in. theodolite built by you for the Massachusetts 

 Hoard of Harbor Commissioners in 1877. 



The horizontal circle of this instrument is graduated to be read to 10" of arc by 

 two equidistant verniers; but it is easily read to 5" by estimation. The resulting 

 n:ean angle is 1 14' 27.66", differing only 0.17" from the mean angle obtained with 

 the -i-in. theodolite. 



The angles resulting from each set with both instruments are arranged side by 

 side in the following table : 



RESULTS FOR COLLIMATOR ANGLE. 



Sect. 4 in. iiixtrinnriit. I'M ire Kil. ,*-/. iitxtrnim ///. 1 'age 183. 



No. 4b. No'. I-.'. 



I 1 14' 26.3" 



II 27.5 



ill 27.5 



1\ 27.5 



V 25.0 



\ I 27.5 



VII L'S.7 



VIII 27.5 



l\ 27.5 



X 25.0 



\l 30.0 



MI 25.0 



Mil 28.7 



\IV 28.7 



\ V 27.5 



ICV1 27.5 



\ \ II 27.5 



\\III 30.0 



\ I X 27.5 



\\ -,.:, . 



1 14' L'7.4!l" 1 11' 



probable ermr of tin- mean angle with No. 154, as computed by the method 

 of lea-t. square.-, U <>.1.V._ After 1he observations were finished as above, - 

 VI. wa- repeated with No. 154. the resulting angle being exactly the same. I am 

 inclined to think that the small variations between ihe angular values resulting 

 from .! due to the. graduation rather than to errors in pointing. In any 



case, they are cert;. iidy well in-ide ot what might reasonably be looked for in the 

 best instrument of its size. y.-rv 1 mlv, 



FRANCIS BLAKE, 

 Late Annistant U. S. Coat Survey. 



