1841.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



425 



the approbation of the scientific world, opticians will no ilonbt add the 

 convenience of a scale, upon the slide part of the tube, for aberration, 

 or determining the precise focal point for any distance : the fixed 

 quantity or constant also can be marked upon the tube ; attention being 

 paid to the diaphragm, both that it be truly circular, and the field of 

 view up to this circle distinct, 6cc., the advantages of these will appear 

 by-and-bye. 

 ' Having made the experiments above mentioned in a public situation 

 close to a large town, and being at the time also connected with a 

 public undertaking, my doing";, of course, did not escape observation. 

 Some part of the pul)lic press has also favoured the idea, and as a sort 

 of cariosity has got abroad respecting the matter, perhaps these papers, 

 tending to' explain my ideas of the matter, may not be altogether un- 

 acceptable to the public; being quite aware of much that has been 

 written upon the subject of measuring distances by the telescope by 

 Sir David Brewster, and other gentlemen eminent for their scientific 

 knowledge. Yet, as the reading-staft' was then little known, and as 

 the practical surveyor, whose every day occupation such subjects must 

 necessarily be, has advantages in this respect over the amateur or 

 theorist, and more especially when theory does not deny him also her 

 assistance — with this apology, I hope that tliis attempt at elucidation 

 of what appears to the many, a complex subject, will meet with the 

 indulgence which it may merit; for my own part, I can state that it is 

 far from me to uphold or putf otf anything of this kind which has not 

 solidity for its foundation, and utility for its superstructure; on the 

 contrary, I think that I cannot do a better service than unfold my ideas 

 upon a subject which has been both pleasing and useful to me, and may 

 be to others likeviise. 



Before I conclude these prefatory remarks, I beg leave to suggest 

 some of the advantages peculiar to this method, and in what opera- 

 tions it can be applied with advantage, leaving it to tlie reader to 

 supply all omissions in the list, whicli his practice or ingenuity may 

 suggest. 



By this method of measuring distances, the reading-staif, with a 

 level having a good telescope, furnishes the surveyor with all the in- 

 struments required for accurately and expeditiously taking a plan and 

 section ; by this method the engineer is enabled to dispense v. ith the 

 assistance of the two chain-men in running a line of levels across a 

 country ; by this method the distance as well as the level is read off 

 from the same instrument, the service of two men and the carriage of 

 the heavy chain. Sec. are saved, which, in thinly peopled districts, or 

 where labour is both scarce and dear, are advantages not altogether 

 inconsiderable ; by this method facilities are given for running lines 

 of levels for either geological, railroad, canal, or road purposes. For 

 the amateur or for trial sections it is much adapted, for it is much 

 more pleasant to be dependent npon the hire of one man than of three 

 men, and, in many cases, the chain-men being strangers to the work, 

 are not good to depend upon; whereas, in the other case, all that is 

 required is the staft-holder, the engineer himself reads off the distance, 

 for which also he himself is thus enabled to vouch ; the distance taken 

 by this method is the true horizontal distance, whereas with the chain 

 in undulating or hilly ground, the distances taken are not the horizon- 

 tal, but have to be reduced to it by the application of tables, &c. This 

 method also has great advantages in taking levels and distances over 

 corn fields or ground covered with crops of any kind, over gardens, 

 rivers, bogs, or swamps, ever ravines and rocky ground, and over other 

 places, either not convenient, or difficult to go directly through from 

 various circumstances. The convenience of this method in the above 

 cases will be fully aporeciated by the practical surveyor ; in taking 

 soundings of rivers, &c., it might be attended with very considerable 

 advantage, as both insuring accuracy and light expense ; in marine and 

 military surveying, also, it might be applied with advantage, &c. &c. 



On the Measurement of Distances by the Telescope, with loth Practical and 

 Theoretical Elucidations. 



The method of taking distances is this; — if the survey is for a section, the 

 level is first taken in the usual way ; then for the distance take the numher 

 of feet, tenths, and hundredtlis subtended by the diameter of the diaphragm 

 of the ohject-glass; that is, the diapluagm upon which the cross lines or wires 

 are stretched ; and this is readily done by screwing up the top or bottom of 

 the said diameter to some primitive division of the staff, and then counting 

 the divisions from top to bottom, or from bottom to top of the field of view ; 

 then this quantity of divisions read otf from the staff, increased by a fixed 

 quantity or constant (each instrument has a constant peculiar to itself), will 

 make a sum or augmented reading which will be in every case either the 

 distance itself, or some determinable proportion of it, depending upon the 

 make of the instrument, &c. 



The ratio of this proportion must he found by actual experiment, of which 

 the following is an example. 



With one of Troughtou's 20-inch levels the reading at the distance of 10 

 chains from the centre of the instrument is 13-80 feet. 



The constant for this instrument is '05 feet, therefore the quantity read off 

 must he increased by the addition of this and it becomes 13-85 feet; at one 

 chain distance the reading is 1-335 feet, and by the addition of the constant 

 it becomes 1-385 feet ; and at the distance of the -J^th part of a chain the 

 reading is -0885 feet, and the constant -05 feet added to this gives -1385 feet 

 for the augmented reading; it is evident that the augmented readings 13-85 

 feet, 1-385 feet, and -1385 feet are exactly in proportion to the distances 10 

 cliains, 1 chain, and -^i\\ of a chain. From these experiments it is evident 

 that the quantities read off with the addition of the constant -05 feet make 

 augmented readings which are proportional to, or make equal ratios with 

 their respective distances. 



This constant (-05 in the above case) is dependent upon, or is a function of 

 the principal focal distance of the ohject-glass, and also of the distance of 

 the said object-glass from the centre of the instrument or station, of the dia- 

 meter of the diaphragm or field of view, and also of the divisions of the staff 

 or reading-rod. 



The diameter of the diaphragm might he diminished Ijy two screws or 

 blunt points, projecting an equal distance into the field of view until the 

 number of divisions of the staff included between the aforesaid points, toge- 

 ther with a similarly contracted proportion of the fised quantity or constant 

 would make an augmented reading, the numerical amount of which would 

 he precisely the same as the number of Uuks in actual distance, and thus by 

 writing chains and parts instead of feet and parts, the augmented readings 

 would give the respective actual distances without any reference to proportion 

 whatever. 



And by enlarging the diaphragm upon the same principle the augmented 

 readings in feet and parts might correspond to chains and parts, the chain in 

 this case being composed of 100 feet instead of 100 Unks of the commor 

 size. 



In the actual experiments where 13-85 feet corresponded to 10 chains the 

 constant was -05 ; but when the diaphragm is contracted so that 10 feet cor- 

 respond to 10 chains in distance, or as each foot of the staff is divided into 

 100 parts, then 1000 such parts give a distance of 1000 links, and the fixed 

 quantity undergoing a corresponding reduction likewise, it will become "036 

 feet, hut for general purposes -04 feet will be quite near enough, for 1385 ; 

 1000 : : -05 : -036 or -04 nearly. 



Having the augmented readings to correspond with the actual distances is 

 no doubt a very great convenience, and it ought to be attained in new in- 

 struments, though there is very little inconvenience in making a scale to suit 

 any proportion, the scale for parts being, as in the case al)ove, to the scale 

 for links in the proportion of 1385 parts for every 1000 links, and, for my 

 own part, I prefer keeping the diaphragm as it is, for the greater the angle 

 or number of divisions of the staff read, the less value each becomes with 

 respect to distance, and, consequently, any error arising from the staft* be- 

 comes of proportionately less value when reduced into distance. 



The constant -05 in the above example is the correction arising from aber- 

 ration of focal distance, and the correction arising from the object-glass not 

 being in the centre of the station conjointly; and first, the correction arising 

 from the aberration of focal distance may be explained in the following man- 

 ner :— 



Let OcB be the object-glass of the telescope, /and d the principal foci, oi 

 foci for parallel rays, or rays from verj' remote objects, and let t'D't' he sup- 

 posed to be very remote, let F be the focus for rays proceeding from an ob- 

 ject or radiant point D at no very great distance from the object-glass OcB, 

 hut beyond its principal anterior focus d. (See fig. 1.)^ 



Hr. 1. 





v^- 



:£.. 



Now by optics the formula for aberration is 

 Principal focal distance x principal focal distance 

 Distance of object from object-glass — principal focal distance 

 fc X cd 



= Aberration 



cV - cd 



-Ff 



