Sinco tho publication of the inaccurate statements containod in a letter published iu tho Kalamazoo Teleyraph, and subsequently in the Post and Tribune of this city regarding the Detroit llivor tunnel, thero has been inuch discussion of the subject. A reporter of tho Fret Press has sinco investigatod the matter, and the inforniation thus gained and published in this connoction may bo regarded as en tirely reliable. The letter alluded to was not, as is clainied, written by auy engineer connected with tho work, and inore - over contains many inaeouracios. The shaft on tlie Datroit side of the river, near the Detroit and Mihvaukeo elevator, was commencod oarly in Ddcembor, 1871, and fioiahed January Sist, 1S72, ou which laet mentioned day bed rock was roached, 108 feet below tho surfttod of the rivor. Tho whole depth of masonry is 114 feet. The upper portion of this, 89 feet, is lo feet in diameter and sixtoen inches thick. Tho rein.iiiiing 23 fet'C it bas a diameter of 9 feot with 12inoh walls. Tho drainage tunnel or drift starts from tho lowor portiou of the sh:ift, eight feet above tho rosk, tbua lcaving a we!l or pump below it in which to aeeurauiulate any water that may come into the shaft or drift. At present there comes into tlio shift at its bottom, below all the work, wator strongly impregnated with sulphuretted hydrogen gas at tho rato of thieo gallons per minute. This causes no serious inoonvenionco, beyond tho necessity of occasion illy bailing it out. An inconsidünible amouut of water, a few gallons per hour, also colleots in the drainage drift, coming from liyers of quicksand eighteen iriches thick, along the top of which the woric bas thus far progressed. Tlio drainage drift bas been excavatad under the river to a point ono hundred and thirty tost distant from the sliaft, a daily avcrago of over fivo foot. The groand through which it passes is a very hard cluy, which has to bo dug out with picks. A layer of bulders ranging from a few fet to a cubie yard in size, is i'uund in tho clay, lying about h ilf way up in tho drift. Soms oftiiom have to be re moved by blastiug. L itterly they have been fouml smaller and loss frequently, and pmportionataly bitter progresa has beon made - about ten feet during the last twenty-four liours. It is thought th:it fchsy will toon run out entirely or lip btilow the bottoiu of the drift, in which Citse tho progross of the work would be at once doubled. But two miners can work at a time, owing to the smitll siz of the drift, but operationa are kept up bobh day and nignt, tho man bjing rlioved every eight hours. The hardnesa of the ground, while it somewhat impedís progress, insures tho seourity of tliu work. Portions of this drift h ivo stood f jr a woek unsupportod, without exhibiting any signs of weakness. Ordinarily, bowever, the tunnel is linod with masotirv within a day or two aftcr being excavated. The lining consista of an eightinch circle of the hardost brick, every ono of which is Bubjeoted to a rigid cxamination aml luid in the bost hydraulio cement. The drift risos from the shaft to tlie cent.r of the river on a grade of one foot in a thousand. The line was located by the engineen above grouml by triangulation, and transferred bolow by mcans of a heavy plumb-bob inunersed in water, and suspended down the shaft bv tino silk oords. As tbedistfuwe botween them was so short that an error of ono thirtysecoad of an inch would throw tbo work out afc the middle of tho river six or eight iuches, a drift has been run back from the shaft fifty feet, and au iron tubo is now boing sunlc to its end, in which a plumb-liuo may be suspended and a lougor range obtained. Tho drainage drift is Dot straight aoross the river, but has two short cuives in it. Withiu a week, work will be commenced on tho shaft at Windaor, and as soon as it is sunk the drainage tunnel will be cxcavatod from it to moet that now being worked from this side of tho rivoT. From what was loarned of thy nature of tho ground in sinking trjp shaft, it is anticipatcd that the main tunnels will be surrounded the wholo longth with good solid ground, suitable for thoir construction, it being principally firm blue clay. The developments thus far havo been quite as favorable as was anticipated at the time when the plans and ostimates were prolarod, and show notbing to diseourago a reasonable belief that the work will be carried to a successful issue.