On certain Questions relating to the Theory of Probabilities. 55 



advantages. Mr. Saxton proposed to break the circuit by a tilt- 

 hammer struck by a projecting piece of glass from the middle of 

 the pendulum^ which acts as a circuit-breaker ; he also contrived 

 an apparatus for making on the sheet the 0, 5, 10, &c. millims. 

 by the omission of one or two breaks respectively. Mr. Saxton's 

 apparatus has been in use ever since at the Seaton station ; its 

 only defect is the want of uniformity in the time of revolution 

 of the cylinder. 



On the 12th of April, Mr. Bond submitted to Prof. Bache a 

 model of an invention made with a view to remedy this remain- 

 ing defect. This instrument^ has been named the Spring Go- 

 vernor. A perfect working instrument was ordered for the use 

 of the Coast Survey at that time. The model was completed 

 and reported upon in November 1850. The cylinder, covered 

 with a paper, revolves once in a minute, and measures time with 

 the precision of an astronomical clock. The sheet, when taken 

 off after being graduated by the clock, has the minute columns 

 vertical. The seconds are marked off horizontally on each mi- 

 nute scale. The eye seizes on the appropriate hour, minute, 

 and whole second, as in an ordinary astronomical table of double- 

 entry ; the fraction of a second may be estimated to a tenth by 

 the eye, or read to a hundredth by a graduated scale. A yearns 

 work of an ordinary observatory may be bound up in a volume 

 of a few hundred pages, and forms a permanent and legible re- 

 cord of the actual dates of the imprinted transit signals. 



By means of the line connecting the observatory at Cam- 

 bridge with Boston, the time for the use of shipping and for the 

 railroads throughout New England is now regularly transmitted 

 by merely passing the circuit through the clock at Cambridge. Its 

 beats are thus given through a distance of one or two hundred 

 miles. One o^ clock has been adopted as the hour for these 

 signals. 



The courtesy with which the Telegraph Companies in different 

 parts of the United States have met applications for the use of 

 their lines for scientific purposes, deserves particular acknow- 

 ledgement, as having contributed most effectually to the success 

 of these operations. 



IX. On certain Questions relating to the Theory of Probabili- 

 ties.—VsiYt III. ByW. F. Donkin, M.A., F.kS., F.R.A.S., 



Savilian Professor of Astronomy in the University of Oxford. 



I PROPOSE in this third and last communication, to offer a 

 few remarks on the method of least squares, chiefly with 

 reference to Mr. Ellis^s paper on that subject in the Philosophical 

 Magazine for November 1850. 



