SCIENCE.-SUPPLEMENT. 



FRIDAY, SEPTEMBER 3, 1886. 



PROCEEDINGS OF THE SECTION OF ME- 

 CHANICAL SCIENCE AND ENGINEER- 

 ING. 



A CONTINUED improvement was manifest in this 

 section, both in attendance and interest, and it 

 may now be considered as fairly established by the 

 side of the older sections, and likely to become one 

 of the largest in the association. 



The most valuable i^aper presented was one on 

 the ' Strength and proportions of toothed wheels,' 

 by Prof. William Harkness of the naval observa- 

 tory. This paper, of which about half — over 80 p. 

 foolscap — v^as presented, is the result of a number 

 of years" work of a most varied and exliaustive 

 character. In twenty-three sections it treats of 

 the form of teeth ; mathematical theory of the 

 stress on teeth ; review of the formulae of previous 

 authors ; spur and bevel wheels with iron, brass, 

 and wood teeth ; shrouded pinions ; sizes of 

 pinions ; coefficient of safety ; maximum pitcli ; 

 relation of pitch to face ; length of teeth ; their 

 thickness ; strength of rims ; relations between rim 

 and tooth dimensions ; sizes and number of arms ; 

 naves ; keys and bosses ; weight and kinetic energy ; 

 applications to special cases ; recapitulation of 

 formulae ; bibliography. In designing clockwork 

 for the transit of Venus and other purijcses, the 

 author found no formulae upon which he could 

 rely, those in use giving results widely different 

 from each other, in exceptional cases showing 

 differences of fifteen hundred per cent ; he there- 

 fore set about determining, in a scientitic manner, 

 a formula upon which some reliance might be 

 placed. We have already had occasion to call 

 attention to the remarkable results accomplished 

 when a mechanical problem is attacked in this 

 way. The work of Professor Rogers in developing 

 a method by which precision-screws are economi- 

 cally furnished for machine tools, showed how an 

 astronomer could handle a practical problem, and 

 Professor Harkness has worked by tlie methods of 

 higher mathematics. He has made and collected 

 a large number of measurements of gears in 

 actual use and of recognized good proportions, and 

 after ascertaining, by the principles of mechanics, 

 the general shape of a correct formula, he has 

 applied the method of least squares to determine 

 the exact form of the same, with the values of the 



constant terms, which would best agree with these 

 measurements. Over forty authors on the subject 

 are reviewed, from Buchanan, 1808, and Tredgold, 

 1825, to Redtenbacher, Weisbach, and Reuleaux. 

 One formula, given by Roberton in 1808, was 

 shown to be absurd by Carmichael in 1814, but 

 was neverthele^s copied by Farey in 1827, in 

 an excellent work on the steam-engine, and has 

 been in use ever since. Roberton's proof of the 

 formula was that from his experiments he was 

 satisfied he could not be far wrong. In one author, 

 marked, and indeed unlooked-for, advantages ap- 

 pear from the use of the metric system ; in a wheel 

 of 2.30 m. diameter, calculated by means of it, the 

 number of teeth is reduced to one tooth 3.21 m. 

 thick and nearly one space. Another uses figures 

 in a demonstration which, interpreted, require 

 that a brass tooth half an inch thick and one inch 

 wide shall carry 13,000 pounds, though the author 

 by mistake got it 130 pounds. 500 i-epresenting 

 the safe amount, attention was called to the heavy 

 tooth-stresses of 800 to 900 customary in watches 

 and chronometers, and to that of about 1900 in 

 spring clocks. When put in print, this work can- 

 not fail to be of great and permanent value. 



Prof. W. A. Rogers, as chairman of the com- 

 mittee on acciu-ate standards, tools, and methods 

 in the machine shop, gave an account of his 

 work in that direction, and presented a r-esume of 

 his experiments in the use of the microscope in 

 connection with machine tools. In this method, 

 dimensions are read through that instrument from 

 accurately divided scales, or, in some cases, deter- 

 mined by calipers or gauges accurately set by 

 means of a comparator. By tliis system the work- 

 man receives from the tool-room of the shop the 

 necessary number of calipers accurately set to the 

 required dimensions by a skilled attendant in 

 charge of the comparator. It is evident that in 

 this way a high and uniform degree of accuracy 

 may be obtained, with much saving of time and 

 avoidance of errors, in which latter respect we 

 would suggest that calipers be returned to the tool- 

 room unchanged, and their settings checked. For 

 all good work, these methods must sui^ercede the 

 present inaccurate and inconvenient use of scales 

 of but moderate precision, and the setting of cali- 

 pers by the workman, and they will obviate the 

 necessity of the present expensive standard gauges. 



The sort of work done by these gentlemen will 

 mark an era in the development of machine con- 

 struction. 



