20 UNITED STATES COAST AND GEODETIC SURVEY. 



the Keport of the British Association for the Advancement of Science 

 for 1883, and has since, together with the system of notation adopted 

 by that committee, come into universal use. 



The gear ratios or the number of teeth of each of the gearwheels 

 conveying motion from the vertical shafts to the respective compo- 

 nent shafts were obtained by converting the decimal expression of 

 the speed ratio given in Darwin's table to the nearest unit in the 

 seventh place into two vulgar fractions, which, when multipUed by 30, 

 the angular speed of the vertical shafts in degrees per mean solar 

 hour, will most nearly approach the former decimal expression. 

 By refactoring these ratios it was possible to obtain such diameters 

 of the respective gear wheels as permitted of considerable saving of 

 space when locating the components. 



The number of the teeth of the gear wheels are given in Table C, 

 in the columns headed I, II, III, and IV. The product of the gear 

 ratios I: II and III: IV of a component multiplied by 30, the angular 

 speed of the vertical shaft per dial hour, is the hourly speed of that 

 component as produced by the gears. The difference between this 

 and the theoretical speed, both given in the table, multiplied by the 

 number of hours in a year, is shown for each component in the column 

 headed '^Errors of gears per di^-l year." 



It wiU be seen that the errors in the speeds of all the large com- 

 ponents are less than a quarter degree ; only a few of the unimportant 

 ones amount to more than half a degree in a year, quantities which are 

 altogether negligible. 



Gear wJieels. — In making the designs the durability or the hfe of the 

 machine was kept in view. This is altogether a question of the wear- 

 ing out of those parts which can not be readily renewed. The most 

 important of these, besides the bearings of the component shafts 

 before mentioned, are the gear wheels. These were cut with cutters 

 specially made to order for producing teeth of the well-known invo- 

 lute type, but with an additional bottom clearance of about 15 per 

 cent of the height of the tooth. This permits of adjustment for 

 taking out play due to wear of a greater amount than can occur in 

 many year's use. 



Releasahle gears. — The releasable gears heretofore mentioned are 

 used when setting the machine for a new station, for disengaging or 

 releasing each component from the remainder of the train and setting 

 it to its proper amplitude and epoch, after whi^h it is again secured to 

 the vertical shaft. As the moving or slipping of any one of them 

 would vitiate the result, special care was taken in designing the 

 clamping device, which is shown in the adjoined illustrations. 

 (Plate 13, fig. a.) A collar Ay with a thread at its upper end and a 

 flange at the bottom, is fastened to the shaft by means of three coim- 

 terbored steel screws. The gear wheel, B, fitting closely upon this 



