CHAP. XIII.] OBSERVATIONS FOR ERROR 309 



hourly variation ; and in taking out the log. cosecant and log. 

 cotangent | E.T. we shall be dealing with whole seconds 

 instead of fractions. 



c 



6. For A, add together the logarithms of , the tangent of 



the latitude, and cosecant of half-elapsed time ; and for B 



c 

 the logarithms of -, the tangent of the declination, and the 



cotangent of half-elapsed time. Either subtract the log. of 

 15 from each of these sums, to reduce the results to time at 

 once, or take out the natural numbers of the sums as they 

 stand, and when A and B have been added or subtracted, 

 divide the result by 15, to reduce it to time. 



N.B, — Tables are given in various works on nautical astro- 

 nomy to facilitate the calculation of A and B ; but as these 

 are only made out for every so many minutes of elapsed time, 

 interpolation is necessary when working with any pretence to 

 accuracy, and very little is gained by their use in their present 

 form. 



7. To the mean middle time of the set, apply the equation 

 of equal altitudes with its proper sign (rule given below), which 

 will give the time shown by the watch at apparent noon. 

 N.B. — When working several sets, calculate them simultane- 

 ously as far as this, and mean the results, thus getting the mean 

 time shown by the watch at apparent noon. 



8. Find the mean time of apparent noon, by applying the 

 equation of time with its proper sign to or 24 hours, and 

 take the difference between this and mean time shown by the 

 watch, for the Error of the latter, subtracting one from the 

 other, according as it is intended to show the watch as fast or 

 slow on mean time. 



A universal system must be adopted of showiner all chrono- All 



Watches 



meters and hack-watches as fast or slow of the standard and to be 

 on mean time, not some one way and some another, wliich either 

 leads to confusion. It does not much matter which is taken. Fast of 

 The writer has always shown them as slow on mean time. ^.^^"^ 

 Thus all chronometers are shown slow of the standard, and 

 the standard and all others slow on mean time of place, or of 

 Greenwich, as the case may be. 



