320 HYDROGRAPHICAL SURVEYING [chap. xiii. 



changes between the first observation and the last, and there- 

 fore the sums of the middle times do not vary. This is due 

 to the difference in declination being small, and to the fact 

 that the middle time of observation is only 10 minutes 

 16 seconds from the " time of crossing," or the time at which 

 the stars had equal altitudes, the one rising and the other 

 setting, and is represented by the " | interval." 



In the second instance the equation of equal altitude 

 changes very rapidly ; the difference in declination is large, 

 and the " | interval " is also somewhat large— viz., 44 minutes 

 20 seconds ; but the " | interval " may, nevertheless, be ex- 

 tended to upwards of an hour, if necessary, without affecting 

 the accuracy of the result. 



The acceleration in the change of equation of equal altitudes 

 may be considered as practically uniform for the short 

 intervals of four or five minutes necessary to obtain sets of 

 observations, and therefore, although it A\dll be noticed that 

 the sums of the middle times change rapidly, yet it will never- 

 theless be perfectly accurate to take the means and calculate 

 the equation of equal altitude corresponding to the " h interval" 

 for the middle observation, no matter how rapidly the equa- 

 tions may change. 



It should be observed that in the case of two stars differing 

 much in declination, a small error in the latitude may produce 

 an appreciable error in the equation of equal altitudes. 



For the same elapsed time and differences of declination, 

 this error varies as sec. lat., the formula being — 



error in latitude 

 Error in equation of equal altitudes = — x 



sec. I. X cosec | E. T. x tan g. 



In latitude 45° the error from this cause is twice what it 

 would be at the Equator, and in latitude 60° it is four times as 

 great, since sec. 45° = 2, and sec. 60°= 4. 



Also, if the latitude and elapsed time remain the same, 

 the error varies as tan g, or practically directly as S, for small 

 values of g up to 10°. 



The following table shows the error in equation of equal 

 altitudes resulting from an error of 5" in latitude, using 

 stars with varying differences of declination in different 



