242 THE REV. W. WHEWELL ON THE DETERMINATION OP THE 



quadrature, diminishes the parallaxes in that part of her orbit, and makes their greatest 

 values less than they are in other situations. 



The Bristol observations give the same result, which was established by our ex- 

 amination in a manner somewhat different. In 1836 the sum of the parallax correc- 

 tions of height for all the twelve hours, from the parallax 60' to the mean 57'*2, was 

 315 parts ; from 57''2 to 55' it was 246 parts ; the simple ratio of the parallaxes would 

 give 315 to 247-5. 



VIII. Does the parallax correction of time vary as the parallax ? 



The observations just referred to enable us to answer this question in the affirma- 

 tive. In 1836 the corrections of time from 60' to 57'*2 were 125, and from 57'*2 to 55' 

 they were 96 parts ; the simple ratio of the parallaxes gives 125 to 98*2. 



IX. Does the declination correction of heights vary as the square of the declination 9 

 According to the theory, the correction for declination, both in the time and the 



height, will vary as the square of the declination, or as the square of its sine nearly, 

 the correction being supposed to be applied to the declination 0°. And it was shown 

 in the examination of the London tides*, that this is the law which prevails with 

 tolerable regularity in the mean of nineteen years* observations, both for the times 

 and heights. We may perhaps consider this rule therefore as established by much 

 better evidence than two or three years' observations can supply. Still it is not un- 

 important to examine how far this rule manifests itself in the result of short series of 

 observations. The Plymouth tides were examined with reference to this point. The 

 diurnal, semimenstrual, and parallax corrections being determined and subtracted, 

 the residues of the heights were for each hour expressed by ordinates corresponding 

 to the degrees of declination (taken in groups 0°..3°, 3°. .9°, 9°.. 15°, 15°. .21°, 21°. .28°). 

 It appeared that in each year (from 1834 to 1837) the curve thus obtained was nearly 

 a straight line, and it was still more nearly so in the mean of the years. This result 

 appeared to show that the declination correction of heights is proportional to the de- 

 clination itself, and not to its square. But the Bristol observations give a different 

 result. Thus in 1835 the correction in height (for all the twelve hours together) from 

 decl. 7°-3 to mean decl. 18°-6 was 192 parts ; and from 18°-6 to 24°-4 it was 173 parts. 

 This proportion of 192 to 173 is very nearly agreeable to the proportion of the squares 

 of the declinations ; indeed it is a still higher ratio ; for the proportion of the squares 

 gives 192 to 164, while the simple ratio of the declination would give 192 to 98. In 

 1836 the correction in height from decl. 8° to the mean 19°7 was 227 parts; and 

 from 19°*7 to 25° it was 138. The law of the squares would require the proportion 

 227 to 166, the law of the simple ratio, 227 to 103. In this case the result is nearly 

 intermediate between the square and the simple ratio, but the mean of the two years 

 gives the law of the square of the declination very nearly. And this result, agreeing 

 with the London mean of nineteen years, may be considered as sufficiently established ; 



* Researches, Second Series, Philosophical Transactions, 1834, pp. 24. 32* 



