48 OUTLINES OF NATURAL PHILOSOPHY. 



degree, in any latitude, above the degree at the 

 equator, when divided by the square of the sine of 

 the latitude, should always give the same quotient; 

 or the excess of the degrees of the meridian above 

 the degree at the equator, should be as the squares 

 of the sines of the latitudes. 



o- m[\y JJ) 



= 3 sin (/ + ,OX sin (/-*)' 



D' D = sin (A' -f A) X sin (A' A). 

 m 



c. If, then, D' and D are two contiguous degrees, so 



thatA'=A+l,D' D = sin(2A+l)xsin 1 ; 



and since sin 1 = .01745, D' . D = 



ScX .01745 . 



- - - sin (2 A + 1). 



The contiguous degrees, therefore, differ by a quan- 

 tity proportional to the sine of twice the middle 

 latitude. The difference is a maximum, when 

 2 A + 1 = 90, or when the middle latitude is 



45. 



The 



