PHILOSOPHICAL WRITINGS OF THE LATE DR. DALTON. 21 



fourth order, having four similar infinite legs, two on each 

 side of AC, which the curves touch in A both above and 

 below. If from A, AB be set ofF= AO; BV produced will 

 be an asymptote, parallel to which there is another equally 

 distant from A, and on the contrary side of it. The space 

 contained under the four legs, and two asymptotes is equal to 

 a circle whose radius = AO." (Diary, 1793, p, 42. J 



The Ladies* Diary and Supplement for 1793 contain 

 answers from Mr. Dalton to four of the queries and one of 

 the principal mathematical questions. He also furnished a 

 solution to the prize, but after obliging two of his other cor- 

 respondents, the editor expresses himself as ** particularly 

 sorry thut [his] limits will not permit [him] to insert the 

 general investigations of [his] learned correspondents. 

 Amicus (Mr. Wildbore) and Mr. John Dalton." In the 

 Supplement he discusses the question whether " the outward 

 arc of the enlightened part of the moon's apparent disc is at 

 any time apparently less than a semicircle," which had been 

 proposed as an " astronomical query, by a Lunarian." On 

 this subject he remarks, that " the outward arc of the 

 enlightened part of the moon is commonly said to be a 

 semicircle, and for the most part is nearly so ; yet, strictly 

 speaking, it is generally greater, and sometimes less, than a 

 semicircle. The moon's disc as seen from the earth, is not 

 bounded by a great circle of the moon, but by a parallel or 

 lesser circle, and the visible segment is less than a hemisphere. 

 The circle separating the light and dark parts of the moon is 

 likewise a parallel circle; the dark segment being less and 

 the light one greater than the hemisphere. Now, when the 

 dark segment of the moon is greater than the segment visible 

 at the earth, which happens when the moon is in perigee, 

 then two extremities of some diameter of the visible disc may 

 be involved in the dark segment, and consequently the en- 

 lightened arc will at that time be less than a semicircle, but 

 this can only take place about the change." The reason 



