VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. ^ 341 



The arithmetical complement is 0,02701 



Its double is 0,05402 



Which is the supplement versed sine of twice TO degrees. 



Now, as the arithmetical complement of the log. sines of arcs, are the dis- 

 tances on the line of sines between 90", and the divisions to those arcs ; there- 

 fore the distances between 90° and any arc, being twice repeated, will give the 

 division of the supplemental versed sine to twice the co-sine of that arc. 



XIV. Concerning an Improvement nf refracting Telescopes. By Mr. Jdhn Dol- 

 lond.* Dated Feb. 1i, 1753. p. 103. 



It is well known, that the perfection of refracting telescopes is very much 

 limited by the aberration of the rays of light from the geometrical focus ; which 



* Mr. John Dollond, f. r. s. was "born \706, in Spitalfields, London, where his father had settled 

 as a silk weaver, having fled from Fiance on account of the persecutions after the revocation of the 

 edict of Nantz. Here our author was bred to his father's profession, which he continued during a 

 great part of his life. But being of a very studious and philosophical turn of mind, his leisure hours, 

 even while a youih, were chiefly employed in mathematical pursuits. And though by the death of 

 his father, which happened in the infancy of our author, his education gave way to the necessities of 

 the family, yet at the age of 15 he amused himself by constructing sundials, drawing geometrical 

 schemes, and solving problems. Add to this, that an early marriage, and an increasing family, left 

 him but little opportunity of pursuing his favourite studies. Yet even under the pressure of a close 

 application to business, for the support of his family, the energy and perseverance of his genius urged 

 him, by abridging the hours of rest, to extend his mathematical knowledge, making a considerable 

 proficiency in optics and astronomy, to which he now chiefly devoted his attention ; having in the 

 earlier stages of life prepared himself for the higher parts of those branches by a competent knowledge 

 of algebra and geometry. To these he added the study of anatomy, particularly that of the eye; 

 and even made a considerable proficiency in the Latin and Greek languages. 



His eldest son Peter he brought up to the same profession with himself; and for several years they 

 carried on their manufacture together in Spitalfields ; but the employment neither suited the expec- 

 tations nor disposition of the son, who having received much information on mathematicsl and philo- 

 sophical subjects from the instructions of his father, and observing the great respect which professional 

 men had for his father's knowledge in optics, he determined to apply that knowledge to the benefit 

 of himself and the family; and accordingly, under the directions of his father, he commenced op- 

 tician. Success attended these efforts ; so that in the year 1732, our author also, embracing the 

 opportunity of pursuing a profession congenial with his mind, joined his son, and in consequence of 

 his theoretical knowledge, soon became a proficient in the practical parts of optics. His first attention 

 was directed to improve the combination of the eye-glasses of refracting telescopes ; henoe be 

 proceeded till he produced telescopes furnished with 5 eye-glasses, which greatly excelled all former 

 ones, and of which he gave an account to the r. s. in the paper above printed. He soon after made 

 a very useful improvement in Savery's micrometers ; for instead ot employing two entire object- 

 glasses, as Savery and Bouguer had done, he used only one glass cut into 2 equal parts, one of them 

 sliding laterally by the other ; by which contrivance Mr. Short was enabled to apply it to the reflect- 

 ing telescope with much advantage ; an account of which was communicated to the r. s, by our au- 

 thor, and printed in the same +8th vol. of the Phil. Trans, p. 178. Thus Mr. Dollond's celebrity in op- 

 tics soon became universal; and in consequence the friendship and protection of the most emineut men 



